An Elastic Frictional Contact Problem with Unilateral Constraint

Maxime Couderc (1) , Mircea Sofonea (1)

1 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations

We consider a mathematical model which describes the equilibrium of an elastic body in contact with two obstacles. We derive its weak formulation which is in a form of an elliptic quasi-variational inequality for the displacement field. Then, under a smallness assumption, we establish the existence of a unique weak solution to the problem. We also study the dependence of the solution with respect to the data and prove a convergence result. Finally, we consider an optimization problem associated with the contact model for which we prove the existence of a minimizer and a convergence result, as well.

Mots clés: Elastic material; Frictional contact; Quasi-variational inequality; Weak solution; Convergence results; Optimization problem

Domaines: Mathématiques [math]

Maxime Couderc, Mircea Sofonea. An Elastic Frictional Contact Problem with Unilateral Constraint. Mediterranean Journal of Mathematics, 2018, 15 (5), ⟨10.1007/s00009-018-1243-4⟩. ⟨hal-01930270⟩