**Meet the editor**

Dr. Farzad Ebrahimi was born in Qazvin, Iran, in 1979. He graduated in mechanical engineering, from the University of Tehran, Iran, in 2002. He received his Msc and PhD in mechanical engineering, with a specialization in applied design from the University of Tehran, Iran, in 2009. Since 2002, he has been working at the "Smart Materials and Structures Lab" Research Center of the fac-

ulty of mechanical engineering at the University of Tehran. Now he is an assistant professor in the department of mechanical engineering at Imam Khomeini International University, Qazvin. He has authored more than 30 papers and also authored/edited 6 books in the fields of "Vibration Analysis", "functionally graded structures" and "Piezoelectric Transducers".

Contents

**Preface IX**

**"Bio-Engineering" 1**

Josipa Borcic and Alen Braut

Chapter 2 **Application of Finite Element Analysis in Implant Dentistry 21**

Chapter 3 **Finite Element Analysis of the Stress on**

Liangjian Chen

Chapter 5 **Finite Element Analysis**

Chapter 6 **Finite Element Analysis**

Govindaraj Thangavel

Chapter 7 **The IEEE Model for a Ground Rod in**

Chapter 4 **Finite Element Modelling of**

**the Implant-Bone Interface of Dental Implants with Different Structures 55**

**a Multi-Bone Joint: The Human Wrist 77**  Magnús Kjartan Gíslason and David H. Nash

**Section 2 Recent Advances of Finite Element Analysis in "Electrical Engineering" 99**

> **of Stationary Magnetic Field 101**  Elena Otilia Virjoghe, Diana Enescu, Mihail-Florin Stan and Marcel Ionel

**of the Direct Drive PMLOM 131**

**a Two Layer Soil – A FEM Approach 143**

António Martins, Sílvio Mariano and Maria do Rosário Calado

**Section 1 Recent Advances of Finite Element Analysis in**

Chapter 1 **Finite Element Analysis in Dental Medicine 3**

B. Alper Gultekin, Pinar Gultekin and Serdar Yalcin

## Contents

### **Preface XI**

Preface

multiplied rapidly.

Finite Element Analysis (FEA) was developed as a numerical method of stress analysis, but now it has been extended as a general method of solution to many complex engineering and physical science problems. In the past few decades, the FEA has been developed into a key indispensable technology in the modeling and simulation of various engineering systems. In the development of an advanced engineering system, engineers have to go through a very rigorous process of modeling, simulation, visualization, analysis, designing, prototyping, testing, and finally, fabrication/construction. As such, techniques related to modeling and simulation in a rapid and effective way play an increasingly important role in building advanced engineering systems, and therefore the application of the FEA has

This book reports on the state of the art research and development findings on this very broad matter through original and innovative research studies exhibiting various investigation directions. The book has been grouped into three major domains: Biomedical engineering, electrical engineering, civil engineering. It is meant to provide a small but valuable sample of contemporary research activities around the world in this field and it is expected to be useful to a large number of researchers. Through its 17 chapters the reader will have access to works related to Dental Medicine, Implants, Sandwich Panels, Tunnel excavation, Stiffener run-outs, Tubular Footbridges, DC circuit breaker, Permanent Magnet Motors, MEMS and several other exciting topics.

The present book is a result of contributions of experts from international scientific community working in different aspects of Finite Element Analysis. The introductions, data, and references in this book will help the readers know more about this topic and help them explore this exciting and fast-evolving field. The text is addressed not only to researchers, but also to professional engineers, students and other experts in a variety of disciplines, both academic and industrial seeking to gain a better understanding of what has been done in the field recently, and what kind of open problems are in this area. It has been written at a level suitable for the use in a graduate course on applications of finite element modeling and analysis (Electrical,

civil and biomedical engineering studies, for instance).

## Preface

VI Contents

Chapter 8 **FEA in Micro-Electro-Mechanical Systems**

**Finite Element Technique 183**

Hao Ren and Jun Yao

Kazumi Kurihara

Marco Riva

Simona Roatesi

Chapter 15 **Finite Element Modelling of**

Jian Sun and Jürgen Kosel

**(MEMS) Applications: A Micromachined Spatial Light Modulator (μSLM) 161**

Chapter 9 **Steady-State and Transient Performance Analysis of**

Chapter 10 **Finite-Element Modelling and Analysis of Hall Effect**

Chapter 12 **Integrated FEA and Raytracing in Instrumentation for Astronomy: Smart Structures Evaluation**

**in "Civil & Structural Engineering" 275**

**and Structural Optimization 253**

**Section 3 Recent Advances of Finite Element Analysis**

Chapter 13 **Damage-Tolerant Design of Stiffener Run-Outs: A Finite Element Approach 277**  S. Psarras, S.T. Pinho and B.G. Falzon

Chapter 14 **Finite Element Analysis for the Problem of Tunnel**

and Luciano Rodrigues Ornelas de Lima

**Spots in Interconnects and Packages 377**

Chapter 16 **Finite Element Analysis of Loading Area Effect**

Salih Akour and Hussein Maaitah

Chapter 17 **The Finite Element Analysis of Weak**

Kirsten Weide-Zaage

**Permanent-Magnet Machines Using Time-Stepping**

**and Extraordinary Magnetoresistance Effect 201**

**by Introducing Stress Concentration Region (SCR) 225**

**Excavation Successive Phases and Lining Mounting 301**

**the Dynamic Behaviour of Tubular Footbridges 333**

José Guilherme Santos da Silva, Ana Cristina Castro Fontenla Sieira, Gilvan Lunz Debona, Pedro Colmar Gonçalves da Silva Vellasco

**on Sandwich Panel Behaviour Beyond the Yield Limit 353**

Chapter 11 **High Sensitive Piezoresistive Cantilever MEMS Based Sensor**

Sh Mohd Firdaus, Husna Omar and Ishak Abd Azid

Finite Element Analysis (FEA) was developed as a numerical method of stress analysis, but now it has been extended as a general method of solution to many complex engineering and physical science problems. In the past few decades, the FEA has been developed into a key indispensable technology in the modeling and simulation of various engineering systems. In the development of an advanced engineering system, engineers have to go through a very rigorous process of modeling, simulation, visualization, analysis, designing, prototyping, testing, and finally, fabrication/construction. As such, techniques related to modeling and simulation in a rapid and effective way play an increasingly important role in building advanced engineering systems, and therefore the application of the FEA has multiplied rapidly.

This book reports on the state of the art research and development findings on this very broad matter through original and innovative research studies exhibiting various investigation directions. The book has been grouped into three major domains: Biomedical engineering, electrical engineering, civil engineering. It is meant to provide a small but valuable sample of contemporary research activities around the world in this field and it is expected to be useful to a large number of researchers. Through its 17 chapters the reader will have access to works related to Dental Medicine, Implants, Sandwich Panels, Tunnel excavation, Stiffener run-outs, Tubular Footbridges, DC circuit breaker, Permanent Magnet Motors, MEMS and several other exciting topics.

The present book is a result of contributions of experts from international scientific community working in different aspects of Finite Element Analysis. The introductions, data, and references in this book will help the readers know more about this topic and help them explore this exciting and fast-evolving field. The text is addressed not only to researchers, but also to professional engineers, students and other experts in a variety of disciplines, both academic and industrial seeking to gain a better understanding of what has been done in the field recently, and what kind of open problems are in this area. It has been written at a level suitable for the use in a graduate course on applications of finite element modeling and analysis (Electrical, civil and biomedical engineering studies, for instance).

#### XII Preface

I am honored to be editing such a valuable book, which contains contributions of a selected group of researchers describing the best of their work. I would like to express my sincere gratitude to all of them for their outstanding chapters. I also wish to acknowledge the InTech editorial staff, in particular Oliver Kurelic, for indispensable technical assistance in book preparation and publishing.

#### **Dr. Farzad Ebrahimi**

**Section 1**

**Recent Advances of Finite Element Analysis**

**in "Bio-Engineering"**

Faculty of Engineering, Mechanical Engineering Department, International University of Imam Khomeini, Qazvin, I.R.Iran

**Recent Advances of Finite Element Analysis in "Bio-Engineering"**

X Preface

I am honored to be editing such a valuable book, which contains contributions of a selected group of researchers describing the best of their work. I would like to express my sincere gratitude to all of them for their outstanding chapters. I also wish to acknowledge the InTech editorial staff, in particular Oliver Kurelic, for indispensable

> **Dr. Farzad Ebrahimi** Faculty of Engineering,

> > Qazvin, I.R.Iran

Mechanical Engineering Department, International University of Imam Khomeini,

technical assistance in book preparation and publishing.

**Chapter 1**

© 2012 Borcic and Braut, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Borcic and Braut, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Finite Element Analysis in Dental Medicine**

Studying dental structures and surrounding tissues in the oral cavity presents the basis for understanding the occurrence of pathological process and enables the correct approach and treatment. Oral rehabilitation is inherently difficult, due to the functional and parafunctional forces within the mouth that result in extremely complex structural responses by the oral tissue [1]. The success of restorative materials depends on their properties to withstand and resist occlusal forces and successfully support the remaining oral structure [2]. Studies examining the biomechanical behavior of oral structures require sophisticated simulations

There were numerous ways and attempts of experimental research, but due to the complexity of dental structures, composed of various tissue materials mechanically and chemically interconnected, and due to complex tooth morphology and surrounding structures, these attempts failed to obtain precise and reliable results. Researches have used photoelastic methods, computer simulation methods and finite element analysis to conduct stress analyses of sound and restored teeth in order to predict their fracture resistance. Conventional methods such as photoelasticity and the strain-gauge methods are inadequate to predict reliable stress distribution in the tooth [4]. The use of traditional load-to-failure bench-top testing is unable to recreate the failure mechanisms seen clinically; hence the use of FEA is gaining popularity because of its ability to accurately asses the complex biomechanical behavior of irregular prosthetic structures and heterogeneous material in a

Finite element analysis (FEA) is a numerical method of analyzing stresses and deformations in structures which originated from the need for solving complex structural problems in civil and aeronautical engineering. In order to achieve this goal, the structures are broken

Josipa Borcic and Alen Braut

http://dx.doi.org/10.5772/50038

**1. Introduction**

Additional information is available at the end of the chapter

of the fundaments of the stomatognathic system [3].

non-destructive, repeatable manner [5].

**2. Finite element analysis**

## **Finite Element Analysis in Dental Medicine**

Josipa Borcic and Alen Braut

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/50038

## **1. Introduction**

Studying dental structures and surrounding tissues in the oral cavity presents the basis for understanding the occurrence of pathological process and enables the correct approach and treatment. Oral rehabilitation is inherently difficult, due to the functional and parafunctional forces within the mouth that result in extremely complex structural responses by the oral tissue [1]. The success of restorative materials depends on their properties to withstand and resist occlusal forces and successfully support the remaining oral structure [2]. Studies examining the biomechanical behavior of oral structures require sophisticated simulations of the fundaments of the stomatognathic system [3].

There were numerous ways and attempts of experimental research, but due to the complexity of dental structures, composed of various tissue materials mechanically and chemically interconnected, and due to complex tooth morphology and surrounding structures, these attempts failed to obtain precise and reliable results. Researches have used photoelastic methods, computer simulation methods and finite element analysis to conduct stress analyses of sound and restored teeth in order to predict their fracture resistance. Conventional methods such as photoelasticity and the strain-gauge methods are inadequate to predict reliable stress distribution in the tooth [4]. The use of traditional load-to-failure bench-top testing is unable to recreate the failure mechanisms seen clinically; hence the use of FEA is gaining popularity because of its ability to accurately asses the complex biomechanical behavior of irregular prosthetic structures and heterogeneous material in a non-destructive, repeatable manner [5].

## **2. Finite element analysis**

Finite element analysis (FEA) is a numerical method of analyzing stresses and deformations in structures which originated from the need for solving complex structural problems in civil and aeronautical engineering. In order to achieve this goal, the structures are broken

down into many small simple segments or elements, each with specific physical properties (figure 1). Than, an operator uses a computer program in order to obtain a model of stresses produced by various loads [6,7]. A major advantage of finite element analysis (FEA) is its ability to solve complex biomechanical problems for witch other study methods are inadequate. Stress, strain and some other qualities can be calculated in every point throughout the structure. FEA is also being used as part of the design process to simulate possible structure failure, as a mean to reduce the need for making prototypes, and reducing a need for performing actual experiments, that are usually expensive and time-consuming [8]. This method allows researches to overcome some ethical and methodological limitations and enables them to verify how the stresses are transferred throughout the materials [9].

