Quasistatic adhesive contact delaminating in mixed mode and its numerical treatment

Author:

Kružík Martin1,Panagiotopoulos Christos G2,Roubíček Tomáš3

Affiliation:

1. Institute of Information Theory and Automation of the ASCR, Prague, Czech Republic; Faculty of Civil Engineering, Czech Technical University, Prague, Czech Republic

2. Group of Elasticity and Strength of Materials, Department of Continuum Mechanics, School of Engineering, University of Seville, Spain

3. Mathematical Institute, Charles University, Prague, Czech Republic; Institute of Thermomechanics of the ASCR, Prague, Czech Republic

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.

Publisher

SAGE Publications

Subject

Mechanics of Materials,General Materials Science,General Mathematics

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