Preprint

Inserted: 24 mar 2025
Last Updated: 25 mar 2025

Year: 2025

Abstract:

We provide an adaptive finite element approximation for a model of quasi-static crack growth in dimension two. The discrete setting consists of integral functionals that are defined on continuous, piecewise affine functions, where the triangulation is a part of the unknown of the problem and adaptive in each minimization step. The limit passage is conducted simultaneously in the vanishing mesh size and discretized time step, and results in an evolution for the continuum Griffith model of brittle fracture with isotropic surface energy FriedrichSolombrino16 which is characterized by an irreversibility condition, a global stability, and an energy balance. Our result corresponds to an evolutionary counterpart of the static Gamma-convergence result in BabadjianBonhomme23 for which, as a byproduct, we provide an alternative proof.

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