Accepted Paper

Inserted: 29 sep 2023
Last Updated: 2 aug 2024

Journal: Calc. Var. Partial Differential Equations
Year: 2024

Abstract:

Variational models for cohesive fracture are based on the idea that the fracture energy is released gradually as the crack opening grows. Recently, Conti, Focardi, and Iurlano (2016) proposed a variational approximation via $\Gamma$-convergence of a class of cohesive fracture energies by phase-field energies of Ambrosio-Tortorelli type, which may be also used as regularization for numerical simulations. In this paper we address the question of the asymptotic behaviour of critical points of the phase-field energies in the one-dimensional setting: we show that they converge to a selected class of critical points of the limit functional. Conversely, each critical point in this class can be approximated by a family of critical points of the phase-field functionals.

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