A Viscoelastic Sliding Contact Problem with Normal Compliance, Unilateral Constraint and Memory Term

作者：Sofonea Mircea; Souleiman Yahyeh

来源：Mediterranean Journal of Mathematics, 2016, 13(5): 2863-2886.

DOI：10.1007/s00009-015-0661-9

• viscoelastic material
• frictional contact
• normal compliance
• unilateral constraint
• memory term
• history-dependent variational inequality
• weak solution

We consider a mathematical model which describes the equilibrium of a viscoelastic body in frictional contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with unilateral constraint and memory term, associated to a sliding version of Coulomb's law of dry friction. We present a description of the model, list the assumption on the data and derive a variational formulation of the problem, which is in a form of a system coupling a nonlinear equation for the stress field with a variational inequality for the displacement field. Then we prove an existence and uniqueness result, Theorem 4.1. The proof is based on a recent result on history-dependent quasivariational inequalities proved in Sofonea and Xiao (Appl Anal. doi: 2015). We proceed with a convergence result in the study of the contact problem, Theorem 5.1. It states the continuous dependence of the solution with respect to the relaxation tensor, the surface memory function and the applied forces.

• 出版日期2016-10