Finite Element Analysis in Dental Medicine 5

The decision to use 2D or 3D models to investigate biomechanical behavior of complex structures, by FEA, depends on many inter-related factors, such as the complexity of the geometry, material, properties, mode of analysis, etc. Although 2D models are simpler, easier to build and less time consuming, they do not represent the complexity of the real problem. 2D model might be considered when studying the qualitative biomechanical behavior, but for the quantitative stress analysis the 2D models overestimate stress magnitudes and do not represent the realistic model. 3D model may provide more reliable data that more accurately represent non-linear and anisotropic materials. 3D models should be carefully created with appropriate mesh density [3]. Khera et al. were the pioneers in the utilization of 3D models. The models were obtained from sectional images of human mandible, but this is no longer required due to the use of a computerized tomography (CT)

The 3D geometry of the tooth (figure 2) can be reconstructed in two ways. The old traditional method consists of embedding the tooth in red epoxy and sectioning it perpendicularly to the long axis by a precise saw (figure 3). Each section is than digitally photographed and the 3D geometry of the tooth is being constructed from these crosssections using specialized computer program. The solid model is transferred into a finite element analysis program, where a 3D mesh is being created, and subsequently the stress

**2.1. Finite element model**

distribution analysis performed (figure 4) [4, 25].

[10].

**Figure 2.** Natural tooth

In the area of dentistry, FEA has been used to simulate the bone remodeling process, to study internal stresses in teeth and different dental materials, and to optimize the shape of restorations. Because of the large inherent variations in biological material properties and anatomy, mechanical testing involving biomaterials usually require a large number of samples. With FEA the necessity of traditional specimens can be avoided, and by using a mathematical model it also eliminates the need for large number of experimental teeth. It has been used to represent simulated tooth mechanical behavior under occlusal loads in details [8].

**Figure 1.** Elements of an FEA model.

## **2.1. Finite element model**

4 Finite Element Analysis – New Trends and Developments

**Figure 1.** Elements of an FEA model.

down into many small simple segments or elements, each with specific physical properties (figure 1). Than, an operator uses a computer program in order to obtain a model of stresses produced by various loads [6,7]. A major advantage of finite element analysis (FEA) is its ability to solve complex biomechanical problems for witch other study methods are inadequate. Stress, strain and some other qualities can be calculated in every point throughout the structure. FEA is also being used as part of the design process to simulate possible structure failure, as a mean to reduce the need for making prototypes, and reducing a need for performing actual experiments, that are usually expensive and time-consuming [8]. This method allows researches to overcome some ethical and methodological limitations and enables them to verify how the stresses are transferred throughout the materials [9].

In the area of dentistry, FEA has been used to simulate the bone remodeling process, to study internal stresses in teeth and different dental materials, and to optimize the shape of restorations. Because of the large inherent variations in biological material properties and anatomy, mechanical testing involving biomaterials usually require a large number of samples. With FEA the necessity of traditional specimens can be avoided, and by using a mathematical model it also eliminates the need for large number of experimental teeth. It has been used to represent simulated tooth mechanical behavior under occlusal loads in details [8].

The decision to use 2D or 3D models to investigate biomechanical behavior of complex structures, by FEA, depends on many inter-related factors, such as the complexity of the geometry, material, properties, mode of analysis, etc. Although 2D models are simpler, easier to build and less time consuming, they do not represent the complexity of the real problem. 2D model might be considered when studying the qualitative biomechanical behavior, but for the quantitative stress analysis the 2D models overestimate stress magnitudes and do not represent the realistic model. 3D model may provide more reliable data that more accurately represent non-linear and anisotropic materials. 3D models should be carefully created with appropriate mesh density [3]. Khera et al. were the pioneers in the utilization of 3D models. The models were obtained from sectional images of human mandible, but this is no longer required due to the use of a computerized tomography (CT) [10].

The 3D geometry of the tooth (figure 2) can be reconstructed in two ways. The old traditional method consists of embedding the tooth in red epoxy and sectioning it perpendicularly to the long axis by a precise saw (figure 3). Each section is than digitally photographed and the 3D geometry of the tooth is being constructed from these crosssections using specialized computer program. The solid model is transferred into a finite element analysis program, where a 3D mesh is being created, and subsequently the stress distribution analysis performed (figure 4) [4, 25].

**Figure 2.** Natural tooth

Finite Element Analysis in Dental Medicine 7

before and after the performed therapy procedures, and periodical follow-ups of the therapy success. Technologies such as micro-CT scanning open up the possibility for complex 3D modeling [11]. However, the process of going from image to mesh involves a number of

The results obtained from a FEA on the restored system contain information about the stress distribution of each component of the restoration, instead of only a single value of failure load typical of in vitro results. A correct interpretation of FEA results should be based on the stresses and strength of each component of the system. To obtain accurate conclusions from these interpretations, three conditions must be fulfilled. First, FEA should adequately represent the real stress values; second, strength of the different materials must be known;

It is not possible to implement the results from FEA directly into a clinical situation, but it has to design the model in such a way that is mimics the real situation as closely as possible. FEA analysis must be interpreted with a certain amount of caution. Most of the researches modeled dental structures as isotropic and not othotropic. The finite element model represents a static situation at the moment of load application and not an actual clinical situation. In reality, the loading of the structure is more dynamic and cyclic. The materials of the various tooth structures were assumed to be isotropic, homogenous and elastic, and that they remain such under applied loads. More precise measurements can be obtained if the material properties are set as anizotrophic and non-homogeneous, but such setup requires much more complex mathematical calculations. It is better to use a non-linear elastic-plastic

The values from finite element analysis are presented as maximum and minimum principal stresses. Most of the previously published studies have analyzed the results from Von Mises maximal stress [15-19]. This is probably associated to the fact that this is the normal criterion for the most engineering analyses, which usually deal with ductile materials such as steel and aluminum [13]. It is known that the Von Mises criterion is only valid for the ductile materials with equal compressive or tensile strength, but materials exhibiting brittle behavior such as ceramics, cements or resin composites presents reported values of compressive strength significantly greater than tensile strength [20]. Positive and negative values indicate that the corresponding regions are subjected to tensile or compressive

The response of the structure is different if asymmetrical loading is considered. When the tooth is compressively loaded, displacements do not appear to be significant because of the rather large compressive yield strength. The situation is different if the asymmetrical loading is considered, when the tensile stress occurs. The dental tissues are more resilient to compressive than tensile forces. Any occlusal contact that can create tensile stress, also creates the possibility to create a lesion in tooth structure. When lateral loads are applied, tensile stresses generated in the areas are of higher values than when vertical loads are

material model than the linear models that are used in most FEA studies [14].

processing steps, each with potential geometric errors [12].

third, an adequate failure criterion must be used [13].

**2.2. Interpretation of the FEA results**

stresses (figure 5) [21].

**Figure 3.** Embedded tooth in red epoxy.

**Figure 4.** 3D model of the sound tooth

The second, latest method of reconstructing a 3D tooth model is performed with the aid of CT. It facilitates and speeds up the acquisition and produces more accurate model. With this method the surrounding soft structures can be also included, larger areas scanned and reconstructed, while the structures itself still remain in the patient mouth. The next big advantage of CT model rendering consists of the possibility to scan the same structure before and after the performed therapy procedures, and periodical follow-ups of the therapy success. Technologies such as micro-CT scanning open up the possibility for complex 3D modeling [11]. However, the process of going from image to mesh involves a number of processing steps, each with potential geometric errors [12].

## **2.2. Interpretation of the FEA results**

6 Finite Element Analysis – New Trends and Developments

**Figure 3.** Embedded tooth in red epoxy.

**Figure 4.** 3D model of the sound tooth

The second, latest method of reconstructing a 3D tooth model is performed with the aid of CT. It facilitates and speeds up the acquisition and produces more accurate model. With this method the surrounding soft structures can be also included, larger areas scanned and reconstructed, while the structures itself still remain in the patient mouth. The next big advantage of CT model rendering consists of the possibility to scan the same structure The results obtained from a FEA on the restored system contain information about the stress distribution of each component of the restoration, instead of only a single value of failure load typical of in vitro results. A correct interpretation of FEA results should be based on the stresses and strength of each component of the system. To obtain accurate conclusions from these interpretations, three conditions must be fulfilled. First, FEA should adequately represent the real stress values; second, strength of the different materials must be known; third, an adequate failure criterion must be used [13].

It is not possible to implement the results from FEA directly into a clinical situation, but it has to design the model in such a way that is mimics the real situation as closely as possible. FEA analysis must be interpreted with a certain amount of caution. Most of the researches modeled dental structures as isotropic and not othotropic. The finite element model represents a static situation at the moment of load application and not an actual clinical situation. In reality, the loading of the structure is more dynamic and cyclic. The materials of the various tooth structures were assumed to be isotropic, homogenous and elastic, and that they remain such under applied loads. More precise measurements can be obtained if the material properties are set as anizotrophic and non-homogeneous, but such setup requires much more complex mathematical calculations. It is better to use a non-linear elastic-plastic material model than the linear models that are used in most FEA studies [14].

The values from finite element analysis are presented as maximum and minimum principal stresses. Most of the previously published studies have analyzed the results from Von Mises maximal stress [15-19]. This is probably associated to the fact that this is the normal criterion for the most engineering analyses, which usually deal with ductile materials such as steel and aluminum [13]. It is known that the Von Mises criterion is only valid for the ductile materials with equal compressive or tensile strength, but materials exhibiting brittle behavior such as ceramics, cements or resin composites presents reported values of compressive strength significantly greater than tensile strength [20]. Positive and negative values indicate that the corresponding regions are subjected to tensile or compressive stresses (figure 5) [21].

The response of the structure is different if asymmetrical loading is considered. When the tooth is compressively loaded, displacements do not appear to be significant because of the rather large compressive yield strength. The situation is different if the asymmetrical loading is considered, when the tensile stress occurs. The dental tissues are more resilient to compressive than tensile forces. Any occlusal contact that can create tensile stress, also creates the possibility to create a lesion in tooth structure. When lateral loads are applied, tensile stresses generated in the areas are of higher values than when vertical loads are

applied onto the same areas. The increase in the load does not cause a change in the overall stress pattern, but increases the values. The loading, that the tooth is subjected to, may cause cracks in the tooth, but not necessarily its immediate failure. Most of the failures of dental materials used for tooth restorations are caused by tensile stress. Precise occlusal adjustments of teeth occlusal surfaces should be performed to prevent such events. The average chewing force varies between 11 and 150 N, whereas force peaks are 200N in the anterior, 350N in the posterior and 1000N with bruxism [22].

Finite Element Analysis in Dental Medicine 9

changes can occur depending upon the magnitude of the force, which can affect the tooth

The properties of tooth are not homogenous, but are anisptropic like dentin (due to its capillary morphological structure) or enamel (due to its prismatic structure) [23]. Various studies have shown that the failure was confined mostly to the occlusal walls and margins, and was usually seen on the buccal surfaces of lower molars and premolars (figure 6 and 7) [24,25]. Excursive mandibular movements place the buccal cusps in tension or in compression and open up the occlusal margins (figure 8). Enamel near the cemento-enamel junction is highly stressed because the reactive forces have to flow into and through this thin wedge of tissue for it to be transmitted into the root of the tooth and subsequently into the supporting alveolus bone [2]. This is the reason why the restorations inserted into the cervical region can be subjected to high compressive stresses even though these areas are

morphology in extreme (premature contacts) or repetitive cases (fatigue) [11].

not susceptible to direct contact during mastication [26,4].

