On the numerical treatment of nonconvex energy problems of mechanics (Q1905960)

The paper presents three numerical methods for the treatment of nonconvex nonsmooth minimization problems arising in structural and continuum mechanics. All the methods approximate the nonconvex energy problem by convex subproblems. The first method is based on the decomposition of the contingent cone of the superpotential of the problem into convex components. The second one uses an iterative scheme in order to approximate the hemivariational inequality problem by a sequence of variational inequalities. Finally, the third method is based on the fact that nonconvexity in mechanics is closely related to irreversible effects that affects the Hessian matrix of the superpotential. All methods are applied to solve the same problems, and the obtained results are compared.