# High-accuracy phase-field models for brittle fracture based on a new family of degradation functions

## TL;DR

This paper introduces a new family of degradation functions for phase-field models of brittle fracture, significantly improving accuracy in predicting crack initiation and growth while maintaining elastic response.

## Contribution

A novel parametric family of degradation functions is proposed, enhancing phase-field fracture models' predictive accuracy and preserving elastic behavior before fracture occurs.

## Key findings

- Superiority over classical quadratic degradation functions in numerical tests
- Improved prediction of critical loads for crack nucleation
- Enhanced modeling of crack propagation dynamics

## Abstract

Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In the phase-field framework, the surface energy associated with crack formation is calculated by evaluating a functional defined in terms of a scalar order parameter and its gradients, which in turn describe the fractures in a diffuse sense following a prescribed regularization length scale. Imposing stationarity of the total energy leads to a coupled system of partial differential equations, one enforcing stress equilibrium and another governing phase-field evolution. The two equations are coupled through an energy degradation function that models the loss of stiffness in the bulk material as it undergoes damage. In the present work, we introduce a new parametric family of degradation functions aimed at increasing the accuracy of phase-field models in predicting critical loads associated with crack nucleation as well as the propagation of existing fractures. An additional goal is the preservation of linear elastic response in the bulk material prior to fracture. Through the analysis of several numerical examples, we demonstrate the superiority of the proposed family of functions to the classical quadratic degradation function that is used most often in the literature.