Crack Path Prediction in Anisotropic Brittle Materials

TL;DR

This paper introduces a force balance condition derived from diffuse interface models to accurately predict crack paths in anisotropic brittle materials, integrating microscopic failure and macroscopic elasticity.

Contribution

It presents a novel derivation of a force balance condition for crack path prediction using diffuse interface continuum models and validates it through numerical simulations.

Findings

The derived force balance condition accurately predicts crack paths.

The model captures both microscopic failure and macroscopic elasticity effects.

Numerical simulations confirm the validity of the theoretical predictions.

Abstract

A force balance condition to predict quasistatic crack paths in anisotropic brittle materials is derived from an analysis of diffuse interface continuum models that describe both short-scale failure inside a microscopic process zone and macroscopic linear elasticity. The derivation exploits the gradient dynamics and translation symmetry properties of this class of models to define a generalized energy-momentum tensor whose integral around an arbitrary closed path enclosing the crack tip yields all forces acting on this tip, including Eshelby's configurational forces, cohesive forces, and dissipative forces. This condition is validated quantitatively by numerical simulations.