Solvability of a rational contact model with limited interpenetration in viscoelastodynamics

A rational model of a dynamical contact of a viscoelastic body with its support is presented. It is assumed that the contact is frictionless and permits a limited interpenetration which is prescribed. A weak formulation of the problem is given and the existence of its solutions is proved. It is also shown that if the depth of the interpenetration tends to zero, the solutions converge to a solution of the Signorini contact (without interpenetration).

Analysis of electroelastic frictionless contact problems with adhesion

We consider two quasistatic frictionless contact problems for piezoelectric bodies. For the first problem the contact is modelled with Signorini's conditions and for the second one is modelled with normal compliance. In both problems the material's behavior is electroelastic and the adhesion of the contact surfaces is taken into account and is modelled with a surface variable, the bonding field. We provide variational formulations for the problems and prove the existence of a unique weak solution to each model. The proofs are based on arguments of time-dependent variational inequalities, differential equations, and fixed point. Moreover, we prove that the solution of the Signorini contact problem can be obtained as the limit of the solution of the contact problem with normal compliance as the stiffness coefficient of the foundation converges to infinity.