Quasistatic Viscoplasticity with Polynomial Growth Condition and with Frictional Contact

Abstract

We consider a problem in the inelastic deformation theory. There is a body consisted of a viscoplastic material, which is deformed in a quasistatic process i.e. the movement varies slowly. Additionally we assume that the body has a contact with a rigid foundation: the body moves on the foundation with a friction modelled by a dissipative potential. Together with an inelastic constitutive function, it gives a problem that involves two monotone operators: one acting on the body, other acting on its boundary. We prove existence and uniqueness of a solution to this problem where inelastic constitutive function has a polynomial growth at infinity.