The search for substationarity points in the unilateral contact problems with nonmonotone friction

Abstract

Structures involving nonmonotone, possibly multivalued reaction-displacement, or stress-strain laws cannot be effectively treated by the classical numerical methods for nonlinear laws. This type of problems have as a variational formulation a hemivariational inequality, leading to a nonconvex optimization problem. In this paper, a new method is proposed which approximates the nonmonotone problem by a series of monotone ones. The method constitutes an iterative scheme for the approximation of the substationarity Points, i.e., of all the solutions of the corresponding hemivariational inequality. Numerical examples demonstrate the properties of the proposed numerical method.