NUMERICAL-SIMULATION OF EQUILIBRIUM SHOCKS IN MAXIMALLY DISSIPATIVE ELASTIC-SYSTEMS .1. THE ONE-DIMENSIONAL CASE

An algorithm designed for the determination of equilibrium shocks that appear in quasi-static evolution problems associated to elastic nonmo notonous stress-strain laws is presented in the context of one-dimensi onal media. Two basic procedures are involved in the proposed method: (i) enhancement of the finite element in order to describe the weak di scontinuities in any point of its interior and (ii) implementation of a return mapping algorithm for the determination of the shocks, which have to satisfy the inequality constraints imposed by a maximally diss ipative hypothesis. A rigorous proof of the unconditional stability pr operty of the algorithm is also given. The present study is applied to the theoretical model presented by Abeyaratne and Knowles in the cont ext of one-dimensional extensional deformations of bars. The numerical results are in complete agreement with the analytical ones.