An antiplane contact problem for viscoelastic materials with long‐term memory

Abstract

We study a mechanical problem modeling the antiplane shear deformation of a cylinder in frictional contact with a rigid foundation. The material is assumed to be viscoelastic with long‐term memory, the process is quasistatic, and the friction is modeled with Tresca's law. The problem leads to an evolutionary variational inequality that we study in an abstract framework. We then use the abstract result to prove the existence of a unique weak solution to the mechanical model. Moreover, we study its behavior with respect to the memory term and establish a convergence result. 

First Published Online: 14 Oct 2010