No abstract

We consider a dynamic frictionless contact problem between an elastic-viscoplastic body and a reactive foundation. The contact is modelled with normal compliance. The material is elastic-viscoplastic with two internal variables which may describe a temperature parameter and the damage of the system caused by plastic deformations. We derive a weak formulation of the system consisting of a motion equation, an energy equation, and an evolution damage inclusion. We prove existence and uniqueness of the solution, and the positivity of the temperature. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic type inequalities, differential equations and fixed-point arguments.

No abstract

"A dynamic contact problem is considered in the paper. The material behavior is described by electro-elastic-viscoplastic law with piezoelectric effects. The body is in contact with damage and an obstacle. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. The damage of the material caused by elastic deformations. The evolution of the damage is described by an inclusion of parabolic type. The problem is formulated as a coupled system of an elliptic variational inequality for the displacement, variational equation for the electric potential and a parabolic variational inequality for the damage. We establish a variational formulation for the model and we prove the existence of a unique weak solution to the problem. The proof is based on a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed point arguments."

A dynamic contact problem is considered in the paper. The material behavior is described by electrovisco-elastic constitutive law with piezoelectric effects. The body is in contact with a rigide obstacle. Contact is described with the Signorini condition, a version of Coulomb's law of dry friction, and with a regularized electrical conductivity condition. A variational formulation of the problem is derived. Under the assumption that coefficient of friction is small, existence and uniqueness of a weak solution of the problem is proved. The proof is based on evolutionary variational inequalities and fixed points of operators.