We consider a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The adhesion of the contact surfaces, caused by the glue, is taken into account. The material is assumed to be electro-viscoelastic and the foundation is assumed to be electrically conductive. We derive a variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field, a time-dependent variational equation for the electric potential field and a differential equation for the bonding field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of evolution equations with monotone operators and fixed point.

Summary. We consider a dynamic frictionless contact problem for a viscoelastic material with damage. The contact is modeled with normal compliance condition. The adhesion of the contact surfaces is considered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We establish a variational formulation for the problem and prove the existence and uniqueness of the solution. The proofs are based on the theory of evolution equations with monotone operators, a classical existence and uniqueness result for parabolic inequalities, and fixed point arguments.

We consider a dynamic frictionless contact problem for elastic-viscoplastic materials with damage. The contact is modelled with normal compliance condition. The adhesion of the contact surfaces is considered and is modelled with a surface variable, the bonding field whose evolution is described by a first order differential equation. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed-point arguments.

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We consider a mathematical model describing the quasistatic frictional contact between an electro-elasto-viscoplastic body and an adhesive conductive foundation. The contact is described with a normal compliance condition with adhesion, the associated general version of Coulomb's law of dry friction in which the adhesion of contact surfaces is taken into account and a regularized electrical conductivity condition. The existence of a unique weak solution is established under smallness assumption on the surface conductance. The proof is based on arguments of time-dependent variational inequalities, differential equations and Banach fixed point theorem.