Adhesive contact delaminating at mixed mode, its thermodynamics and analysis

Details Adhesive contact delaminating at mixed mode, its thermodynamics and analysis Adhesive contact delaminating at mixed mode, its thermodynamics and analysis

2011-10-12

arxiv.org/abs/1110.2794v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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