Calculus of Variations and Geometric Measure Theory

M. Bonacini - S. Conti - F. Iurlano

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

created by bonacini on 24 Apr 2020
modified by iurlano on 04 Jan 2022


Accepted Paper

Inserted: 24 apr 2020
Last Updated: 4 jan 2022

Journal: Arch. Ration. Math. Anal.
Year: 2020

ArXiv: 2004.11290v2 PDF


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 Gamma-convergence from a phase-field model of the generalized Ambrosio-Tortorelli type, which may be used as regularization for numerical simulations.