Variational-hemivariational approach to a quasistatic viscoelastic problem with normal compliance, friction and material damage

Abstract

This work studies a model for quasistatic frictional contact between a viscoelastic body and a reactive foundation. The constitutive law is assumed to be nonlinear and contains damage effects modeled by a parabolic differential inclusion. Contact is described by the normal compliance condition and a subdifferential frictional condition. A variational-hemivariational formulation of the problem is provided and the existence and uniqueness of its solution is proved. The proof is based on a surjectivity result for pseudomonotone coercive operators and a fixed point argument.