@article {2018, title = {Peristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots}, journal = {Frontiers in Robotics and AI}, volume = {5}, year = {2018}, month = {09/2018}, abstract = {

Peristalsis, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a {\textquotedblleft}phase coordination{\textquotedblright} principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.

}, keywords = {Biomimetic robots, Crawling motility, Lumbricus terrestris, Metameric robots, Optimization, Peristalsis, Self-propulsion, Soft robotics}, issn = {2296-9144}, doi = {10.3389/frobt.2018.00099}, url = {https://www.frontiersin.org/article/10.3389/frobt.2018.00099}, author = {Daniele Agostinelli and Fran{\c c}ois Alouges and Antonio DeSimone} } @article {20.500.11767_81735, title = {Predicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions}, journal = {SOFT ROBOTICS}, volume = {5}, year = {2018}, pages = {410{\textendash}424}, doi = {10.1089/soro.2017.0099}, url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6094362/}, author = {Nicola Giuliani and Luca Heltai and Antonio DeSimone} } @article { refId0, title = {On the genesis of directional friction through bristle-like mediating elements}, journal = {ESAIM: COCV}, volume = {23}, number = {3}, year = {2017}, pages = {1023-1046}, abstract = {

We propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl{\textendash}Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry.

}, doi = {10.1051/cocv/2017030}, url = {https://doi.org/10.1051/cocv/2017030}, author = {Paolo Gidoni and Antonio DeSimone} } @article {20.500.11767_11953, title = {A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling}, journal = {COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, volume = {316}, year = {2017}, pages = {522{\textendash}546}, doi = {10.1016/j.cma.2016.08.008}, url = {http://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H}, author = {Luca Heltai and Kiendl, J. and Antonio DeSimone and Alessandro Reali} } @article {Gidoni2017, title = {Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler}, journal = {Meccanica}, volume = {52}, number = {3}, year = {2017}, month = {Feb}, pages = {587{\textendash}601}, abstract = {

We formulate and solve the locomotion problem for a bio-inspired crawler consisting of two active elastic segments (i.e., capable of changing their rest lengths), resting on three supports providing directional frictional interactions. The problem consists in finding the motion produced by a given, slow actuation history. By focusing on the tensions in the elastic segments, we show that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity. In particular, sliding of the supports and hence motion cannot occur when the tensions are in the interior of certain convex regions (stasis domains), while support sliding (and hence motion) can only take place when the tensions are on the boundary of such regions (slip surfaces). We solve the locomotion problem explicitly in a few interesting examples. In particular, we show that, for a suitable range of the friction parameters, specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.

}, issn = {1572-9648}, doi = {10.1007/s11012-016-0408-0}, url = {https://doi.org/10.1007/s11012-016-0408-0}, author = {Paolo Gidoni and Antonio DeSimone} } @article {MolaHeltaiDeSimone2017, title = {Wet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations}, journal = {Journal of Ship Research}, volume = {61}, number = {1}, year = {2017}, pages = {1{\textendash}14}, abstract = {

We present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov-Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

}, doi = {https://doi.org/10.5957/JOSR.61.1.160016}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @article {Cicconofri2016, title = {Motion planning and motility maps for flagellar microswimmers}, journal = {The European Physical Journal E}, volume = {39}, number = {7}, year = {2016}, month = {Jul}, pages = {72}, abstract = {

We study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

}, issn = {1292-895X}, doi = {10.1140/epje/i2016-16072-y}, url = {https://doi.org/10.1140/epje/i2016-16072-y}, author = {Giancarlo Cicconofri and Antonio DeSimone} } @conference {mola2016ship, title = {Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model}, booktitle = {The 26th International Ocean and Polar Engineering Conference}, volume = {3}, year = {2016}, pages = {511{\textendash}518}, publisher = {International Society of Offshore and Polar Engineers}, organization = {International Society of Offshore and Polar Engineers}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone and Massimiliano Berti} } @article {DESIMONE2015254, title = {Liquid crystal elastomer strips as soft crawlers}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {84}, year = {2015}, pages = {254 - 272}, abstract = {

