Cohesive fracture in 1D: quasi-static evolution and derivation from static phase-field models

Marco Bonacini , Sergio Conti (1) , Flaviana Iurlano (2)

1 Institut fur Angewandte Mathematik - Institut fur Angewandte Mathematik
2 LJLL - Laboratoire Jacques-Louis Lions

In this paper we propose a notion of irreversibility for the evolution of cracks in presence of cohesive forces, which allows for different responses in the loading and unloading processes, motivated by a variational approximation with damage models. We investigate its applicability to the construction of a quasi-static evolution in a simple one-dimensional model. The cohesive fracture model arises naturally via Γ-convergence from a phase-field model of the generalized Ambrosio-Tortorelli type, which may be used as regularization for numerical simulations.

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Marco Bonacini, Sergio Conti, Flaviana Iurlano. Cohesive fracture in 1D: quasi-static evolution and derivation from static phase-field models. 2020. ⟨hal-02553151v1⟩