**Figure 6.** FEA analysis in sound tooth in normal occlusion looking from outside

**3.1. Natural tooth**

**Figure 5.** FEA model of a restored apicotomysed tooth

## **3. Materials and types of reconstructions in dental medicine**

The use of different materials for restoration substantially modifies the stress distribution of an originally healthy tooth. The difference between the elastic modulus of tooth and restorative material may be a source of stress in the dental structures. If the stress exceeds the yield strength of the materials, fracture of the restorative materials or the tooth may occur. The occlusal force leaning against the tooth or dental implant axis causes the structure to bend, and the higher tensile stresses are produced. The oblique force loading on the dental structure is the major cause of dental damage and the further attention should be paid to the importance of the occlusal adjustment [4, 7, 25].

The way the chewing force application is much more important than the dentine and the enamel properties, or even the properties of the restorative materials. The consequences of the same chewing force for different teeth also need to be highlighted because structural changes can occur depending upon the magnitude of the force, which can affect the tooth morphology in extreme (premature contacts) or repetitive cases (fatigue) [11].

#### **3.1. Natural tooth**

8 Finite Element Analysis – New Trends and Developments

anterior, 350N in the posterior and 1000N with bruxism [22].

**Figure 5.** FEA model of a restored apicotomysed tooth

importance of the occlusal adjustment [4, 7, 25].

**3. Materials and types of reconstructions in dental medicine**

The use of different materials for restoration substantially modifies the stress distribution of an originally healthy tooth. The difference between the elastic modulus of tooth and restorative material may be a source of stress in the dental structures. If the stress exceeds the yield strength of the materials, fracture of the restorative materials or the tooth may occur. The occlusal force leaning against the tooth or dental implant axis causes the structure to bend, and the higher tensile stresses are produced. The oblique force loading on the dental structure is the major cause of dental damage and the further attention should be paid to the

The way the chewing force application is much more important than the dentine and the enamel properties, or even the properties of the restorative materials. The consequences of the same chewing force for different teeth also need to be highlighted because structural

applied onto the same areas. The increase in the load does not cause a change in the overall stress pattern, but increases the values. The loading, that the tooth is subjected to, may cause cracks in the tooth, but not necessarily its immediate failure. Most of the failures of dental materials used for tooth restorations are caused by tensile stress. Precise occlusal adjustments of teeth occlusal surfaces should be performed to prevent such events. The average chewing force varies between 11 and 150 N, whereas force peaks are 200N in the

The properties of tooth are not homogenous, but are anisptropic like dentin (due to its capillary morphological structure) or enamel (due to its prismatic structure) [23]. Various studies have shown that the failure was confined mostly to the occlusal walls and margins, and was usually seen on the buccal surfaces of lower molars and premolars (figure 6 and 7) [24,25]. Excursive mandibular movements place the buccal cusps in tension or in compression and open up the occlusal margins (figure 8). Enamel near the cemento-enamel junction is highly stressed because the reactive forces have to flow into and through this thin wedge of tissue for it to be transmitted into the root of the tooth and subsequently into the supporting alveolus bone [2]. This is the reason why the restorations inserted into the cervical region can be subjected to high compressive stresses even though these areas are not susceptible to direct contact during mastication [26,4].

**Figure 6.** FEA analysis in sound tooth in normal occlusion looking from outside

Finite Element Analysis in Dental Medicine 11

restoration may also influence the retention of class V restoration because of the tooth flexure theory. Breakdown of the margins of class V restorations may be the result of

**Figure 8.** FEA analysis in the sound tooth in the case of malocclusion

A growing interest in aesthetic dental restorations has led to the development of innovative materials for aesthetic restorations of teeth. These new systems have focused on physical properties, such as modulus of elasticity, that are more closely matched to natural tissue, in order to decrease stress concentrations within the dental structure and reduce the incidence of failure. The development of adhesives has created a need to measure the adhesive bond strength of restorative materials to mineralized tissue. Several methods for studying have been developed but FEA capable of quantifying the effect of each tested parameter on bond

Composite occlusal restorations have been shown to reduce cuspal flexure compared to an occlusal amalgam restoration [26]. Composite resin in combination with the acid-etch technique and adhesive systems have been used for the restoration of tooth caries and cervical lesions that we commonly call "dental composite restoration". Evaluation of

occlusal loading [2].

strength [30].

**Figure 7.** FEA analysis of the sound tooth (cross section)

## **3.2. Dental restorations**

Many detrimental effects during restorative procedures are reported to be produced because of lack of understanding of biomechanical principles underlying treatment. Biomechanical studies are crucial in order to highlight the behavior of restored tooth to functional forces [27].

It was earlier thought that the only forces that dislodge the tooth restorations were the pulling forces of sticky foods, while little thought was given to the biomechanics of the tooth structure. Later, it was seen that forces applied on the occlusal surface of the tooth could induce stresses in a restoration remote from the point of application of the force [2]. Heymann suggested that two mechanisms operate and cause failure. One is the lateral excursive movements resulting in lateral cuspal movements which generate tensile stresses along tooth restoration interface, and the other one are heavy forces in centric occlusion which cause vertical deformation on the tooth leading to compressive and shear stresses [24]. The presence of an occlusal restoration weakens the tooth structure and increases the stresses. Especially the depth is more critical than the width [26,28,29]. This restoration may also influence the retention of class V restoration because of the tooth flexure theory. Breakdown of the margins of class V restorations may be the result of occlusal loading [2].

10 Finite Element Analysis – New Trends and Developments

**Figure 7.** FEA analysis of the sound tooth (cross section)

Many detrimental effects during restorative procedures are reported to be produced because of lack of understanding of biomechanical principles underlying treatment. Biomechanical studies are crucial in order to highlight the behavior of restored tooth to functional forces [27].

It was earlier thought that the only forces that dislodge the tooth restorations were the pulling forces of sticky foods, while little thought was given to the biomechanics of the tooth structure. Later, it was seen that forces applied on the occlusal surface of the tooth could induce stresses in a restoration remote from the point of application of the force [2]. Heymann suggested that two mechanisms operate and cause failure. One is the lateral excursive movements resulting in lateral cuspal movements which generate tensile stresses along tooth restoration interface, and the other one are heavy forces in centric occlusion which cause vertical deformation on the tooth leading to compressive and shear stresses [24]. The presence of an occlusal restoration weakens the tooth structure and increases the stresses. Especially the depth is more critical than the width [26,28,29]. This

**3.2. Dental restorations**

**Figure 8.** FEA analysis in the sound tooth in the case of malocclusion

A growing interest in aesthetic dental restorations has led to the development of innovative materials for aesthetic restorations of teeth. These new systems have focused on physical properties, such as modulus of elasticity, that are more closely matched to natural tissue, in order to decrease stress concentrations within the dental structure and reduce the incidence of failure. The development of adhesives has created a need to measure the adhesive bond strength of restorative materials to mineralized tissue. Several methods for studying have been developed but FEA capable of quantifying the effect of each tested parameter on bond strength [30].

Composite occlusal restorations have been shown to reduce cuspal flexure compared to an occlusal amalgam restoration [26]. Composite resin in combination with the acid-etch technique and adhesive systems have been used for the restoration of tooth caries and cervical lesions that we commonly call "dental composite restoration". Evaluation of

marginal integrity at the composite resin-tooth interface is required for clinically successful restorations. Polymerization contraction occurs during light curing and may cause marginal disintegration [31]. The maximum stresses due to the shrinkage of the cement layer may cause debonding of the cement layer. This debonding on one side will cause relaxation of stresses at the other side of the restoration and will cause (micro) leakage with all its detrimental effects [14].

Finite Element Analysis in Dental Medicine 13

was a key element since the elasticity modulus of porcelains is matched well with enamel

The widely used method for treatment of structurally weakened teeth is the post and core system. This system can be classified into two basic core system, metal posts and cores that are custom cast as a single piece, and two element designs composing a prefabricated post to which other materials core is subsequently adapted [34]. The difference between the elastic modulus of dentine and the post material may be a source of stress for root structures. Debonding of posts because of contraction stress of the cement was found as the most common mode of failure [27]. The effect of post design is also very important for dentinal stress distribution since the placement of a post can create stresses that lead to root fracture (figure 9) [1]. Increased intracanal stresses below the level of crestal bone would explain the higher incidence of deep root fractures in teeth restored with post-retained crowns Horizontal loads generate more dentinal stress than vertical loads. Shorter posts are associated with more dentinal stress concentration around the post apex. Consequently, extending the apical post beyond the level of alveolar bone is essential to avoid stress concentration in the region of the post apex. However, very long posts are associated with higher intracanal stress values. A higher amount of radicular dentin around the post is important in order to reduce dentinal stress concentration within the root [35]. The use of post materials conflicts with the mechanical resistance of teeth because of mismatch in the stiffness with the residual dental structure [36]. Many studies have shown that fiberglass posts give better biomechanical performance. Titanium posts concentrate stress close to the post-cement interface, promoting weakness of restored tooth. Akkayan [37] observed that the fractures occurring with the use of fiberglass and quartz posts systems could be repaired, whereas this was not the case with zirconium and titanium posts. Thus, fiberglass post can be considered a very good choice because they offer good biomechanical performance, provide excellent aesthetics, and exhibit good adhesion to cementing agents

Clinicians generally agree that NiTi rotary files have good properties to produce desirable tapered root canal forms, but also have a risk of fracture during instrumentation. These instruments have been developed to overcome the rigidity of stainless steel instruments [39]. Design of an instrument is the main factor in their mechanical behavior. Cyclic fatigue, which is a failure process associated with repetitive stressing, and torsion have been

With the application of adhesive technology to endodontics, the term monoblock has become familiar. Monoblock units can be created in a root canal system either by adhesive root sealers in combination with a bondable root filling material or adhesive post systems. The concept of creating mechanically homogenous units within the root dentine is excellent in theory, but accomplishing these ideal monoblock in the canal space is challenging because bonding to dentine is compromised by volumetric changes in resin-based materials, high cavity configuration factors, debris on canal walls, and differences in regional bond

reported as dominant factors in file fracture [40].

[11].

[38].

strengths [27].

The fracture load of the final restoration is the result of the combined effects of bonding between the underlying tooth, the ceramic restoration, and the resin composite cement. Clinical stress distribution in ceramic dental restorations may be quite complex. Several factors are associated with crack initiation and propagation, including the shape, microstructural no homogeneities, the size and distribution of surface flows, residual stresses, ceramic-cement interfacial features, thickness of restorations, different elastic modulus and the magnitude and orientation of the applied load. On the structural factors, the connector areas are the most influential in failure [22]. Traditional load-to–failure testing has proved irrelevant in predicting the clinical performance of ceramics, largely because they cannot recreate the failure mechanisms seen in clinical specimens [5]. The FEA was used to determine the optimal stress distribution in the ceramics bridges that would reduce the risk of connector fracture. The points of greater stress were found within, or near the connector [22].

The FEA demonstrated that with the use of an idealized inlay preparation form and an optimized bridge design emphasizing a broadening of the gingival embrasure, the forces derived from mastication can be adequately distributed to levels which are within the fracture strength of current ceramics [5]. Tensile stresses tend to be more critical than compressive stresses for ceramic materials. The strength of ceramic restorations is significantly affected by the presence of flows or other microscopic defects [32]. Tensile stress concentration at cementation surface of the ceramic layer was suggested to be the predominant factor controlling ceramic failure [33]. Fea showed lower tensile stress levels at the cementation surface than in the area under and between the load points, which could explain the occlusal to cervical direction of fracture seen in the fractographic analysis. Although the polymer crown had a higher fracture resistance than ceramics, a larger amount of the occlusal load was transferred through the tooth, resulting in catastrophic fracture of the tooth. This fracture behavior can limit the use of polymer crowns when compared to ceramic systems [32]. Molar crowns made of stiffer materials are less prone to debonding and crowns made of higher elastic modulus material protect the tooth structures from damage [23].

Veneers used in restorative rehabilitations for anterior teeth are retained by the adhesive systems and resin cements. These restorations are mechanically not strong, because they are made up of a brittle material, but they have good retention due to the resin-dentine bonding. The remaining tooth tissue is the most important factor for the longevity of the veneers where the buccal, cervical region is the most critical region. Teeth totally recover their properties when veneers are placed as a partial enamel substitute. The use of ceramic was a key element since the elasticity modulus of porcelains is matched well with enamel [11].