In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, {\textquoteleft}breathing-like{\textquoteright} deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

}, keywords = {Crawling motility, Directional surfaces, Frictional interactions, Liquid crystal elastomers, Soft biomimetic robots}, issn = {0022-5096}, doi = {https://doi.org/10.1016/j.jmps.2015.07.017}, url = {http://www.sciencedirect.com/science/article/pii/S0022509615300430}, author = {Antonio DeSimone and Paolo Gidoni and Giovanni Noselli} } @article {CICCONOFRI2015233, title = {Motility of a model bristle-bot: A theoretical analysis}, journal = {International Journal of Non-Linear Mechanics}, volume = {76}, year = {2015}, pages = {233 - 239}, abstract = {

Bristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

}, keywords = {Bristle-robots, Crawling motility, Frictional interactions}, issn = {0020-7462}, doi = {https://doi.org/10.1016/j.ijnonlinmec.2014.12.010}, url = {http://www.sciencedirect.com/science/article/pii/S0020746215000025}, author = {Giancarlo Cicconofri and Antonio DeSimone} } @article {doi:10.1098/rspa.2015.0054, title = {A study of snake-like locomotion through the analysis of a flexible robot model}, journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {471}, number = {2184}, year = {2015}, pages = {20150054}, abstract = {


}, doi = {10.1098/rspa.2015.0054}, url = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054}, author = {Giancarlo Cicconofri and Antonio DeSimone} } @article {2015, title = {Three-sphere low-Reynolds-number swimmer with a passive elastic arm}, number = {European Physical Journal E; Volume 38; Issue 5; Article number 42}, year = {2015}, publisher = {Springer}, abstract = {One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer{\textquoteright}s geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers.}, doi = {10.1140/epje/i2015-15042-3}, url = {http://urania.sissa.it/xmlui/handle/1963/34530}, author = {Alessandro Montino and Antonio DeSimone} } @article {GIDONI201465, title = {Crawling on directional surfaces}, journal = {International Journal of Non-Linear Mechanics}, volume = {61}, year = {2014}, pages = {65 - 73}, abstract = {

In this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding {\textquoteleft}along the grain{\textquoteright}, and high resistance when sliding {\textquoteleft}against the grain{\textquoteright}. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

