Solution of interface problems with nonmonotone contact and friction laws using a neural network optimization environment

Abstract

The paper addresses the solution of interface problems which present a degrading behaviour leading to nonmonotone contact and friction laws. The paper is based on a superpotential formulation that leads to hemivariational inequalities, or, equivalently to nonconvex–nonsmooth optimization problems. The above problems are addressed with a heuristic method which effectively replaces the nonconvex–nonsmooth optimization problem by a sequence of quadratic programming problems with inequality constraints. Then, the quadratic optimization problems are transformed into a system of differential equations, which are treated numerically with an appropriate neural network. Finally, a numerical example illustrates the properties of the proposed algorithmic scheme.