An evolution problem in nonsmooth elasto-viscoplasticity Original Research Article

In this note we summarize some of our recent results on the mathematical modeling of contact problems. We concentrate on a dynamical model which describes the frictional contact between a deformable body and a foundation. The material behavior is described with a nonlinear elastic–viscoplastic constitutive law and the frictional contact is modeled with multivalued subdifferential boundary conditions. We derive the variational formulation of the problem which is in the form of a system involving an integral equation coupled with an evolutionary hemivariational inequality. We prove the existence and the regularity properties of a unique weak solution to the model.