Two-Field Weak Solutions for a Class of Contact Models

Abstract

Two contact models are considered, with the behavior of the materials being described by a constitutive law governed by the subdifferential of a convex map. We deliver variational formulations based on the theory of bipotentials. In this approach, the unknowns are pairs consisting of the displacement field and the Cauchy stress tensor. The two-field weak solutions are sought into product spaces involving variable convex sets. Both models lead to variational systems which can be cast in an abstract setting. After delivering some abstract results, we apply them in order to study the weak solvability of the mechanical models as well as the data dependence of the weak solutions.

A Variational Formulation Governed by Two Bipotentials for a Frictionless Contact Model

“…In connection with the calculus of variations, the bipotential theory allowed to deliver two-field variational formulations for many boundary value problems. Such formulations were proposed for several models in contact mechanics, see [9,16,17,18,19,20,21,22], where the existence and uniqueness of the pair solutions consisting of the displacement vector and the Cauchy stress tensor have been studied.…”