}, keywords = {Bio-mimetic micro-robots, Cell migration, Crawling motility, Directional surfaces, Self-propulsion}, issn = {0020-7462}, doi = {https://doi.org/10.1016/j.ijnonlinmec.2014.01.012}, url = {http://www.sciencedirect.com/science/article/pii/S0020746214000213}, author = {Paolo Gidoni and Giovanni Noselli and Antonio DeSimone} } @article {2014, title = {Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost}, number = {Mechanics Research Communications}, year = {2014}, publisher = {Elsevier}, abstract = {We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility.}, keywords = {Cell migration}, doi = {10.1016/j.mechrescom.2013.10.023}, url = {http://urania.sissa.it/xmlui/handle/1963/34449}, author = {Giovanni Noselli and Amabile Tatone and Antonio DeSimone} } @article {2014, title = {An effective model for nematic liquid crystal composites with ferromagnetic inclusions}, number = {SIAM Journal on Applied Mathematics;volume 74; issue 2; pages 237-262;}, year = {2014}, publisher = {Society for Industrial and Applied Mathematics Publications}, abstract = {Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix- ferronematics-as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature.}, doi = {10.1137/130910348}, url = {http://urania.sissa.it/xmlui/handle/1963/34940}, author = {Maria Carme Calderer and Antonio DeSimone and Dmitry Golovaty and Alexander Panchenko} } @proceedings {2014, title = {A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures}, year = {2014}, publisher = {SISSA}, abstract = {We present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed.}, keywords = {ship hydrodynamics}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @article {2012, title = {Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D}, number = {Computer Methods in Applied Mechanics and Engineering}, year = {2014}, publisher = {Elsevier}, abstract = {Isogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM.}, keywords = {Isogeometric Analysis}, doi = {10.1016/j.cma.2013.09.017}, url = {http://hdl.handle.net/1963/6326}, author = {Luca Heltai and Marino Arroyo and Antonio DeSimone} } @conference {mola2014ship, title = {Potential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures}, booktitle = {The 24th International Ocean and Polar Engineering Conference}, volume = {4}, year = {2014}, pages = {815{\textendash}822}, publisher = {International Society of Offshore and Polar Engineers}, organization = {International Society of Offshore and Polar Engineers}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone and Massimiliano Berti} } @article {2014, title = {A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model}, journal = {Proceedings of the Royal Society A 470, 20140333 (2014)}, year = {2014}, publisher = {Royal Society Publishing}, abstract = {We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. {\textquoteleft}breathing-like{\textquoteright} deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations.}, doi = {10.1098/rspa.2014.0333}, author = {Giovanni Noselli and Antonio DeSimone} } @article {2014, title = {Shape control of active surfaces inspired by the movement of euglenids}, number = {Journal of the Mechanics and Physics of Solids;volume 62; issue 1; pages 99-112;}, year = {2014}, publisher = {Elsevier}, abstract = {We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines.}, doi = {10.1016/j.jmps.2013.09.017}, url = {http://urania.sissa.it/xmlui/handle/1963/35118}, author = {Marino Arroyo and Antonio DeSimone} } @article {2014, title = {Spontaneous division and motility in active nematic droplets}, number = {Physical review letters;volume 112; issue 14; article number 147802;}, year = {2014}, publisher = {American Physical Society}, abstract = {We investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamic flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number.}, doi = {10.1103/PhysRevLett.112.147802}, url = {http://urania.sissa.it/xmlui/handle/1963/34902}, author = {Luca Giomi and Antonio DeSimone} } @article {2013, title = {Attainment results for nematic elastomers}, year = {2013}, institution = {SISSA}, abstract = {We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids.}, url = {http://hdl.handle.net/1963/7174}, author = {Virginia Agostiniani and Gianni Dal Maso and Antonio DeSimone} } @article {2013, title = {Crawlers in viscous environments: linear vs nonlinear rheology}, journal = {International Journal of Non-Linear Mechanics 56, 142-147 (2013)}, year = {2013}, publisher = {Elsevier}, abstract = {We study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling.}, doi = {10.1016/j.ijnonlinmec.2013.02.007}, author = {Antonio DeSimone and Federica Guarnieri and Giovanni Noselli and Amabile Tatone} } @article {cacace_chambolle_desimone_fedeli_2013, title = {Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis}, volume = {47}, number = {3}, year = {2013}, pages = {837{\textendash}858}, publisher = {EDP Sciences}, doi = {10.1051/m2an/2012048}, author = {Cacace, S. and Chambolle, A. and Antonio DeSimone and Livio Fedeli} } @article {2013, title = {One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls}, number = {arXiv:1302.0901;}, year = {2013}, publisher = {SISSA}, abstract = {

In this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.

}, url = {http://hdl.handle.net/1963/6467}, author = {Gianni Dal Maso and Antonio DeSimone and Marco Morandotti} } @article {2012, title = {A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions}, journal = {Engineering Analysis with Boundary Elements, 37(1):128 {\textendash} 143, 2013.}, number = {SISSA;06/2012/M}, year = {2013}, publisher = {SISSA}, abstract = {

We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

}, keywords = {Unsteady ship-wave interaction}, url = {http://hdl.handle.net/1963/5669}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @inbook {9897, title = {Computing optimal strokes for low reynolds number swimmers}, booktitle = {Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors,}, number = {The IMA volumes in mathematics and its applications;155}, year = {2012}, publisher = {Springer}, organization = {Springer}, abstract = {

We discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

}, keywords = {Numerical analysis.}, isbn = {9781461439967}, doi = {10.1007/978-1-4614-3997-4_13}, url = {http://hdl.handle.net/1963/6445}, author = {Antonio DeSimone and Luca Heltai and Fran{\c c}ois Alouges and Lefebvre-Lepot Aline} } @article {2012, title = {Crawling motility through the analysis of model locomotors: two case studies}, journal = {The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85}, number = {PMID:22972227;}, year = {2012}, publisher = {Springer}, abstract = {We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.}, doi = {10.1140/epje/i2012-12085-x}, url = {http://hdl.handle.net/1963/7017}, author = {Antonio DeSimone and Amabile Tatone} } @article {2012, title = {Hybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment}, journal = {Nanoscale. 2012 Mar; 4(5):1734-41}, number = {PMID:22301788;}, year = {2012}, publisher = {Royal Society of Chemistry}, abstract = {Nanografted monolayers (NAMs) of DNA show novel physico-chemical properties that make them ideally suited for advanced biosensing applications. In comparison with alternative solid-phase techniques for diagnostic DNA detection, NAMs have the advantage of combining a small size with a high homogeneity of the DNA surface coverage. These two properties favour the extreme miniaturization and ultrasensitivity in high-throughput biosensing devices. The systematic use of NAMs for quantitative DNA (and protein) detection has so far suffered from the lack of a control on key fabrication parameters, such as the ss- or ds-DNA surface coverage. Here we report on a combined experimental-computational study that allows us to estimate the surface density of the grafted DNA by analyzing the sample mechanical response, that is the DNA patch height vs. applied tip load curves. It is shown that the same analysis scheme can be used to detect the occurrence of hybridization with complementary strands in solution and estimate its efficiency. Thanks to these quantitative relationships it is possible to use a single AFM-based setup to: (i) fabricate a DNA NAM, (ii) control the DNA surface coverage, and (iii) characterize its level of hybridization helping the design of NAMs with pre-determined fabrication parameters.}, doi = {10.1039/c2nr11662f}, author = {Alessandro Bosco and Fouzia Bano and Pietro Parisse and Loredana Casalis and Antonio DeSimone and Cristian Micheletti} } @article {2012, title = {Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire}, volume = {29}, number = {SISSA;30/2011/M}, year = {2012}, pages = {715-735}, publisher = {Gauthier-Villars;Elsevier}, abstract = {

The energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

}, keywords = {Nonlinear elasticity}, doi = {10.1016/j.anihpc.2012.04.001}, url = {http://hdl.handle.net/1963/4267}, author = {Virginia Agostiniani and Gianni Dal Maso and Antonio DeSimone} } @proceedings {2012, title = {Mathematical and numerical modeling of liquid crystal elastomer phase transition and deformation}, year = {2012}, publisher = {Cambridge University Press}, abstract = {Liquid crystal (in particular, nematic) elastomers consist of cross-linked flexible polymer chains with embedded stiff rod molecules that allow them to behave as a rubber and a liquid crystal. Nematic elastomers are characterized by a phase transition from isotropic to nematic past a temperature threshold. They behave as rubber at high temperature and show nematic behavior below the temperature threshold. Such transition is reversible. While in the nematic phase, the rod molecules are aligned along the direction of the "nematic director". This molecular rearrangement induces a stretch in the polymer chains and hence macroscopic spontaneous deformations. The coupling between nematic order parameter and deformation gives rise to interesting phenomena with a potential for new interesting applications. In the biological field, the ability to considerably change their length makes them very promising as artificial muscles actuators. Their tunable optical properties make them suitable, for example, as lenses for new imaging systems. We present a mathematical model able to describe the behavior of nematic elastomers and numerical simulations reproducing such peculiar behavior. We use a geometrically linear version of the Warner and Terentjev model [1] and consider cooling experiments and stretching experiments in the direction perpendicular to the one of the director at cross-linking.}, keywords = {Artificial muscle}, isbn = {9781605113807}, doi = {10.1557/opl.2012.249}, url = {http://hdl.handle.net/1963/7020}, author = {Mariarita De Luca and Antonio DeSimone} } @article {2012, title = {Ogden-type energies for nematic elastomers}, journal = {International Journal of Non-Linear mechanics }, volume = {47}, year = {2012}, pages = {402-412}, publisher = {Elsevier}, abstract = {

Ogden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).