12 Finite Element Analysis – New Trends and Developments

detrimental effects [14].

from damage [23].

marginal integrity at the composite resin-tooth interface is required for clinically successful restorations. Polymerization contraction occurs during light curing and may cause marginal disintegration [31]. The maximum stresses due to the shrinkage of the cement layer may cause debonding of the cement layer. This debonding on one side will cause relaxation of stresses at the other side of the restoration and will cause (micro) leakage with all its

The fracture load of the final restoration is the result of the combined effects of bonding between the underlying tooth, the ceramic restoration, and the resin composite cement. Clinical stress distribution in ceramic dental restorations may be quite complex. Several factors are associated with crack initiation and propagation, including the shape, microstructural no homogeneities, the size and distribution of surface flows, residual stresses, ceramic-cement interfacial features, thickness of restorations, different elastic modulus and the magnitude and orientation of the applied load. On the structural factors, the connector areas are the most influential in failure [22]. Traditional load-to–failure testing has proved irrelevant in predicting the clinical performance of ceramics, largely because they cannot recreate the failure mechanisms seen in clinical specimens [5]. The FEA was used to determine the optimal stress distribution in the ceramics bridges that would reduce the risk of connector fracture. The

The FEA demonstrated that with the use of an idealized inlay preparation form and an optimized bridge design emphasizing a broadening of the gingival embrasure, the forces derived from mastication can be adequately distributed to levels which are within the fracture strength of current ceramics [5]. Tensile stresses tend to be more critical than compressive stresses for ceramic materials. The strength of ceramic restorations is significantly affected by the presence of flows or other microscopic defects [32]. Tensile stress concentration at cementation surface of the ceramic layer was suggested to be the predominant factor controlling ceramic failure [33]. Fea showed lower tensile stress levels at the cementation surface than in the area under and between the load points, which could explain the occlusal to cervical direction of fracture seen in the fractographic analysis. Although the polymer crown had a higher fracture resistance than ceramics, a larger amount of the occlusal load was transferred through the tooth, resulting in catastrophic fracture of the tooth. This fracture behavior can limit the use of polymer crowns when compared to ceramic systems [32]. Molar crowns made of stiffer materials are less prone to debonding and crowns made of higher elastic modulus material protect the tooth structures

Veneers used in restorative rehabilitations for anterior teeth are retained by the adhesive systems and resin cements. These restorations are mechanically not strong, because they are made up of a brittle material, but they have good retention due to the resin-dentine bonding. The remaining tooth tissue is the most important factor for the longevity of the veneers where the buccal, cervical region is the most critical region. Teeth totally recover their properties when veneers are placed as a partial enamel substitute. The use of ceramic

points of greater stress were found within, or near the connector [22].

The widely used method for treatment of structurally weakened teeth is the post and core system. This system can be classified into two basic core system, metal posts and cores that are custom cast as a single piece, and two element designs composing a prefabricated post to which other materials core is subsequently adapted [34]. The difference between the elastic modulus of dentine and the post material may be a source of stress for root structures. Debonding of posts because of contraction stress of the cement was found as the most common mode of failure [27]. The effect of post design is also very important for dentinal stress distribution since the placement of a post can create stresses that lead to root fracture (figure 9) [1]. Increased intracanal stresses below the level of crestal bone would explain the higher incidence of deep root fractures in teeth restored with post-retained crowns Horizontal loads generate more dentinal stress than vertical loads. Shorter posts are associated with more dentinal stress concentration around the post apex. Consequently, extending the apical post beyond the level of alveolar bone is essential to avoid stress concentration in the region of the post apex. However, very long posts are associated with higher intracanal stress values. A higher amount of radicular dentin around the post is important in order to reduce dentinal stress concentration within the root [35]. The use of post materials conflicts with the mechanical resistance of teeth because of mismatch in the stiffness with the residual dental structure [36]. Many studies have shown that fiberglass posts give better biomechanical performance. Titanium posts concentrate stress close to the post-cement interface, promoting weakness of restored tooth. Akkayan [37] observed that the fractures occurring with the use of fiberglass and quartz posts systems could be repaired, whereas this was not the case with zirconium and titanium posts. Thus, fiberglass post can be considered a very good choice because they offer good biomechanical performance, provide excellent aesthetics, and exhibit good adhesion to cementing agents [38].

Clinicians generally agree that NiTi rotary files have good properties to produce desirable tapered root canal forms, but also have a risk of fracture during instrumentation. These instruments have been developed to overcome the rigidity of stainless steel instruments [39]. Design of an instrument is the main factor in their mechanical behavior. Cyclic fatigue, which is a failure process associated with repetitive stressing, and torsion have been reported as dominant factors in file fracture [40].

With the application of adhesive technology to endodontics, the term monoblock has become familiar. Monoblock units can be created in a root canal system either by adhesive root sealers in combination with a bondable root filling material or adhesive post systems. The concept of creating mechanically homogenous units within the root dentine is excellent in theory, but accomplishing these ideal monoblock in the canal space is challenging because bonding to dentine is compromised by volumetric changes in resin-based materials, high cavity configuration factors, debris on canal walls, and differences in regional bond strengths [27].

Finite Element Analysis in Dental Medicine 15

in the peri-impant bone interfaces. Different heights and the use of soft liners were relevant in the stress distribution to the bone adjacent to the implants. Better distribution of the stresses

Prosthesis retention remains a much debated topic in the implant literature. Clinical studies comparing cement- and screw- retained implant restorations reveal no differences in outcomes. There is evidence from laboratory and FEA studies that implants with an internal-type connection exhibit better stress distribution with off-axis loading [43]. The combined use of implants and teeth has been questioned because of the differences of mobility between the abutments. Several authors have concluded that the tooth-implant bond does not have a negative influence on the marginal bone and soft tissues, but special care must be taken in planning in order to compensate for the differences in biomechanical

The biomechanical background of orthodontic tooth movement has been explored by many authors, and orthodontic movement principally depends on stress and strain in periodontal ligament (PDL). PDL is a thin connective tissue between the root and bone and play a key role in tooth mobility [12]. Accurate FEA model creation of a tooth and PDL is possible due to the use of micro-CT. Anchorage control in orthodontic treatment is an important factor in treatments outcome. Miniscrews and miniplates are being widely used because of their small size and superiority over endosseous implants due to the fact that they can be immediately loaded. Miniplates have the same features with the plates used in maxillofacial surgery [45]. Good treatment results have been reported by using miniscrews for orthodontic anchorage in various malocclusions, but major problem is their high failure rate. Unlike dental implants, mechanical interdigitation at the cortical bone rather than osseointegration is required for the stability of miniscrews. The placement angle, the type of miniscrews, and the direction of forces significantly affect the distribution area and the amount of stress [46]. Inadequate design and non-homogenous force distribution can cause stress directly effecting on the screws and may impair screws stability. Mobile plates can irritate the surrounding tissue and may cause inflammation. The FEA study revealed that

the new miniplates are highly efficient in reducing stress on the fixation screws [45].

Fractures of the mandibular angle are the most problematic in the facial region because of the high frequency of complications and difficult surgical access to the site [47]. Infection and nonunion are commonly reported after rigid internal fixation of these fractures [48]. The stress analyses obtained from FEA modeling can provide information regarding interactions between hardware and bone during normal patient functioning. A single tension band on the superior borders provided more angle fracture stability than a single bicortical plate placed inferiorly. This results support the use of the single tension band configuration as a

The results of the finite element analysis must be interpreted with a certain amount of caution. Most of the researches modeled dental structures as isotropic and not othotropic.

will provide a more predictable osseointegration [9].

responses between the implant and the tooth [44].

less invasive fixation approach to fractures [47].

**4. General guidelines**

**Figure 9.** 3D modeling of post and core system.

## **3.3. Dental implants and anchorage systems for tooth movements and bone fracture**

Dental implants are widely used to replace decayed teeth or to support prostheses. The failure is associated with bone loss around an implant neck. Bone loss can be activated by excessive implant loading, as by bacterial infection or trauma [41]. Mechanical stress can have positive and negative consequences for bone tissue and for maintaining osseointegration of an oral implant [9]. The prognosis for stress concentration at the bone-implant interface is of the utmost importance in dental implant research [41]. FEA has been widely used in the field of oral implantology to estimate peri-implant stress and strain [42]. The relation between implant design and load distribution at implant-bone interface is important in the search for optimal implant configuration with minimum stress peaks. Another significant factor is bone quality, in mechanical terms; this is determined by bone strength. Increase in implant length and diameter leads to reduction of stress magnitudes within the cortical bone [41]. FEA study shows that non-submerged implants showed higher stress values in the peri-implant bone than submerged ones and the use of soft liner materials considerably reduces the stress levels in the peri-impant bone interfaces. Different heights and the use of soft liners were relevant in the stress distribution to the bone adjacent to the implants. Better distribution of the stresses will provide a more predictable osseointegration [9].

Prosthesis retention remains a much debated topic in the implant literature. Clinical studies comparing cement- and screw- retained implant restorations reveal no differences in outcomes. There is evidence from laboratory and FEA studies that implants with an internal-type connection exhibit better stress distribution with off-axis loading [43]. The combined use of implants and teeth has been questioned because of the differences of mobility between the abutments. Several authors have concluded that the tooth-implant bond does not have a negative influence on the marginal bone and soft tissues, but special care must be taken in planning in order to compensate for the differences in biomechanical responses between the implant and the tooth [44].

The biomechanical background of orthodontic tooth movement has been explored by many authors, and orthodontic movement principally depends on stress and strain in periodontal ligament (PDL). PDL is a thin connective tissue between the root and bone and play a key role in tooth mobility [12]. Accurate FEA model creation of a tooth and PDL is possible due to the use of micro-CT. Anchorage control in orthodontic treatment is an important factor in treatments outcome. Miniscrews and miniplates are being widely used because of their small size and superiority over endosseous implants due to the fact that they can be immediately loaded. Miniplates have the same features with the plates used in maxillofacial surgery [45]. Good treatment results have been reported by using miniscrews for orthodontic anchorage in various malocclusions, but major problem is their high failure rate. Unlike dental implants, mechanical interdigitation at the cortical bone rather than osseointegration is required for the stability of miniscrews. The placement angle, the type of miniscrews, and the direction of forces significantly affect the distribution area and the amount of stress [46]. Inadequate design and non-homogenous force distribution can cause stress directly effecting on the screws and may impair screws stability. Mobile plates can irritate the surrounding tissue and may cause inflammation. The FEA study revealed that the new miniplates are highly efficient in reducing stress on the fixation screws [45].

Fractures of the mandibular angle are the most problematic in the facial region because of the high frequency of complications and difficult surgical access to the site [47]. Infection and nonunion are commonly reported after rigid internal fixation of these fractures [48]. The stress analyses obtained from FEA modeling can provide information regarding interactions between hardware and bone during normal patient functioning. A single tension band on the superior borders provided more angle fracture stability than a single bicortical plate placed inferiorly. This results support the use of the single tension band configuration as a less invasive fixation approach to fractures [47].

## **4. General guidelines**

14 Finite Element Analysis – New Trends and Developments

**Figure 9.** 3D modeling of post and core system.

**fracture**

**3.3. Dental implants and anchorage systems for tooth movements and bone**

Dental implants are widely used to replace decayed teeth or to support prostheses. The failure is associated with bone loss around an implant neck. Bone loss can be activated by excessive implant loading, as by bacterial infection or trauma [41]. Mechanical stress can have positive and negative consequences for bone tissue and for maintaining osseointegration of an oral implant [9]. The prognosis for stress concentration at the bone-implant interface is of the utmost importance in dental implant research [41]. FEA has been widely used in the field of oral implantology to estimate peri-implant stress and strain [42]. The relation between implant design and load distribution at implant-bone interface is important in the search for optimal implant configuration with minimum stress peaks. Another significant factor is bone quality, in mechanical terms; this is determined by bone strength. Increase in implant length and diameter leads to reduction of stress magnitudes within the cortical bone [41]. FEA study shows that non-submerged implants showed higher stress values in the peri-implant bone than submerged ones and the use of soft liner materials considerably reduces the stress levels

The results of the finite element analysis must be interpreted with a certain amount of caution. Most of the researches modeled dental structures as isotropic and not othotropic.

