A variational formulation governed by two bipotentials for a frictionless contact model

Abstract

We consider a frictionless contact model whose constitutive law and contact condition are described by means of subdifferential inclusions. For this model, we deliver a variational formulation based on two bipotentials. Our formulation envisages the computation of a three-field unknown consisting of the displacement vector, the stress tensor and the normal stress on the contact zone, the contact being described by a generalized Winkler condition. Subsequently, we obtain existence and uniqueness results. Some properties of the solution are also discussed, focusing on the data dependence.

Keywords

• contact condition
• subdifferential inclusion
• bipotentials
• three-field weak solution
• data dependence