An electro-elastic-visco-plastic contact problem with adhesion and damage
Received: 1 April 2008 Revised: 30 April 2008
Mathematics Subject Classification (2000): 74M15 - 74F99 - 74H20 - 74H25.
Keywords: Dynamic process, electro-elastic-visco-plastic materials, frictionless contact, normal compliance, adhesion, damage, existence and uniqueness, monotone operator, fixed point, weak solution.
Abstract We consider a dynamic frictionless contact problem for an electro-elastic- visco-plastic body with damage. The contact is modelled with normal compliance. The adhesion of the contact surfaces is taken into account and modelled by a surface variable, the bonding field. We derive variational formulation for the model which is formulated as a system involving the displacement field, the electric potential field, the damage field and the adhesion field. We prove the existence of a unique weak solution to the problem. The proof is based on arguments of evolution equations with monotone operators, parabolic inequalities, differential equations and fixed point.