Weak solvability via bipotentials and approximation results for a class of bilateral frictional contact problems

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

“…On the other hand, by introducing a single bipotential which is in connection with the constitutive law, if instead of (A3) we assume that ψ is a seminorm then with a similar technique to that used in [21] we can deliver for Problem 1 a two-field variational formulation of the form below s (Ω) 3×3 : (µ, ε(v)) L 2 s (Ω) 3×3 +j ψ (v) ≥ (f , v) V for all v ∈ V }. This second variational formulation allows the computation of the pair (u, σ).…”

“…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.…”