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Bipotential versus return mapping algorithms: Implementation of non associated flow rules

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2014
auteur(s) Magnier Vincent; Charkaluk Eric; De Saxce Géry
journal (abréviation) International Journal of Solids and Structures (Int J Solid Struct)
volume (numéro) 51 (15-16)
pages 2857 – 2864
résumé Numerical implementation of constitutive laws involves specific incremental methods. The ”return mapping” (Simo and Hughes, 1998) and the ”bipotential” (de Saxcé, 1992) are one of those, associated respectively to two different classes of materials : the General Standard Materials (GSM) for the return mapping and the Implicit Standard Materials (ISM) for the bipotential. The objective of this paper is then to compare the implementation of those both methods in the case of non associated flow rules in plasticity. In a first section, the properties of the different previous material classes will be recalled and the methods of ”return mapping” and ”bipotential” will be detailed. The comparison of both methods is realised on the non linear kinematic hardening rule of Armstrong-Frederick (Armstrong and Frederick) in a second section and the details are given in a third part. The numerical implementation is realised in Abaqus/Standard 6.11 by the means of a UMat subroutine and the practical simple case of tension-compression is analysed in a last section.
mots clés Non-associated laws; Plasticity; Numerical implementation; Bipotential; Return mapping; Abaqus
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