Variational phase-field modeling of cohesive fracture with flexibly tunable strength surface

TL;DR

This paper introduces a variational phase-field model for cohesive fracture that can incorporate arbitrary strength surfaces, enabling more accurate simulation of crack nucleation and propagation under complex stress conditions.

Contribution

The model allows flexible tuning of the cohesive response and accommodates arbitrary convex strength surfaces, improving upon traditional Griffith-based phase-field models.

Findings

The model produces sharp cohesive cracks and enforces non-interpenetration naturally.

It satisfies stress softening and generates residual stresses inherently.

Numerical simulations validate the theoretical stability and effectiveness.

Abstract

Variational phase-field models of brittle fracture are powerful tools for studying Griffith-type crack propagation in complex scenarios. However, as approximations of Griffith's theory-which does not incorporate a strength criterion-these models lack flexibility in prescribing material-specific strength surfaces. Consequently, they struggle to accurately capture crack nucleation under multiaxial stress conditions. In this paper, inspired by Alessi et al. (2014), we propose a variational phase-field model that approximates cohesive fracture. The model accommodates an arbitrary (convex) strength surface, independent of the regularization length scale, and allows for flexible tuning of the cohesive response. Our formulation results in sharp cohesive cracks and naturally enforces a sharp non-interpenetration condition, thereby eliminating the need for additional energy decomposition strategies. It inherently satisfies stress softening and produces "crack-like" residual stresses by construction. To ensure strain hardening, the ratio of the regularization length to the material's cohesive length must be sufficiently small; however, if crack nucleation is desired, this ratio must also be large enough to make the homogeneous damaged state unstable. We investigate the model in one and three dimensions, establishing first- and second-order stability results. The theoretical findings are validated through numerical simulations using the finite element method, employing standard discretization and solution techniques.