An adhesive unilateral contact problem between visco-elastic heat-conductive 1 bodies in linear Kelvin-Voigt rheology is scrutinized. 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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Riccarda Rossi, Tomáš Roubíček, Adhesive contact delaminating at mixed mode, its thermodynamics and analysis. Interfaces Free Bound. 15 (2013), no. 1, pp. 1–37