A frictionless contact problem for viscoelastic materials

[摘要] We consider a mathematical model which describes the contactbetween a deformable body and an obstacle, the so-calledfoundation. The body is assumed to have a viscoelastic behaviorthat we model with the Kelvin-Voigt constitutive law. The contactis frictionless andis modeled with the well-known Signorinicondition in a form with a zero gap function. We presenttwo alternative yet equivalent weak formulations of the problemand establish existence and uniqueness results for bothformulations. The proofs are based on a general result onevolution equations with maximal monotone operators. We thenstudy a semi-discrete numerical scheme for the problem, in termsof displacements. The numerical scheme has a unique solution. Weshow the convergence of the scheme under the basic solutionregularity. Under appropriate regularity assumptions on thesolution, we also provide optimal order error estimates.

[学科分类] 应用数学