A quasistatic frictional contact problem with normal compliance and finite penetration for elastic materials

Abstract

We consider a quasistatic unilateral contact problem with finite penetration between an elastic body and an obstacle, say a founda- tion. The constitutive law is assumed to be nonlinear and the contact is modelled with normal compliance associated to a version of Coulomb's law of dry friction. Under a smallness assumption on the contact functions, we establish the existence of a weak solution to the problem. The proofs are based on arguments of time-dicretization, compactness and lower semicon- tinuity.