}, keywords = {Nonlinear elasticity}, doi = {10.1016/j.ijnonlinmec.2011.10.001}, author = {Virginia Agostiniani and Antonio DeSimone} } @article {2012, title = {Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution}, journal = {Calculus of variations and partial differential equations 44 (2012) 495-541}, number = {SISSA;46/2010/M}, year = {2012}, publisher = {Springer}, abstract = {

Cam-Clay plasticity is a well established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s , has been proposed in [8] to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t . We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.

}, doi = {10.1007/s00526-011-0443-6}, url = {http://hdl.handle.net/1963/3900}, author = {Gianni Dal Maso and Antonio DeSimone and Francesco Solombrino} } @article {2012, title = {Reverse engineering the euglenoid movement}, journal = {Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879}, year = {2012}, abstract = {Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20\% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340\%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.}, keywords = {microswimmers}, doi = {10.1073/pnas.1213977109}, url = {http://hdl.handle.net/1963/6444}, author = {Marino Arroyo and Luca Heltai and Daniel Mill{\'a}n and Antonio DeSimone} } @conference {Mola2012, title = {A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves}, booktitle = {17th Int. Conf. Ships Shipp. Res.}, year = {2012}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @article {2011, title = {Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions}, journal = {PNAS 108 (2011) 13978}, year = {2011}, publisher = {National Academy of Sciences}, doi = {10.1073/pnas.1100549108}, url = {http://hdl.handle.net/1963/4358}, author = {Luca Cardamone and Alessandro Laio and Rajesh Shahapure and Antonio DeSimone} } @article {2011, title = {An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers}, journal = {SIAM J. Math. Anal.}, volume = { 43}, number = {SISSA;44/2010/M}, year = {2011}, pages = {1345-1368}, publisher = {Society for Industrial and Applied Mathematics}, abstract = {


}, doi = {10.1137/10080083X}, url = {http://hdl.handle.net/1963/3894}, author = {Gianni Dal Maso and Antonio DeSimone and Marco Morandotti} } @article {2011, title = {Gamma-convergence of energies for nematic elastomers in the small strain limit}, journal = {Continuum. Mech. Therm.}, volume = { 23}, number = {SISSA;07/2011/M}, year = {2011}, publisher = {Springer}, chapter = {257}, abstract = {

We study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

}, keywords = {Liquid crystals}, doi = {10.1007/s00161-011-0180-2}, url = {http://hdl.handle.net/1963/4141}, author = {Virginia Agostiniani and Antonio DeSimone} } @article {Fedeli2011, title = {Metastable equilibria of capillary drops on solid surfaces: a phase field approach}, journal = {Continuum Mechanics and Thermodynamics}, volume = {23}, number = {5}, year = {2011}, month = {Sep}, pages = {453{\textendash}471}, abstract = {

We discuss a phase field model for the numerical simulation of metastable equilibria of capillary drops resting on rough solid surfaces and for the description of contact angle hysteresis phenomena in wetting. The model is able to reproduce observed transitions of drops on micropillars from Cassie{\textendash}Baxter to Wenzel states. When supplemented with a dissipation potential which describes energy losses due to frictional forces resisting the motion of the contact line, the model can describe metastable states such as drops in equilibrium on vertical glass plates. The reliability of the model is assessed by a detailed comparison of its predictions with experimental data on the maximal size of water drops that can stick on vertical glass plates which have undergone different surface treatments.

}, issn = {1432-0959}, doi = {10.1007/s00161-011-0189-6}, url = {https://doi.org/10.1007/s00161-011-0189-6}, author = {Livio Fedeli and Turco, Alessandro and Antonio DeSimone} } @article {2011, title = {Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers}, journal = {Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387}, number = {SISSA;33/2009/M}, year = {2011}, publisher = {World Scientific}, abstract = {We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms.}, keywords = {Optimal swimming}, doi = {10.1142/S0218202511005088}, url = {http://hdl.handle.net/1963/3657}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai} } @article {2011, title = {Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications}, journal = {Journal of the Mechanics and Physics of Solids 59 (2011) 787-803}, number = {SISSA;62/2010/M}, year = {2011}, abstract = {We provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments.}, url = {http://hdl.handle.net/1963/4065}, author = {Pierluigi Cesana and Antonio DeSimone} } @article {2011, title = {Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling}, journal = {Calculus of Variations and Partial Differential Equations 40 (2011) 125-181}, number = {SISSA;36/2009/M}, year = {2011}, publisher = {Springer}, abstract = {

Cam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.

