Adhesive contact delaminating at mixed mode, its thermodynamics and analysis

TL;DR

This paper develops a thermodynamically consistent model for mixed-mode adhesive delamination in heat-conductive viscoelastic materials, analyzing the effects of mode-mixity and proving the existence of solutions.

Contribution

It introduces a novel anisothermal model incorporating mode-mixity dependence and proves the existence of weak solutions using a semi-implicit discretization scheme.

Findings

Mode-mixity significantly influences delamination behavior.

The model captures thermal and mechanical coupling effects.

Existence of solutions is rigorously established.

Abstract

An adhesive unilateral contact between visco-elastic heat-conductive bodies in linear Kelvin-Voigt rheology is scrutinised. 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 of Mode I (opening) and of Mode II (shearing). Such mode-mixity dependence of delamination is a very pronounced (and experimentally confirmed) phenomenon typically considered in engineering models. An anisothermal, thermodynamically consistent model is derived, considering a heat-conductive viscoelastic material and the coupling via thermal expansion and adhesion-depending heat transition through the contact surface. We prove the existence of weak solutions by passing to the limit in a carefully designed semi-implicit time-discretization scheme.