Quasistatic adhesive contact delaminating in mixed mode and its numerical treatment

TL;DR

This paper models quasistatic adhesive delamination in mixed mode, considering mode-dependent energy dissipation, and introduces an efficient FEM discretization with proven convergence, supported by computational experiments.

Contribution

It presents a novel FEM discretization for mixed-mode delamination with convergence proof, incorporating mode-dependent energy dissipation effects.

Findings

FEM discretization effectively models mixed-mode delamination.

Convergence of the numerical scheme is rigorously proven.

Computational experiments demonstrate modeling accuracy and efficiency.

Abstract

An adhesive unilateral contact between visco-elastic bodies at small strains and in a Kelvin-Voigt rheology is scrutinized, neglecting inertia. The flow-rule for debonding the adhesive is considered rate independent, unidirectional, and non-associative due to dependence on the mixity of modes of delamination, namely Mode I (opening) needs (=dissipates) less energy than Mode II (shearing). Such mode-mixity dependence of delamination is a very pronounced (and experimentally confirmed) phenomenon typically considered in engineering models. An efficient semi-implicit-in-time FEM discretization leading to recursive quadratic mathematical programs is devised. Its convergence and thus the existence of weak solutions is proved. Computational experiments implemented by BEM illustrate the modeling aspects and the numerical efficiency of the discretization.