}, keywords = {Cam-Clay plasticity}, doi = {10.1007/s00526-010-0336-0}, url = {http://hdl.handle.net/1963/3670}, author = {Gianni Dal Maso and Antonio DeSimone and Francesco Solombrino} } @article {2011, title = {Quasistatic evolution of sessile drops and contact angle hysteresis}, journal = {Arch. Rational Mech. Anal. 202 (2011) 295-348}, year = {2011}, publisher = {Springer}, abstract = {We consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of quasistatic evolutions with prescribed initial configuration. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations.}, doi = {10.1007/s00205-011-0427-x}, url = {http://hdl.handle.net/1963/4912}, author = {Giovanni Alberti and Antonio DeSimone} } @article {2010, title = {Optimally swimming Stokesian Robots}, number = {SISSA;54/2010/M}, year = {2010}, abstract = {We study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.}, url = {http://hdl.handle.net/1963/3929}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai and Aline Lefebvre and Benoit Merlet} } @conference {10.1007/978-90-481-9195-6_4, title = {A Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena}, booktitle = {IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials}, year = {2010}, pages = {51{\textendash}63}, publisher = {Springer Netherlands}, organization = {Springer Netherlands}, address = {Dordrecht}, abstract = {

We discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

}, isbn = {978-90-481-9195-6}, author = {Antonio DeSimone and Livio Fedeli and Turco, Alessandro}, editor = {Hackl, Klaus} } @article {2010, title = {The role of membrane viscosity in the dynamics of fluid membranes}, number = {SISSA;55/2010/M}, year = {2010}, abstract = {Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3.}, url = {http://hdl.handle.net/1963/3930}, author = {Marino Arroyo and Antonio DeSimone and Luca Heltai} } @inbook {2009, title = {Biological Fluid Dynamics, Non-linear Partial Differential Equations}, booktitle = {Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554}, number = {SISSA;21/2008/M}, year = {2009}, url = {http://hdl.handle.net/1963/2630}, author = {Antonio DeSimone and Fran{\c c}ois Alouges and Aline Lefebvre} } @article {2009, title = {Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers}, journal = {Netw. Heterog. Media 4 (2009) 667-708}, year = {2009}, publisher = {American Institute of Mathematical Sciences}, abstract = {In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields.}, doi = {10.3934/nhm.2009.4.667}, url = {http://hdl.handle.net/1963/3788}, author = {Marco Cicalese and Antonio DeSimone and Caterina Ida Zeppieri} } @article {2009, title = {Quasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions}, journal = {Math. Models Methods Appl. Sci. 19 (2009) 1643-1711}, number = {SISSA;78/2008/M}, year = {2009}, abstract = {We study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behaviour and time discontinuities.\\nThe behavior of the solutions at the jump times is studied by a viscous approximation.}, doi = {10.1142/S0218202509003942}, url = {http://hdl.handle.net/1963/3395}, author = {Gianni Dal Maso and Antonio DeSimone} } @article {2009, title = {Relaxation dynamics of fluid membranes}, journal = {Phys. Rev. E 79 (2009) 031915}, year = {2009}, publisher = {American Physical Society}, abstract = {We study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest.}, doi = {10.1103/PhysRevE.79.031915}, url = {http://hdl.handle.net/1963/3618}, author = {Marino Arroyo and Antonio DeSimone} } @article {2009, title = {Strain-order coupling in nematic elastomers: equilibrium configurations}, journal = {Math. Models Methods Appl. Sci. 19 (2009) 601-630}, number = {SISSA;24/2008/M}, year = {2009}, abstract = {We consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations.}, url = {http://hdl.handle.net/1963/2700}, author = {Pierluigi Cesana and Antonio DeSimone} } @article {2009, title = {Stratos: a code for 3D free surface flows with floating constraints}, number = {SISSA;41/2009/M}, year = {2009}, abstract = {This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers......}, url = {http://hdl.handle.net/1963/3701}, author = {Antonio DeSimone and B. Bianchi and Luca Heltai} } @article {2009, title = {Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II}, number = {SISSA;42/2009/M}, year = {2009}, abstract = {The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations.