Phase-field fracture irreversibility using the slack variable approach

TL;DR

This paper introduces a novel method for enforcing fracture irreversibility in phase-field models by transforming the inequality constraint into an equality using slack variables, and incorporates it via Lagrange multipliers and penalty methods, validated through numerical experiments.

Contribution

The paper presents a new variationally consistent approach to model fracture irreversibility in phase-field methods using slack variables, Lagrange multipliers, and penalty techniques.

Findings

Effective enforcement of irreversibility constraint demonstrated in benchmark problems.

Method is variationally consistent with traditional phase-field fracture models.

Numerical results confirm the robustness of the proposed approach.

Abstract

In this manuscript, the phase-field fracture irreversibility constraint is transformed into an equality-based constraint using the slack variable approach. The equality-based fracture irreversibility constraint is then introduced in the phase-field fracture energy functional using the Lagrange Multiplier Method and the Penalty method. Both methods are variationally consistent with the conventional variational inequality phase-field fracture problem, unlike the history-variable approach. Thereafter, numerical experiments are carried out on benchmark problems in brittle and quasi-brittle fracture to demonstrate the efficacy of the proposed method.