The finite element model represented a static situation at the moment of load application and not an actual clinical situation. In reality, the loading of the structure is more dynamic and cyclic. More precise measurements could be obtained if the material properties are set as anisotropic and non-homogeneous, but such setup requires much more complex mathematical calculations.

Finite Element Analysis in Dental Medicine 17

mathematical model it eliminates the need of large number of teeth. The use of more detailed 3D models is helpful in understand critical problems related to the restorative material choice and optimal application procedures. Improved computer and modeling techniques render

When the tooth is compressively loaded, displacements do not appear to be significant because of its rather large compressive yield strength. The situation is different when asymmetrical loading is considered and tensile stress occurs. The dental tissues are more resilient to compressive than tensile forces. Any occlusal contact that can create tensile stress, also creates the possibility to create a lesion in tooth structure. Most of the failures of dental materials used for tooth restorations are caused by tensile stress. Precise occlusal adjustments of teeth occlusal surfaces should be performed to prevent such events. The difference between the elastic modulus of tooth and restorative material may be a source of stress in the dental structures. If the stress exceeds the yield strength of the materials,

The FEA helps to improve preparation designs, indicates the right material or combination of materials to be used in various load and stress conditions in order to reduce material

*Department of Oral and Maxillofacial Surgery, Medical Faculty, School of Dental Medicine,*

*Department of Restorative Dentistry and Endodontics, Medical Faculty, School of Dental Medicine,*

[1] Silva NR, Castro CG, Santos-Filho PCF, Silva GR, Campos RE, Soares OV, Soares CJ. Influence of different post design and composition on stress distribution in maxillary

[2] Vasudeva G, Bogra P, Nikhil V, Singh V. Effect of occlusal restoration on stresses around class V restoration interface: A finite-element study. Indian J Dent Res

[3] Poiate IAVP, Vasconcellos AB, Mori M, Poiate E Jr. 2D and 3D finite element analysis of central incisor generated by computerized tomography. Computer method and

[4] Borcic J, Antonic R, Muhvic Urek M, Petricevic N, Nola-Fuchs P, Catic A , Smojver I. 3-

central incisor: Finite element analysis. Indian J Dent Res 2009;20:153-158.

D Stress Analysis in Premolar, Coll. Antropol. 31 (2007) 4: 315–319.

the FEA a very reliable and accurate approach in biomechanical applications.

fracture of the restorative materials or the tooth may occur.

and/or tooth failure in clinical practice.

*University of Rijeka, Rijeka, Croatia*

*University of Rijeka, Rijeka, Croatia*

**Author details**

Josipa Borcic\*

Alen Braut

 \*

**6. References**

2011;22:295-302.

Corresponding Author

programs in biomedicine 2011;104:292-299.

To obtain better understanding of the tooth lesions, which is important for the clinical treatment and restoration of damage, analyses of stress distribution in the oral cavity under various loading condition are highly desirable. FEA is a valuable tool for investigation of stress distribution within various types of reconstructions and prosthodontic appliances in dental medicine.

The dental profession is influenced by various sources of information, which may be considered as "evidence-based" (controlled clinical studies) and "expert opinion". A realistic approach is to identify the strengths and weaknesses of the available clinical data and combine it with clinical experience [43]. Most researchers in FEA assumed that all materials used were homogenous, isotropic and linearly elastic. However, this assumption does not reflect the exact situation. The periodontal ligament has nonlinear mechanical properties and the bone is inhomogeneous [9,35]. The 3D analysis permits high efficiency when the biomechanical behavior of the structure needs to be evaluated under different loading conditions. In the last four decades many studies have shown how the Finite Element Analysis applied to dental mechanics has become a popular numerical method to investigate the critical aspects related to stress distribution. The use of more detailed 3D models could be helpful in understanding critical problems related to the restorative material choice and optimal application procedures. Improved computer and modeling techniques render the FEA a very reliable and accurate approach in biomechanical applications [9].

The results from FEA confirm the concept that the interfaces of materials with different module of elasticity represent the weak point of restorative systems. Restorations with material having a similar elastic modulus to tooth can save and strengthen the remaining tooth structure [27]. Combining fatigue experiments with FEA may eliminate, or at least minimize, experimental limitations by correlating fatigue failure to stress instead of specific testing configuration.

## **5. Conclusions**

There are numerous ways and attempts of experimental research, but due to complexity of dental structures, composed of various tissue materials mechanically and chemically interconnected, and due to complex tooth morphology and surrounding structures, most of these attempts fail to present precise and reliable results.

The 3D analysis permits high efficiency when the biomechanical behavior of the structure should be evaluated under different loading conditions. In the biomedical fields, the FEA is an important tool since it can avoid the necessity of traditional specimens, and by using a mathematical model it eliminates the need of large number of teeth. The use of more detailed 3D models is helpful in understand critical problems related to the restorative material choice and optimal application procedures. Improved computer and modeling techniques render the FEA a very reliable and accurate approach in biomechanical applications.

When the tooth is compressively loaded, displacements do not appear to be significant because of its rather large compressive yield strength. The situation is different when asymmetrical loading is considered and tensile stress occurs. The dental tissues are more resilient to compressive than tensile forces. Any occlusal contact that can create tensile stress, also creates the possibility to create a lesion in tooth structure. Most of the failures of dental materials used for tooth restorations are caused by tensile stress. Precise occlusal adjustments of teeth occlusal surfaces should be performed to prevent such events. The difference between the elastic modulus of tooth and restorative material may be a source of stress in the dental structures. If the stress exceeds the yield strength of the materials, fracture of the restorative materials or the tooth may occur.

The FEA helps to improve preparation designs, indicates the right material or combination of materials to be used in various load and stress conditions in order to reduce material and/or tooth failure in clinical practice.

## **Author details**

Josipa Borcic\*

16 Finite Element Analysis – New Trends and Developments

mathematical calculations.

dental medicine.

applications [9].

testing configuration.

**5. Conclusions**

The finite element model represented a static situation at the moment of load application and not an actual clinical situation. In reality, the loading of the structure is more dynamic and cyclic. More precise measurements could be obtained if the material properties are set as anisotropic and non-homogeneous, but such setup requires much more complex

To obtain better understanding of the tooth lesions, which is important for the clinical treatment and restoration of damage, analyses of stress distribution in the oral cavity under various loading condition are highly desirable. FEA is a valuable tool for investigation of stress distribution within various types of reconstructions and prosthodontic appliances in

The dental profession is influenced by various sources of information, which may be considered as "evidence-based" (controlled clinical studies) and "expert opinion". A realistic approach is to identify the strengths and weaknesses of the available clinical data and combine it with clinical experience [43]. Most researchers in FEA assumed that all materials used were homogenous, isotropic and linearly elastic. However, this assumption does not reflect the exact situation. The periodontal ligament has nonlinear mechanical properties and the bone is inhomogeneous [9,35]. The 3D analysis permits high efficiency when the biomechanical behavior of the structure needs to be evaluated under different loading conditions. In the last four decades many studies have shown how the Finite Element Analysis applied to dental mechanics has become a popular numerical method to investigate the critical aspects related to stress distribution. The use of more detailed 3D models could be helpful in understanding critical problems related to the restorative material choice and optimal application procedures. Improved computer and modeling techniques render the FEA a very reliable and accurate approach in biomechanical

The results from FEA confirm the concept that the interfaces of materials with different module of elasticity represent the weak point of restorative systems. Restorations with material having a similar elastic modulus to tooth can save and strengthen the remaining tooth structure [27]. Combining fatigue experiments with FEA may eliminate, or at least minimize, experimental limitations by correlating fatigue failure to stress instead of specific

There are numerous ways and attempts of experimental research, but due to complexity of dental structures, composed of various tissue materials mechanically and chemically interconnected, and due to complex tooth morphology and surrounding structures, most of

The 3D analysis permits high efficiency when the biomechanical behavior of the structure should be evaluated under different loading conditions. In the biomedical fields, the FEA is an important tool since it can avoid the necessity of traditional specimens, and by using a

these attempts fail to present precise and reliable results.

*Department of Oral and Maxillofacial Surgery, Medical Faculty, School of Dental Medicine, University of Rijeka, Rijeka, Croatia*

## Alen Braut

*Department of Restorative Dentistry and Endodontics, Medical Faculty, School of Dental Medicine, University of Rijeka, Rijeka, Croatia*

## **6. References**

<sup>\*</sup> Corresponding Author

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Finite Element Analysis in Dental Medicine 19

fabricated posts on maxillary central incisors restored with crown. Journal of Oral

[21] Lang L, Wang RF. Validation of finite element analysis in dental ceramics research.

[22] Rezaei SMM, Heidarifar H, Arezodar FF, Azary A, Mokhtarykhoee S. Influence of Connector Width on the Stress Distribution of Posterior Bridges under Loading. Journal

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[25] Borcic J, Anic I, Smojver I, Catic A, Miletic I, Pezelj Ribaric S. 3D finite element model and cervical lesion formation in normal occlusion and in malocclusion. Journal of Oral

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[27] Belli S, Eraslan O, Eskitascioglu G, Karbhari V. Monoblocks in root canals: a finite elemental stress analysis study. International Endodontic Journal 2011;44:817-826. [28] Hood JA. Biomechanical of the intact, prepared and restored tooth. Some implication an adaptive finite-element approach fo the analysis of dental restorations. International

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[33] Dong XD, Darvell B. Stress distribution and failure mode of dental ceramic structures

[34] Adanir N, Belli S. Stress analysis of a maxillary central incisor restored with different

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[20] Craig R, Powers JM. Restorative Dental Materials. St Louis Mosby 2002;11

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18 Finite Element Analysis – New Trends and Developments

Dental Journal 2011;56:301-311.

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finite element analysis. J Prosthodont 2009;18:393-402.

[5] Thompson MC, Field CJ, Swain MV. The all-ceramic, inlay supported fixed partial denture. Part 2. Fixed partial denture design: a finite element analysis. Australian

[6] Ding X, Zhu XH, Liao SH, Zhang XH, Chen H. Implant-bone interfaces stress distribution in immediately loaded implants of different diameters: a three-dimensional

[7] Zienkiewicz OC, Taylor RL. The Finite Element Method. 5th ed. Oxford, England:

[8] Haiyan L, Jianying L, Zhenmin Z, Fok ASL. Fracture simulation of restored teeth using a continuum damage mechanics failure model. Dental Materials 2011;27:e125-e133. [9] Santos MBF, Silva Neto JP, Consani RLX, Mesquita MF. Three-dimensional finite element analysis of stress distribution in peri-implant bone with relined dentures and

[11] Matson MR, Lewgoy HR, Barros Filho DA, Amore R, Anido-Anido A, Alonso RCB, Carrilho MRO, Ansuate-Netto C. Finite element analysis of stress distribution in intact and porcelain veneer restored teeth. Computer Methods in Biomechanics and

[12] Hohmann A, Kober C, Young P, Dorow C, Geiger M, Boryor A, Sander FM, Sander C, Sander FG. Influence of different modeling strategies for the periodontal ligament on finite element simulation results. American Journal of Orthodontics and Dentofacial

[13] Perez-Gonzalez A, Iserte-Vilar JL, Gonzalez-Lluch C. Biomedical Engineering http://www.biomedical-engineering-online.com/content/10/1/44 (accessed 10 March

[14] Jongsma LA, Jager Ir. N, Kleverlaan CJ, Feilzer AJ. Reduced contraction stress formation obtained by a two-step cementation procedure for fiber posts. Dental

[15] Pegoretti A, Fambri L, Zappini G, Biachetti M. Finite element analysis of glass fibre

[16] Asmussen E, Peutzfeldt A, Sahafi A. Finite element analysis of stresses in endodontically treated, dowel-restored teeth. Journal of Prosthetics Dentistry

[17] Genocese K, lamberti L, pappalettere C. Finite element analysis of a new customized composite post system for endodontically treated teeth. Journal of Biomechanics

[18] Sorrentino R, Aversa R, Ferro V, Auriemma T, Zarone F, Ferrari M et al. Threedimensional finite element analysis of strain and stress distributions in endodontically treated maxillary central incisors restored with different post, core and crown materials.

