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A dynamic problem with adhesion and damage in electro-viscoelasticity with long-term memory. (English) Zbl 1160.74035
Summary: We consider a dynamic frictionless contact problem for an electro-viscoelastic body with long-term memory and 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 svstem involving the displacement field, the electric potential field, the damage field and the adhesion field. We prove the existence of unique weak solution to the problem. The proof is based on evolution equations with monotone operators, parabolic inequalities, differential equations and fixed point argument.

MSC:
74M15 Contact in solid mechanics
74F15 Electromagnetic effects in solid mechanics
74H20 Existence of solutions of dynamical problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
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