Numerical Solution of a Non-Smooth Variational Problem Arising in Stress Analysis: The Scalar Case

Abstract

A non-smooth constrained minimization problem arising in the stress analysis of a plastic body is considered. A numerical method for the computation of the load capacity ratio is presented to determine if the elastic body fractures under external traction. In the scalar case, the maximum principle allows one to reduce the problem to a convex one under linear constraints. An augmented Lagrangian method, together with an approximation by finite elements is advocated for the computation of the load capacity ratio and the corresponding elastic stress. The generalized eigenvalues and eigenvectors of the corresponding operator are computed for various two-dimensional bodies and fractures are discussed.