[19] Gonzalez-Lluch C, Rodriguez-Cervantes PJ, Sancho-Bru JL, perez-Gonzalez A, barjau-Escribano A, Vergara-Monedero M et al. Influence of material and diameter of pre-

reinforced composite endodontic post. Biomaterials 2002;23:2667-2682.

different heights of healing caps. Journal of Oral Rehabilitation 2011;38:691-6. [10] Khera SC, Goel VK, Chen RCS, Gurusami SA. A three-dimensional element model.

	- [35] Al-Omiri MK, Rayyan MR, Abu-Hammad O. Stress analysis of endodontically treated teeth restored with post-retained crowns: A finite element analysis study. The Journal of the American Dental Association 2011;142:289-300.

**Chapter 2**

© 2012 Gultekin et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Gultekin et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Application of Finite Element Analysis in**

Since Brånemark's discovery, dental implants have become the most common restorative technique for the rehabilitation of edentulism. Many factors can impact the survival of implant-supported restorations. The most important factor for determining the long-term success of osseointegration is the state of the peri-implant bone [1-3]. Ideal biomechanical conditions directly affect bone remodeling and help to maintain the integrity of non-living structures such as the implant, abutment, and superstructures (Figures 1-7). Oral dental implant interventions involving surgical and restorative procedures for the rehabilitation of various causes of edentulism are associated with several risks. In particular, mechanical and technical risks plays a major role in implant dentistry, resulting in increased rates of repairs, unnecessary costs and lost time, and even complications that may not be easily corrected (Figures 8-10) [4-7]. Therefore, the potential mechanical and technical risks of failure or associated complications need to be evaluated before undertaking such interventions, since the application of necessary precautions may improve the survival of implant-supported restorations. Consequently, the number of biomechanical studies in the field of implant

Several methods based on photoelastic, strain-gauge, and finite element analysis (FEA) based studies have been used to investigate stress in the peri-implant region and in the components of implant-supported restorations [8-11]. FEA is a numerical stress analysis technique that is widely used to assess engineering and biomechanical problems before they occur [12,13]. A finite element model is constructed by dividing solid objects into several elements that are connected at a common nodal point. Each element is assigned appropriate material properties corresponding to the properties of the object being modeled. The first step is to subdivide the complex object geometry into a suitable set of smaller 'elements' of 'finite' dimensions. When combined with the 'mesh' model of the investigated structures,

dentistry has dramatically increased in an effort to reduce failure rates.

B. Alper Gultekin, Pinar Gultekin and Serdar Yalcin

Additional information is available at the end of the chapter

**Implant Dentistry**

http://dx.doi.org/10.5772/48339

**1. Introduction**

## **Application of Finite Element Analysis in Implant Dentistry**

B. Alper Gultekin, Pinar Gultekin and Serdar Yalcin

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/48339

## **1. Introduction**

20 Finite Element Analysis – New Trends and Developments

2011;37:1152-1157.

Dentistry 2012;6:9-15.

Orthopedics 2011;140:e273-e280.

192.

3014.

of the American Dental Association 2011;142:289-300.

[35] Al-Omiri MK, Rayyan MR, Abu-Hammad O. Stress analysis of endodontically treated teeth restored with post-retained crowns: A finite element analysis study. The Journal

[36] Ausiello P, Franciosa P, Martorelli M, Watts D. Mechanical behaviour of post-restored

[37] Akkayan B, Gulmez T. Resistance to fracture of endodontically treated teeth restored with different post systems. Journal of Prosthetic Dentistry 2002;23:2667-2682. [38] Cooney JP, Caputo AA, Trabert KC. Retention and stress distribution of tapered-end

[39] LeeMH, Versluis A, Kim BM, Lee CJ, Hur B, Kom HC. Journal of Endodontics

[40] Sattapan B, Nervo GJ, palamara JE, Messer HH. Defects in rotary nickel-titanium files

[41] Demenko V, Linetskiy I, Nesvit K, Shevchenko A. Ulitmate masticatory force as a

[42] Geng JP, Tan KB, Liu GR. Application of finite element analysis in implant dentistry: a

[43] Lewis MB, Klineberg I. Prosthodontic considerations designed to optimize outcomes for single-tooth implants. A review of the literature. Australian Dental Journal 2011;56:181-

[44] Lanza MDS, Seraidarian PI, Jansen WC, Lanza MD. Stress analysis of a fixed implantsupported denture by the finite element method (FEM) when varying the number of

[45] Nalbantgil D, Tozlu M, Ozdemir F, Oztoprak MO, Arun T. FEM analysis of a new miniplate: stress distribution on the plate, screws and the bone. European Journal of

[46] Suzuki A, Masuda T, Takahashi I, Deguchi T, Suzuki O, Takana-Yamamoto T. Changes in stress distribution of orthodontic miniscrews and surrounding bone evaluated by 3 dimensional finite element analysis. Americam Journal of Orthodontics and Dentofacial

[47] Kimsal J, Baack B, Candelaria L, Khraishi T, Lovald S. Biomechanical analysis of mandibular angle fractures. Journal of Oral and Maxillofacial Surgery 2011;69:3010-

[48] Mathog RH, Toma V, Clayman L et al. Nonunion of the mandible: An analysis of

contributing factors. Journal of Oral and Maxillofacial Surgery 2000;59:746.

criterion in implant selection. Journal of Dental Research 2011;90:1211-1215.

review of the literature. Journal of Prosthetic Dentistry 2001;85:585-598.

upper canine teeth: A 3D FE analysis. Dental Materials 2011;27:1285-1294.

endodontic posts. Journal of Prosthetics Dentistry 1986;55:540-546.

after clinical use. Jounal of Endodontics 2000;26:161-165.

teeth used as abutments. J Appl Oral Sci 2011;19:655-661.

Since Brånemark's discovery, dental implants have become the most common restorative technique for the rehabilitation of edentulism. Many factors can impact the survival of implant-supported restorations. The most important factor for determining the long-term success of osseointegration is the state of the peri-implant bone [1-3]. Ideal biomechanical conditions directly affect bone remodeling and help to maintain the integrity of non-living structures such as the implant, abutment, and superstructures (Figures 1-7). Oral dental implant interventions involving surgical and restorative procedures for the rehabilitation of various causes of edentulism are associated with several risks. In particular, mechanical and technical risks plays a major role in implant dentistry, resulting in increased rates of repairs, unnecessary costs and lost time, and even complications that may not be easily corrected (Figures 8-10) [4-7]. Therefore, the potential mechanical and technical risks of failure or associated complications need to be evaluated before undertaking such interventions, since the application of necessary precautions may improve the survival of implant-supported restorations. Consequently, the number of biomechanical studies in the field of implant dentistry has dramatically increased in an effort to reduce failure rates.

Several methods based on photoelastic, strain-gauge, and finite element analysis (FEA) based studies have been used to investigate stress in the peri-implant region and in the components of implant-supported restorations [8-11]. FEA is a numerical stress analysis technique that is widely used to assess engineering and biomechanical problems before they occur [12,13]. A finite element model is constructed by dividing solid objects into several elements that are connected at a common nodal point. Each element is assigned appropriate material properties corresponding to the properties of the object being modeled. The first step is to subdivide the complex object geometry into a suitable set of smaller 'elements' of 'finite' dimensions. When combined with the 'mesh' model of the investigated structures,

© 2012 Gultekin et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Gultekin et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

each element can adopt a specific geometric shape (i.e., triangle, square, tetrahedron, etc.) with a specific internal strain function. Using these functions and the actual geometry of the element, the equilibrium equations between the external forces acting on the element and the displacement occuring at each node can be determined [9].

Application of Finite Element Analysis in Implant Dentistry 23

**Figure 2.** After flap elevation, the cortical bone is visible

**Figure 3.** Dental implant with an abutment to be placed in the ridge created by the missing molar

**Figure 1.** Missing molar in the mandible, to be treated with a dental implant-supported restoration

In implant dentistry literature, commonly used materials in FEA studies can be classified as either implant, peri-implant bone (cortical and cancellous bone), and restoration (Figure 11). This method allows application of simulated forces at specific points in the system and stress analysis in the peri-implant region and surrounding structures. 2-D and 3-D models can be created and models for every treatment alternative can be explored. However, 2-D models cannot simulate the behavior of 3-D structures as realistically as 3-D models, so most recent studies have focused on 3-D modeling [14-17].

**Figure 2.** After flap elevation, the cortical bone is visible

the displacement occuring at each node can be determined [9].

each element can adopt a specific geometric shape (i.e., triangle, square, tetrahedron, etc.) with a specific internal strain function. Using these functions and the actual geometry of the element, the equilibrium equations between the external forces acting on the element and

**Figure 1.** Missing molar in the mandible, to be treated with a dental implant-supported restoration

recent studies have focused on 3-D modeling [14-17].

In implant dentistry literature, commonly used materials in FEA studies can be classified as either implant, peri-implant bone (cortical and cancellous bone), and restoration (Figure 11). This method allows application of simulated forces at specific points in the system and stress analysis in the peri-implant region and surrounding structures. 2-D and 3-D models can be created and models for every treatment alternative can be explored. However, 2-D models cannot simulate the behavior of 3-D structures as realistically as 3-D models, so most

**Figure 3.** Dental implant with an abutment to be placed in the ridge created by the missing molar

Application of Finite Element Analysis in Implant Dentistry 25

**Figure 6.** Abutment is prepared and attached to the implant

**Figure 7.** Porcelain-fused metal implant-supported restoration in use with optimum treatment planning

**Figure 4.** Implant is placed in the ridge

**Figure 5.** Occlusal view of the implant after 2 months of healing

**Figure 6.** Abutment is prepared and attached to the implant

**Figure 4.** Implant is placed in the ridge

**Figure 5.** Occlusal view of the implant after 2 months of healing

**Figure 7.** Porcelain-fused metal implant-supported restoration in use with optimum treatment planning

Application of Finite Element Analysis in Implant Dentistry 27

**Figure 10.** Severe bone defect is seen after implant removal; advanced bone regeneration techniques are

needed to replace the implant

**Figure 11.** Modeling of bone, implant, abutment, and restoration

**Figure 8.** Intraoral picture of a broken implant due to excessive loading after 1 year of use

**Figure 9.** Severe bone resorption after 2 years of loading; implant and superstructure have no mechanical failure, but peri-implant bone could not resist excessive loading (biomechanical failure because of improper occlusal adjustment)

Application of Finite Element Analysis in Implant Dentistry 27

26 Finite Element Analysis – New Trends and Developments

**Figure 8.** Intraoral picture of a broken implant due to excessive loading after 1 year of use

**Figure 9.** Severe bone resorption after 2 years of loading; implant and superstructure have no mechanical failure, but peri-implant bone could not resist excessive loading (biomechanical failure

because of improper occlusal adjustment)

**Figure 10.** Severe bone defect is seen after implant removal; advanced bone regeneration techniques are needed to replace the implant

**Figure 11.** Modeling of bone, implant, abutment, and restoration

## **2. Modelization of living structure (bone)**

To improve the quality of FEA research, strict attention should be paid to the modelization procedure as one of the most important part of FEA studies. The features of the model should resemble the physical properties of the actual structure as closely as possible, with respect to dimension and material properties. The most difficult and complex part of the modelization process involves capturing the detailed properties of living structures. Therefore, in general, specifications drawn from chapters of a detailed anatomy book or from tomographic scans of a jaw from a cadaveric human specimen can be used for the modeling procedure. Volumetric data obtained from tomography devices or magnetic resonance imaging are digitally reconstructed [18,19]. Then, the material properties applied to the elements can be varied according to the modeling requirements of a particular situation. Computed tomography offers another advantage for realistic modeling in not only the development of anatomic structures, but also the inclusion of material properties according to different bone density values [20,21]. In some studies, the bone is totally or partially modeled as a simple rectangle, elipsoid, or U-shape [18]. In detailed studies, especially with data obtained from scanners, bone can be modeled in a very realistical manner; however, this increased level of geometric detail will result in increased working and computing time. According to the treatment alternatives being investigated, cortical bone can be layered in milimeters or can be neglected altogether in order to simulate weak bone properties similar to those found in the posterior maxilla (Figure 12). Bone properties related to density can be calibrated to range from very soft to dense bone, according to the individual research protocol. If only a specific area and/or condition of the mandible or maxilla is being investigated, there is no need to visualize and construct a model of entire jaw. Limiting the scope or features of the model will distinctly decrease the working time and costs, as previously discussed. A region of interest can be extracted using a number of techniques, such as a Boolean process (Figures 13-15), and any implant design can be adopted for the study. Regions of interest may change according to the study protocol. Portions of the mandible or maxilla, maxillary sinus region, and temporomandibular joint are the most common anatomical areas used in studies related to implantology. In the existing literature 2-D FEA bone models are generally simplified as a rectangular shape [14]. However, recent studies have used 3-D bone modeling to better represent the realistic anatomy of these complex structures [22-24].

