Limit analysis and frictional contact: formulation and numerical solution

Abstract

The evaluation of structural integrity involves the determination of a limit state. If there is plasticity, limit analysis theory takes place. The aim of this paper is to present a limit analysis formulation considering friction at the contact interface. The deduction of this formulation involves the study of contact mechanics, unilateral conditions at normal direction and a slipping rule for the tangential direction. Concerning the contact between a rigid and a deformable body, at limit state there is permanent contact between the bodies and the contact length is supposed known. These hypotheses enable the development of a limit analysis formulation considering friction dissipation. The solution of a limit analysis problem is based on duality between the static, kinematic, mixed and the set of optimum conditions and its relation with the solution of a non-linear programming optimization problem with constraints. The solution is based on Newton method with contraction and relaxation techniques, associated with condensation technique to solve the linear complementarity problem at contact. As an application, the influence of friction coefficient at tool-specimen interface on the wedge indentation is evaluated.