On a phase--field model of damage for hybrid laminates with cohesive interface

TL;DR

This paper develops a rate-independent phase-field model for damage in hybrid laminates with cohesive interfaces, using energetic evolution and a novel approach to handle interface opening variables.

Contribution

It introduces a new strategy to ensure equivalence between fictitious and real interface variables under general loading conditions in damage modeling.

Findings

Established a regularity condition for energetic evolutions.

Demonstrated the model's ability to handle complex loading-unloading cycles.

Provided a theoretical framework for damage evolution in hybrid laminates.

Abstract

In this paper we investigate a rate--independent model for hybrid laminates described by a damage phase--field approach on two layers coupled with a cohesive law governing the behaviour of their interface in a one-dimensional setup. For the analysis we adopt the notion of energetic evolution, based on global minimisation of the involved energy. Due to the presence of the cohesive zone, as already emerged in literature, compactness issues lead to the introduction of a fictitious variable replacing the physical one which represents the maximal opening of the interface displacement discontinuity reached during the evolution. A new strategy which allows to recover the equivalence between the fictitious and the real variable under general loading--unloading regimes is illustrated. The argument is based on temporal regularity of energetic evolutions. This regularity is achieved by means of a careful balance between the convexity of the elastic energy of the layers and the natural concavity of the cohesive energy of the interface.