Application of Finite Element Analysis in Implant Dentistry 29

element model (FEM). In the study mentioned above, sections were digitized into the DICOM 3.0 format and visualized using 3-D Doctor software (Able Software Corp., Lexington, MA, USA). Cortical bone of 2 mm uniform thickness, and cancellous bone were also modeled (Figure 17). In this study, cortical and cancellous bone model components were considered homogenous. However, in fact, cancellous bone in particular has widely variable density properties. The non-uniform nature of the density of this anatomic structure may affect the magnitude and distribution of stress concentration after loading. These simplifications are common in studies that employ FEA and are aimed at limiting the computing difficulties associated with performance of these studies [18,26,27]. To develop more realistic models of living structures, future studies may include variable density properties obtained from bone density values measured in Hounsfield Units or from other advanced data obtained from computed tomography scans performed with individual

**Figure 12.** Cortical thickness of the posterior maxilla is neglected; only cancellous bone properties are

patients (Figure 18) [28-30].

modeled

In a previous FEA study, the human mandible model was based on a cadaveric mandible obtained from the anatomy department [25]. The edentulous cadaver mandible was scanned using a dental volumetric computed tomography device (ILUMA, Orthocad, CBCT scanner, 3M ESPE, St. Paul, MN, USA) (Figure 16). Volumetric data were reconstructed in 0.2 mm thick sections. The mandibular height and width were at least 10 mm and 5 mm, respectively. More detailed anatomic representations could be created in future studies through the use of computed tomography scanners that can slice objects into thinner sections, but this may increase the working time and development cost of the final finite element model (FEM). In the study mentioned above, sections were digitized into the DICOM 3.0 format and visualized using 3-D Doctor software (Able Software Corp., Lexington, MA, USA). Cortical bone of 2 mm uniform thickness, and cancellous bone were also modeled (Figure 17). In this study, cortical and cancellous bone model components were considered homogenous. However, in fact, cancellous bone in particular has widely variable density properties. The non-uniform nature of the density of this anatomic structure may affect the magnitude and distribution of stress concentration after loading. These simplifications are common in studies that employ FEA and are aimed at limiting the computing difficulties associated with performance of these studies [18,26,27]. To develop more realistic models of living structures, future studies may include variable density properties obtained from bone density values measured in Hounsfield Units or from other advanced data obtained from computed tomography scans performed with individual patients (Figure 18) [28-30].

28 Finite Element Analysis – New Trends and Developments

anatomy of these complex structures [22-24].

**2. Modelization of living structure (bone)**

To improve the quality of FEA research, strict attention should be paid to the modelization procedure as one of the most important part of FEA studies. The features of the model should resemble the physical properties of the actual structure as closely as possible, with respect to dimension and material properties. The most difficult and complex part of the modelization process involves capturing the detailed properties of living structures. Therefore, in general, specifications drawn from chapters of a detailed anatomy book or from tomographic scans of a jaw from a cadaveric human specimen can be used for the modeling procedure. Volumetric data obtained from tomography devices or magnetic resonance imaging are digitally reconstructed [18,19]. Then, the material properties applied to the elements can be varied according to the modeling requirements of a particular situation. Computed tomography offers another advantage for realistic modeling in not only the development of anatomic structures, but also the inclusion of material properties according to different bone density values [20,21]. In some studies, the bone is totally or partially modeled as a simple rectangle, elipsoid, or U-shape [18]. In detailed studies, especially with data obtained from scanners, bone can be modeled in a very realistical manner; however, this increased level of geometric detail will result in increased working and computing time. According to the treatment alternatives being investigated, cortical bone can be layered in milimeters or can be neglected altogether in order to simulate weak bone properties similar to those found in the posterior maxilla (Figure 12). Bone properties related to density can be calibrated to range from very soft to dense bone, according to the individual research protocol. If only a specific area and/or condition of the mandible or maxilla is being investigated, there is no need to visualize and construct a model of entire jaw. Limiting the scope or features of the model will distinctly decrease the working time and costs, as previously discussed. A region of interest can be extracted using a number of techniques, such as a Boolean process (Figures 13-15), and any implant design can be adopted for the study. Regions of interest may change according to the study protocol. Portions of the mandible or maxilla, maxillary sinus region, and temporomandibular joint are the most common anatomical areas used in studies related to implantology. In the existing literature 2-D FEA bone models are generally simplified as a rectangular shape [14]. However, recent studies have used 3-D bone modeling to better represent the realistic

In a previous FEA study, the human mandible model was based on a cadaveric mandible obtained from the anatomy department [25]. The edentulous cadaver mandible was scanned using a dental volumetric computed tomography device (ILUMA, Orthocad, CBCT scanner, 3M ESPE, St. Paul, MN, USA) (Figure 16). Volumetric data were reconstructed in 0.2 mm thick sections. The mandibular height and width were at least 10 mm and 5 mm, respectively. More detailed anatomic representations could be created in future studies through the use of computed tomography scanners that can slice objects into thinner sections, but this may increase the working time and development cost of the final finite

**Figure 12.** Cortical thickness of the posterior maxilla is neglected; only cancellous bone properties are modeled

Application of Finite Element Analysis in Implant Dentistry 31

**Figure 15.** Part of the mandible modeled with superstructure, implant, and surrounding bone

**Figure 16.** The edentulous mandible obtained from a cadaver was scanned using a dental volumetric

tomography device

**Figure 13.** Mandible is modeled and region of interest is selected

**Figure 14.** Region of interest is extracted by Boolean process

Application of Finite Element Analysis in Implant Dentistry 31

30 Finite Element Analysis – New Trends and Developments

**Figure 13.** Mandible is modeled and region of interest is selected

**Figure 14.** Region of interest is extracted by Boolean process

**Figure 15.** Part of the mandible modeled with superstructure, implant, and surrounding bone

**Figure 16.** The edentulous mandible obtained from a cadaver was scanned using a dental volumetric tomography device

Application of Finite Element Analysis in Implant Dentistry 33

**3. Modelization of non-living structure (materials)**

the Poisson effect [9,13,32,33].

with the goal of the modeling exercise.

Non-living mechanical structures such as implants, abutments, and restorations can be simulated in detail and can substantially influence the calculated stress and strain values, similar to living structures. These materials can be digitally modeled in FEA studies using previously determined isotropic, transversely isotropic, orthotropic, and/or anisotropic properties [31]. In an isotropic material, the relevant material properties are the same in all directions, resulting in only 2 independent material constants, such as Young's modulus and Poisson's ratio [9,13,31]. Young's modulus (MPa), also known as the tensile modulus, is a quantity used to characterize materials and is a measure of the stiffness of an elastic material. Young's modulus is also called the elastic modulus or modulus of elasticity, because Young's modulus is the most commonly used elastic modulus [9,13,32,33]. When a sample object is stretched, Poisson's ratio is the ratio of the contraction or transverse strain (perpendicular to the applied load), to the extension or axial strain (in the direction of the applied load). When a material is compressed in 1 direction, it tends to expand in the other 2 directions perpendicular to the direction of compression. This phenomenon is called the Poisson effect. Poisson's ratio is a measure of

An anisotropic material has material properties that vary by direction [31]. Isotropic material properties are used in most FEA studies related to implant dentistry [18,25,34]. For instance, the material properties of living bone are anisotropic, and inhomogeneous. These properties of real bone greatly affect stress and strain patterns. In addition, bone density may differ among various regions of the same jaw and areas of differing densities may only be separated by milimeters. For simplification and to overcome computing difficulties, in most cases, the materials are modeled as homogenous, isotropic, and linearly elastic [35-39]. However, some studies have modeled the bone block using anisotropic properties (i.e., the material properties differ with respect to direction) [26]. The material properties of both living and non-living structures are chosen in accordance

In some studies, implants are modeled using a screw design but without threads (Figure 19). This may simplify the computing process, but does not reflect the reality of implant geometry. If one or more study parameters are related to implant dimensions, there is little doubt that inclusion of implant threads in the model is quite important to the quality of the research. Most clinicians are interested in the magnitude and distribution of stress that may induce microdamage to the bone and result in crestal bone resorption; therefore, macro and micro threads are crucial in the modeling stage of an implant study. The implant thread design influences the induced bone stress around the implant, which contributes to crestal bone loss, and can jeopardize the maintenance of osseointegration [40-43]. In recent FEA studies, implant threads are modeled in detail (Figure 20,21). There are 2 ways to model implant and abutment materials. One way is to obtain all of the geometric information (e.g., length, diameter, macro-micro thread configuration) in

**Figure 17.** Volumetric data were reconstructed in 0.2 mm thick sections

**Figure 18.** Bone density values can be measured according to gray scale using advanced 3-D radiographic techniques

## **3. Modelization of non-living structure (materials)**

32 Finite Element Analysis – New Trends and Developments

**Figure 17.** Volumetric data were reconstructed in 0.2 mm thick sections

**Figure 18.** Bone density values can be measured according to gray scale using advanced 3-D

radiographic techniques

Non-living mechanical structures such as implants, abutments, and restorations can be simulated in detail and can substantially influence the calculated stress and strain values, similar to living structures. These materials can be digitally modeled in FEA studies using previously determined isotropic, transversely isotropic, orthotropic, and/or anisotropic properties [31]. In an isotropic material, the relevant material properties are the same in all directions, resulting in only 2 independent material constants, such as Young's modulus and Poisson's ratio [9,13,31]. Young's modulus (MPa), also known as the tensile modulus, is a quantity used to characterize materials and is a measure of the stiffness of an elastic material. Young's modulus is also called the elastic modulus or modulus of elasticity, because Young's modulus is the most commonly used elastic modulus [9,13,32,33]. When a sample object is stretched, Poisson's ratio is the ratio of the contraction or transverse strain (perpendicular to the applied load), to the extension or axial strain (in the direction of the applied load). When a material is compressed in 1 direction, it tends to expand in the other 2 directions perpendicular to the direction of compression. This phenomenon is called the Poisson effect. Poisson's ratio is a measure of the Poisson effect [9,13,32,33].

An anisotropic material has material properties that vary by direction [31]. Isotropic material properties are used in most FEA studies related to implant dentistry [18,25,34]. For instance, the material properties of living bone are anisotropic, and inhomogeneous. These properties of real bone greatly affect stress and strain patterns. In addition, bone density may differ among various regions of the same jaw and areas of differing densities may only be separated by milimeters. For simplification and to overcome computing difficulties, in most cases, the materials are modeled as homogenous, isotropic, and linearly elastic [35-39]. However, some studies have modeled the bone block using anisotropic properties (i.e., the material properties differ with respect to direction) [26]. The material properties of both living and non-living structures are chosen in accordance with the goal of the modeling exercise.