}, url = {http://hdl.handle.net/1963/3700}, author = {Antonio DeSimone and Luca Heltai and Cataldo Manigrasso} } @article {2008, title = {Globally stable quasistatic evolution in plasticity with softening}, journal = {Netw. Heterog. Media 3 (2008) 567-614}, number = {SISSA;23/2007/M}, year = {2008}, abstract = {We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.}, url = {http://hdl.handle.net/1963/1965}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora and Massimiliano Morini} } @article {2008, title = {Optimal Strokes for Low Reynolds Number Swimmers: An Example}, journal = {J. Nonlinear Sci. 18 (2008) 277-302}, year = {2008}, publisher = {Springer}, abstract = {Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).}, doi = {10.1007/s00332-007-9013-7}, url = {http://hdl.handle.net/1963/4006}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Aline Lefebvre} } @article {2008, title = {Relaxation of some transversally isotropic energies and applications to smectic A elastomers}, journal = {Math. Models Methods Appl. Sci. 18 (2008) 1-20}, number = {SISSA;01/2007/M}, year = {2008}, doi = {10.1142/S0218202508002693}, url = {http://hdl.handle.net/1963/1912}, author = {James Adams and Sergio Conti and Antonio DeSimone and Georg Dolzmann} } @article {2008, title = {A vanishing viscosity approach to quasistatic evolution in plasticity with softening}, journal = {Arch. Ration. Mech. Anal. 189 (2008) 469-544}, number = {SISSA;38/2006/M}, year = {2008}, abstract = {We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples.}, doi = {10.1007/s00205-008-0117-5}, url = {http://hdl.handle.net/1963/1844}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora and Massimiliano Morini} } @article {2007, title = {Critical voltages and blocking stresses in nematic gels}, journal = {Eur. Phys. J. E 24 (2007) 303-310}, number = {SISSA;31/2007/M}, year = {2007}, abstract = {We use a recently proposed model to study the dynamics of director remodeling in nematic gels under combined electro-mechanical loading. Focusing on a model specimen, we describe the critical volt-ages that must be exceeded to achieve mesogen reorientation, and the blocking stresses that prevent alignment of the nematic mesogens with the electric field. The corresponding phase diagram shows that the dynamic thresholds defined above are different from those predicted on the sole basis of energetics. Multistep loading programs are used to explore the energy landscape of our model specimen, showing the existence of multiple local minima under the same voltage and applied stress. This leads us to conclude that hysteresis should be expected in the electro-mechanical response of nematic gels.}, doi = {10.1140/epje/i2007-10240-2}, url = {http://hdl.handle.net/1963/2553}, author = {Antonio DeSimone and Antonio Di Carlo and Luciano Teresi} } @article {2007, title = {A new model for contact angle hysteresis}, number = {SISSA;37/2006/M}, year = {2007}, abstract = {We present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released energy and dissipation, and it describes the stick-slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto-plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence.}, url = {http://hdl.handle.net/1963/1848}, author = {Antonio DeSimone and Natalie Gruenewald and Felix Otto} } @article {2007, title = {Quasistatic evolution problems for pressure-sensitive plastic materials}, journal = {Milan J. Math. 75 (2007) 117-134}, number = {SISSA;27/2007/M}, year = {2007}, abstract = {We study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity.}, doi = {10.1007/s00032-007-0071-y}, url = {http://hdl.handle.net/1963/1962}, author = {Gianni Dal Maso and Alexey Demyanov and Antonio DeSimone} } @article {2007, title = {Soft elasticity and microstructure in smectic C elastomers}, number = {SISSA;05/2006/M}, year = {2007}, abstract = {Smectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable.}, doi = {10.1007/s00161-006-0031-8}, url = {http://hdl.handle.net/1963/1811}, author = {Antonio DeSimone and James Adams and Sergio Conti} } @article {2007, title = {Time-dependent systems of generalized Young measures}, number = {SISSA;98/2005/M}, year = {2007}, abstract = {In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time.