The benefits of anisotropic mesh adaptation for brittle fractures under plane-strain conditions

We develop a reliable a posteriori anisotropic first order estimator for the numerical simulation of the Francfort and Marigo model of brittle fracture, after its approximation by means of the Ambrosio-Tortorelli variational model. We show that an adaptive algorithm based on this estimator reproduces all the previously obtained well-known benchmarks on fracture development with particular attention to the fracture directionality. Additionally, we explain why our method, based on an extremely careful tuning of the anisotropic adaptation, has the potential of outperforming significantly in terms of numerical complexity the ones used to achieve similar degrees of accuracy in previous studies.