Derivation of a stability and non-bifurcation criterion for frictional contact problems

Bifurcation and stability of irreversible systems in plasticity have widely been studied in the literature devoted to Solid Mechanics and are now well understood. The same criteria are of great importance in frictional contact problems as they define the allowable limits of the service domain for frictional contact interfaces prior to their failure due to those mechanisms. In this paper, it is shown that uniqueness, bifurcation and stability in the sense of Hill can be obtained for associated friction, via the established asymptotic equivalence with elastic-perfect plasticity, when the intermediate elastic-plastic layer tends towards the contact interface. The problem formulation and its discretization by the finite element method then lead to the solving of an eigenvalue problem in the vicinity of the limit state for which a static condensation can be performed on the discrete contact interface. The application of the derived stability and non-bifurcation criterion is finally illustrated through two worked examples.