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

TL;DR

This paper introduces a new irreversibility concept for crack evolution with cohesive forces, deriving a 1D quasi-static model from phase-field approximations, enhancing understanding and simulation of cohesive fractures.

Contribution

It proposes a novel irreversibility notion for cohesive crack evolution and derives a 1D quasi-static model from phase-field approximations using Gamma-convergence.

Findings

Irreversibility concept allows different responses in loading/unloading.

Derivation of 1D quasi-static evolution from phase-field models.

Phase-field models serve as regularizations for numerical simulations.

Abstract

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.