Dynamic frictionless contact in linear viscoelasticity

In this work, we formulate a dynamic frictionless contact problem with linear viscoelasticity of Kelvin–Voigt type, based on the Signorini contact conditions. We show existence of solutions, and investigate the possibility for obtaining an energy balance. Employing time discretization and the finite-element method, we compute numerical solutions. Our numerical scheme is implemented with non-smooth Newton's method which solves the complementarity problem. The numerical results support the idea that the energy losses in the limit of the numerical solution are equal to the losses due to viscosity.