}, url = {http://hdl.handle.net/1963/1795}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora and Massimiliano Morini} } @article {2006, title = {2-d stability of the N{\'e}el wall}, journal = {Calc. Var. Partial Differential Equations 27 (2006) 233-253}, year = {2006}, abstract = {We are interested in thin-film samples in micromagnetism, where the magnetization m is a 2-d unit-length vector field. More precisely we are interested in transition layers which connect two opposite magnetizations, so called N{\'e}el walls.}, doi = {10.1007/s00526-006-0019-z}, url = {http://hdl.handle.net/1963/2194}, author = {Antonio DeSimone and Hans Knuepfer and Felix Otto} } @article {2006, title = {Quasistatic evolution problems for linearly elastic-perfectly plastic materials}, journal = {Arch. Ration. Mech. Anal. 180 (2006) 237-291}, number = {arXiv.org;math/0412212v1}, year = {2006}, abstract = {The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain.}, doi = {10.1007/s00205-005-0407-0}, url = {http://hdl.handle.net/1963/2129}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora} } @inbook {2006, title = {Recent analytical developments in micromagnetics}, booktitle = {The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381.}, number = {SISSA;76/2004/M}, year = {2006}, isbn = {978-0-12-480874-4}, url = {http://hdl.handle.net/1963/2230}, author = {Antonio DeSimone and Robert V. Kohn and Stefan M{\"u}ller and Felix Otto} } @article {2005, title = {Self-similar folding patterns and energy scaling in compressed elastic sheets}, journal = {Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549}, year = {2005}, publisher = {Elsevier}, abstract = {Thin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves.}, doi = {10.1016/j.cma.2004.07.044}, url = {http://hdl.handle.net/1963/3000}, author = {Sergio Conti and Antonio DeSimone and Stefan M{\"u}ller} } @article {2005, title = {Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains}, journal = {Int. J. Numer. Anal. Met. 29 (2005) 73-101}, number = {SISSA;74/2004/M}, year = {2005}, abstract = {Stress-dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics.\\nIn this paper, a method to construct thermodynamically consistent (isotropic, three-invariant) elasto-plastic models based on a given stress-dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws.}, doi = {10.1002/nag.405}, url = {http://hdl.handle.net/1963/2165}, author = {Antonio DeSimone and Claudio Tamagnini} } @article {2005, title = {Wetting of rough surfaces: a homogenization approach}, journal = {Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97}, number = {SISSA;75/2004/M}, year = {2005}, abstract = {The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case.}, doi = {10.1098/rspa.2004.1364}, url = {http://hdl.handle.net/1963/2253}, author = {Antonio DeSimone and Giovanni Alberti} } @article {2004, title = {Coarse-grained models of materials with non-convex free-energy: two case studies}, journal = {Computer methods in applied mechanics and engineering , 193 (2004) 5129-5141}, year = {2004}, publisher = {Elsevier}, abstract = {Bridging across length scales is one of the fundamental challenges in the computational modelling of material systems whose mechanical response is driven by rough energy landscapes. The typical feature of such systems is that of exhibiting fine scale microstructures. Two case studies, namely, nematic elastomers and ferromagnetic shape memory alloys, are presented to illustrate the use of modern techniques from (non-convex) calculus of variations in developing coarse-grained models of microstructure-driven material response.}, doi = {10.1016/j.cma.2003.12.064}, url = {http://hdl.handle.net/1963/4884}, author = {Antonio DeSimone} } @article {2004, title = {Energetics and switching of quasi-uniform states in small ferromagnetic particles}, journal = {M2AN Math. Model. Numer. Anal. 38 (2004) 235-248}, year = {2004}, publisher = {EDP Sciences}, abstract = {We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size.}, doi = {10.1051/m2an:2004011}, url = {http://hdl.handle.net/1963/2999}, author = {Fran{\c c}ois Alouges and Sergio Conti and Antonio DeSimone and Ivo Pokern} }