Numerical treatment of the nonmonotone (zig-zag) friction and adhesive contact problems with debonding. Approximation by monotone subproblems

Abstract

Nonmonotone friction problems or adhesive contact friction problems introduce zig-zag-type laws which cannot be effectively treated by the classical numerical methods for nonlinear stress-strain laws. In order to calculate accurately the arising free boundaries we propose a new approximation method of the nonmonotone problem by monotone ones. The proposed method finds its justification in the approximation of a hemivariational inequality by a sequence of variational inequalities. Also, the case of debonding is considered by an appropriate fixed point type algorithm. Numerical examples illustrate the numerical method.