Abstract
An algorithm designed for the determination of equilibrium shocks that appear in quasi-static evolution problems associated to elastic nonmonotonous stress-strain laws is presented in the context of one-dimensional media. Two basic procedures are involved in the proposed method: (i) enhancement of the finite element in order to describe the weak discontinuities 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 dissipative hypothesis. A rigorous proof of the unconditional stability property of the algorithm is also given. The present study is applied to the theoretical model presented by Abeyaratne and Knowles in the context of one-dimensional extensional deformations of bars. The numerical results are in complete agreement with the analytical ones.
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Pontifícia Universidade Católica do Rio de Janeiro
Visiting Professor at Stanford University during the development of this work.
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Mamiya, E.N., Simo, J.C. Numerical simulation of equilibrium shocks in maximally dissipative elastic systems. Part I: The one-dimensional case. J Elasticity 35, 175–211 (1994). https://doi.org/10.1007/BF00115542
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DOI: https://doi.org/10.1007/BF00115542