Primal and Dual Variational Formulation of a Frictional Contact Problem

Mircea Sofonea (1) , David Danan (1) , Cong Zheng (2)

1 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations
2 Department of Mathematics [Hangzhou]

This paper represents a continuation of Barboteu et al. (Analysis of a contact problem with unilateral constraint and slip-dependent friction, Math Mech Sol, 2015). There, a mathematical model which describes the frictional contact between an elastic body and a foundation was considered. The variational and numerical analysis of the problem was provided by considering a weak formulation in terms of displacements, the so-called primal variational formulation. The aim of the current paper is to study the problem using a weak formulation in terms of the stress, the so-called dual variational formulation. We start by presenting the model, the assumption on the data and some preliminary results. Then we state and prove an equivalence result, Theorem 4.1. We proceed with an existence and uniqueness results, Theorem 5.1. The proofs are based on arguments of monotonicity, convexity and lower semicontinuity.

Mots clés: weak solution; variational inequality; dual variational formulation; primal variational formulation; unilateral constraint; Elastic material; frictional contact; normal compliance

Domaines: Mathématiques [math]

Mircea Sofonea, David Danan, Cong Zheng. Primal and Dual Variational Formulation of a Frictional Contact Problem. Mediterranean Journal of Mathematics, 2016, 13 (2), pp.857-872. ⟨10.1007/s00009-014-0504-0⟩. ⟨hal-01143021⟩