In some studies, implants are modeled using a screw design but without threads (Figure 19). This may simplify the computing process, but does not reflect the reality of implant geometry. If one or more study parameters are related to implant dimensions, there is little doubt that inclusion of implant threads in the model is quite important to the quality of the research. Most clinicians are interested in the magnitude and distribution of stress that may induce microdamage to the bone and result in crestal bone resorption; therefore, macro and micro threads are crucial in the modeling stage of an implant study. The implant thread design influences the induced bone stress around the implant, which contributes to crestal bone loss, and can jeopardize the maintenance of osseointegration [40-43]. In recent FEA studies, implant threads are modeled in detail (Figure 20,21). There are 2 ways to model implant and abutment materials. One way is to obtain all of the geometric information (e.g., length, diameter, macro-micro thread configuration) in

milimeters from the manufacturer. The second option is to scan implants and abutment materials and digitally reconstruct them. Efficient and realistic models can be obtained by using either option. In general, for the digital preparation of crown models, an anatomy atlas of the tooth can be used as a reference to calculate the form and both mesiodistal and buccolingual dimensions [44]. The prosthetic superstructure can be simulated according to various treatment protocols. Superstructure can also be modeled as a geometric figure, such as a simple rectangular shape, but this may interfere with the realism of the model (Figure 22).

Application of Finite Element Analysis in Implant Dentistry 35

bonded [9,18,25,31,34]. Implant, abutment, abutment screw, framework, and porcelain structures are considered to be a single unit (Figure 24). In contrast, there are some studies that use a contact condition between the abutment and implant set as a frictional coefficient [26]. In these studies, the corresponding material properties are used and modeled separately. Most studies also model the implant as rigidly anchored in the bone model along its entire interface and with total osseointegration. It is impossible to visualize these interface conditions in real life, but simplifications in interface conditions will inevitably result in considerable inaccuracy. The most common drawback of FEA from the clinical perspective is that many features that directly affect model accuracy, such as loading conditions, material properties, and interface conditions are neglected or ignored. In most cases, researchers neglect one or more features in their studies. Moreover, bias may result from interpretation of data obtained from an FEA study to that obtained from another. Within a single study, these simplifications are consistent for all the simulated models; therefore, the accuracy of the analysis from the stress distribution viewpoint is not affected, as long as the models are compared with each other in the same

study [9,18,25,31,34].

**Figure 20.** Implants are modeled with micro and macro threads

**Figure 19.** Implants are modeled without threads

In a previous study, the crown model was simulated as porcelain fused to metal restoration. To calculate the mesiodistal width of the second premolar and first molar, Wheeler's Atlas of Anatomical Natural Tooth Morphology was used (Figure 23) [44]. The atlas was used again for digital preparation of the crown models. Properties of chromium-cobalt alloy were used for the framework and feldspatic porcelain as used to simulate the second premolar and the first molar of a mandibular model. The metal thickness of the framework was 0.8 mm and the porcelain thickness was at least 2.0 mm. The thickness of porcelain changes with the creation of pits and trabeculae of the tooth surface. In most FEA studies, not only the cement thickness but also the interface between the materials is assumed to be 100% bonded [9,18,25,31,34]. Implant, abutment, abutment screw, framework, and porcelain structures are considered to be a single unit (Figure 24). In contrast, there are some studies that use a contact condition between the abutment and implant set as a frictional coefficient [26]. In these studies, the corresponding material properties are used and modeled separately. Most studies also model the implant as rigidly anchored in the bone model along its entire interface and with total osseointegration. It is impossible to visualize these interface conditions in real life, but simplifications in interface conditions will inevitably result in considerable inaccuracy. The most common drawback of FEA from the clinical perspective is that many features that directly affect model accuracy, such as loading conditions, material properties, and interface conditions are neglected or ignored. In most cases, researchers neglect one or more features in their studies. Moreover, bias may result from interpretation of data obtained from an FEA study to that obtained from another. Within a single study, these simplifications are consistent for all the simulated models; therefore, the accuracy of the analysis from the stress distribution viewpoint is not affected, as long as the models are compared with each other in the same study [9,18,25,31,34].

34 Finite Element Analysis – New Trends and Developments

**Figure 19.** Implants are modeled without threads

(Figure 22).

milimeters from the manufacturer. The second option is to scan implants and abutment materials and digitally reconstruct them. Efficient and realistic models can be obtained by using either option. In general, for the digital preparation of crown models, an anatomy atlas of the tooth can be used as a reference to calculate the form and both mesiodistal and buccolingual dimensions [44]. The prosthetic superstructure can be simulated according to various treatment protocols. Superstructure can also be modeled as a geometric figure, such as a simple rectangular shape, but this may interfere with the realism of the model

In a previous study, the crown model was simulated as porcelain fused to metal restoration. To calculate the mesiodistal width of the second premolar and first molar, Wheeler's Atlas of Anatomical Natural Tooth Morphology was used (Figure 23) [44]. The atlas was used again for digital preparation of the crown models. Properties of chromium-cobalt alloy were used for the framework and feldspatic porcelain as used to simulate the second premolar and the first molar of a mandibular model. The metal thickness of the framework was 0.8 mm and the porcelain thickness was at least 2.0 mm. The thickness of porcelain changes with the creation of pits and trabeculae of the tooth surface. In most FEA studies, not only the cement thickness but also the interface between the materials is assumed to be 100%

**Figure 20.** Implants are modeled with micro and macro threads

Application of Finite Element Analysis in Implant Dentistry 37

**Figure 23.** Digital preparation of crown models

**Figure 24.** Implant, abutment, abutment screw, framework, and porcelain structure are modeled as 1 unit

**Figure 21.** Implants are modeled with threads and abutments

**Figure 22.** Superstructure modeled into a rectangular shape

Application of Finite Element Analysis in Implant Dentistry 37

**Figure 23.** Digital preparation of crown models

36 Finite Element Analysis – New Trends and Developments

**Figure 21.** Implants are modeled with threads and abutments

**Figure 22.** Superstructure modeled into a rectangular shape

**Figure 24.** Implant, abutment, abutment screw, framework, and porcelain structure are modeled as 1 unit

Almost all of the elastic properties of selected living and non-living materials are available in the literature [9,25,31,34]. Young's modulus and Poisson's ratio are used in models to simulate reality as closely as possible. For example, alveolar bone (both cortical and cancellous portions), implant, abutment, metal framework, and porcelain can be included in the model properties.

Application of Finite Element Analysis in Implant Dentistry 39

between marginal bone loss and occlusal forces; including the engineering principles, biomechanical relationships to living tissues, and the mechanical properties of bone surrounding implants [50]. In recent years, a greater amount of materials used for oral implantology are fabricated from titanium and titanium alloy. The Young's modulus of titanium is 5-10 times greater than that of cortical ridge bone surrounding implants [51]. The fundamental engineering principle, composite beam analysis, expresses the concept that when 2 materials of different Young's modulus are placed in direct contact with no intervening material and 1 material loaded, a stress contour will be described at the point where the 2 materials come into contact [52]. For oral implantology, these stress contours are of greater magnitude at the crestal bone. Therefore, the loading condition is another important part of FEA studies. Each component modelization stage contributes to the final analysis after loading. In other words, from the beginning to the end, all procedures and FEA stages add to the ability to extrapolate the results of bite forces surrounding the peri-

Bite forces may be defined as compressive, tensile, or shear forces. Compressive forces attempt to push materials toward each other. Tensile forces pull objects apart. Shear forces on implants cause sliding. The most detrimental forces that can increase the stress around the implant-bone interface and prosthetic assembly are tensile and shear forces. These forces tend to harm material integrity and cause stress build-up. In general, the implant-prosthetic unit can adapt to compressive forces [51]. In actual mastication, the repeated pattern of cyclic forces transmits loading via the restoration and dental implants to peri-impant bone. This generates different amounts of stress around the ridge and also in the prosthetic structure. However, randomized cyclic forces are not easily simulated. Therefore, most FEA studies use static axial and/or non-axial forces. Non-axial loads generate distinctive stress in the ridge especially in the cortical bone. The main remodeling differences between axial and non-axial loading are affected mostly by the horizontal component of the resultant stresses [53]. Therefore, for realistic simulation, combined oblique loads (axial and non-axial) are generally used. One study, comparing dynamic with static loading, revealed that dynamic loading resulted in greater stress levels than static loading [54]. Dynamic loading has consistently been found to have more osteogenic potential than static loading [55]. Sagat et al. investigated the influence of static force on peri-implant stress. In varied models, 100 N static forces were applied vertically and separately to the anterior and posterior parts of a bridge [18]. In another study, static forces of 100 N were applied at 30 degrees obliquely and separately to the lingual inclination of the buccal cusps of a crown (Figures 25,26) [25]. In another study, loading was simulated by applying an oblique load (vertical load of 100 N and horizontal load of 20 N) from buccal to palatal region at 4 different locations. An equivalent load of 200 N was applied in the vertical direction and 40 N in the buccal-palatal direction. The application point of the force was on the central and distal fossae of the crown [48]. Eskitascioglu et al. used an average occlusal force of 300 N applied to a missing second premolar implant-supported crown. Three-point vertical loads were applied to the tip of the buccal cusp (150 N) and distal fossa (150 N); the tip of the buccal cusp (100 N), distal fossa

implant region and prosthetic structures.

(100 N), and mesial fossa (100 N) [56].

## **4. Boundary conditions**

A boundary condition is the application of force and constraint. The different ways to apply force and moment include a concentrated load (at a point or single node), force on a line or edge, a distributed load (force varying as an equation), bending moments, and torque [45]. In structural analysis, boundary conditions are applied to those regions of the model where the displacements and/or rotations are known. Such regions may be constrained to remain fixed (have zero displacement and/or rotation) during the simulation or may have specified, non-zero displacements and/or rotations. The directions in which motion is possible are called degrees of freedom (DOF). Zero-displacement constraints must be placed on some boundaries of the model to ensure an equilibrium solution. The constraints should be placed on nodes that are located far from the region of interest to prevent overlap of the stress or strain fields associated with reaction forces with the bone-implant interface. In maxillary FEA models, the nodes along the external lines of the cortical bone of the oral and nasopharyngeal cavities were fixed in all directions [46].

In most FEA studies that include models of the mandible, the boundary conditions are set as a fixed boundary [9]. Zhou et al. developed a more realistic 3-D mandibular FEA model from transversely scanned computed tomography imaging data. The functions of the muscles of mastication and the ligamentous and functional movements of the temporomandibular joints (TMJs) were simulated by means of cable elements and compressive gap elements, respectively. Using this mandibular FEA model, it was concluded that cable and gap elements could be used to set boundary conditions, improving the model mimicry and accuracy [47]. Chang et al. used a technique in which only half of the model was meshed, thus symmetry boundary conditions were prescribed at the nodes on the symmetry plane. Models were constrained in all directions at the nodes on the mesial and symmetrical distal bone surfaces [48]. Expanding the domain of the model can reduce the influence of inaccurate modeling of the boundary conditions. This, however, will be at the expense of computing and modeling time. Teixera et al. concluded that in a 3-D mandibular model, modeling the mandible at distances greater than 4.2 mm mesial or distal from the implant did not result in any significant increase in FEA accuracy [49]. Use of infinite elements is another potential method for modeling boundary conditions [9].

## **5. Loading conditions**

Marginal bone loss in the peri-implant region may be the result of excessive occlusal force [50]. Extensive investigations are needed to establish and understand the correlation between marginal bone loss and occlusal forces; including the engineering principles, biomechanical relationships to living tissues, and the mechanical properties of bone surrounding implants [50]. In recent years, a greater amount of materials used for oral implantology are fabricated from titanium and titanium alloy. The Young's modulus of titanium is 5-10 times greater than that of cortical ridge bone surrounding implants [51]. The fundamental engineering principle, composite beam analysis, expresses the concept that when 2 materials of different Young's modulus are placed in direct contact with no intervening material and 1 material loaded, a stress contour will be described at the point where the 2 materials come into contact [52]. For oral implantology, these stress contours are of greater magnitude at the crestal bone. Therefore, the loading condition is another important part of FEA studies. Each component modelization stage contributes to the final analysis after loading. In other words, from the beginning to the end, all procedures and FEA stages add to the ability to extrapolate the results of bite forces surrounding the periimplant region and prosthetic structures.

38 Finite Element Analysis – New Trends and Developments

nasopharyngeal cavities were fixed in all directions [46].

the model properties.

**4. Boundary conditions**

**5. Loading conditions**

Almost all of the elastic properties of selected living and non-living materials are available in the literature [9,25,31,34]. Young's modulus and Poisson's ratio are used in models to simulate reality as closely as possible. For example, alveolar bone (both cortical and cancellous portions), implant, abutment, metal framework, and porcelain can be included in