NUMERICAL TREATMENT OF PROBLEMS INVOLVING NONMONOTONE BOUNDARY OR STRESS-STRAIN LAWS

In order to describe the softening behavior of the materials, nonmonot one possible multivalued laws have been recently introduced. These law s are derived by nonconvex, generally nonsmooth energy functions calle d superpotentials that give rise to hemivariational inequalities. Due to the lack of convexity and the nonsmoothness of the underlying super potentials these problems have generally nonunique solutions. On the o ther hand, problems involving monotone laws lead to variational inequa lities that can be easily treated using modern convex minimization alg orithms. The present paper proposes a new method for the solution of t he nonmonotone problem by approximating it using monotone ones. The pr oposed method finds its justification in the approximation of a hemiva riational inequality by a sequence of variational This approach leads to effective reliable and versatile numerical algorithms for hemivaria tional inequalities. The numerical method proposed is examples. (C) 19 97 Civil-Comp Ltd and Elsevier Science Ltd.