degradation function that is used most often in the literature.'
address:
- 'Department of Mathematics, University of Bergen, Allégaten 41, 5007 Bergen, Norway'
- 'Christian Michelsen Research, Fantoftvegen 38, 5072 Bergen, Norway'
- 'Department of Civil and Environmental Engineering, Princeton University, E-208 E-Quad, Princeton, NJ 08544, USA'
author:
- Juan Michael Sargado
- Eirik Keilegavlen
- Inga Berre
- Jan Martin Nordbotten
bibliography:
- 'Reference.bib'
title: |
    High-accuracy phase-field models for brittle fracture based on\
    a new family of degradation functions
---

Fracture ,phase-field ,degradation function ,damage

Introduction
============

The accurate simulation of fracture evolution in solids is a major challenge for computational algorithms, in large part due to crack paths that are generally unknown a priori. In this regard, phase-field approaches have shown great potential with their ability to automatically determine the direction of crack propagation through minimization of an energy functional. The phase-field framework naturally handles the emergence of phenomena such as crack nucleation and branching without the need to introduce additional criteria. In particular, formulations derived from the variational theory of [@Francfort1998] have received a lot of attention from the applied mechanics community due to its strong ties to Griffith’s theory for brittle fracture. Phase-field models belong 