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

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.

References in corpus (3)

• The deal.II finite element library: design, features, and insights
• Mesh adaptivity for quasi-static phase-field fractures based on a residual-type a posteriori error estimator
• Residual-type A Posteriori Estimators for a Singularly Perturbed Reaction-Diffusion Variational Inequality -- Reliability, Efficiency and Robustness

Cited by in corpus (1)

• A new shape optimization approach for fracture propagation