A posteriori estimator for the adaptive solution of a quasi-static fracture phase-field model with irreversibility constraints

TL;DR

This paper introduces a residual-based a posteriori error estimator for a time-discrete phase-field fracture model, focusing on robustness with respect to the regularization parameter, and demonstrates its effectiveness through numerical examples.

Contribution

It develops a new a posteriori error estimator tailored for quasi-static phase-field fracture models with irreversibility constraints, emphasizing robustness against the regularization parameter.

Findings

Estimator performs well on standard fracture test cases

Robustness confirmed for various phase-field regularization parameters

Numerical results validate the effectiveness of the proposed estimator

Abstract

Within this article, we develop a residual type a posteriori error estimator for a time discrete quasi-static phase-field fracture model. Particular emphasize is given to the robustness of the error estimator for the variational inequality governing the phase-field evolution with respect to the phase-field regularization parameter $\epsilon$. The article concludes with numerical examples highlighting the performance of the proposed a posteriori error estimators on three standard test cases; the single edge notched tension and shear test as well as the L-shaped panel test.