Diffuse interface approach to brittle fracture

TL;DR

This paper introduces a continuum model for brittle fracture that uses strain tensor gradients to simulate crack propagation without extra fields, validated through controlled and complex applications.

Contribution

The model uniquely incorporates strain tensor gradients into a single-field continuum framework for brittle fracture simulation.

Findings

Model reduces to linear elasticity at small strains

Accounts for crack energy saturation at large strains

Successfully validated in controlled and complex scenarios

Abstract

We present a continuum model for the propagation of cracks and fractures in brittle materials. The components of the strain tensor $\epsilon$ are the fundamental variables. The evolution equations are based on a free energy that reduces to that of linear elasticity for small $\epsilon$, and accounts for cracks through energy saturation at large values of $\epsilon$. We regularize the model by including terms dependent on gradients of $\epsilon$ in the free energy. No additional fields others than the strain tensor $\epsilon$ are introduced, and then the whole dynamics is perfectly defined. We validate the model in controlled cases, and present a couple of non trivial applications.