Gradient Damage Models Coupled with Plasticity and Nucleation of Cohesive Cracks

Abstract

In the framework of rate-independent systems, a family of elastic-plastic-damage models is proposed through a variational formulation. Since the goal is to account for softening behaviors until the total failure, the dissipated energy contains a gradient damage term in order to limit localization effects. The resulting model owns a great flexibility in the possible coupled responses, depending on the constitutive parameters. Moreover, considering the one-dimensional quasi-static problem of a bar under simple traction and constructing solutions with localization of damage, it turns out that in general a cohesive crack appears at the center of the damage zone before the rupture. The associated cohesive law is obtained in a closed form in terms of the parameters of the model

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

“…The discussion of the role of the constitutive assumptions on the emerging macroscopic behaviours shows that damage and plastic localisations may interact to produce cohesive-like cracks. This result has been confirmed through rigorous asymptotic analysis in [29,30,32], showing the convergence of a special case of the model presented in [4] to a cohesive sharp crack model. References [28] and [37] recently proposed an alternative interesting phase-field model of cohesive fracture without introducing plastic effects.…”

“…Alessi et al [4] have recently shown, through a variational framework, that coupling a gradient-damage model with plasticity can lead to macroscopic behaviours assimilable to ductile and cohesive fracture. Here, we further expand this approach considering specific constitutive functions frequently used in phase-field models of brittle fracture.…”

“…A more general class of models for coupling damage and plasticity has been presented and analysed in [4,5]. These works introduce the regularisation only on the damage variable, through a gradient term penalised by an internal material length, while keeping plasticity local and allowing the development of sharp plastic localisations.…”

“…The aim of this paper is to extend the analysis of the variational model presented in [4]. Therein, an ad-hoc choice of the constitutive laws was used to obtain closed form solutions.…”

“…In Sec. 2, the main ingredients of the gradient damage-plasticity model of [4,5] are recalled. We deduce within a variational framework the evolution laws, where the displacement and the gradient of damage fields are allowed to be discontinuous in space.…”