Martin Kružík
ÚTIA AV ČR, Praha

Quasistatic adhesive contact in delamination and its numerical treatment

joint work with T. Roubíček and C. Panagiotopoulos
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.