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A complete stress update algorithm for the non-associated Drucker-Prager model including treatment of the apex

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2003
auteur(s) Hjiaj Mohammed; Fortin Jérôme; De Saxce Géry
journal International Journal of Engineering Science
volume (numéro) 41 (10)
pages 1109 – 1143
résumé Numerical techniques based on convex analysis are applied to the non-associated Drucker–Prager model (without hardening) for which the plastic behavior is completely described by a unique function, called bi-potential. Among advantages of the present approach, motivated by mechanical considerations, a variational stress update algorithm along with coupled extremum principles can be derived. The time-integration algorithm is considered in detail and it is shown how the method can conveniently treat the singular point present in the Drucker–Prager model (apex). The existence of weak extremum principles allows using Mathematical Programming techniques and thereby obtains a robust algorithm even in the presence of large time increment and strong non-associativity. Numerical examples of incremental limit analysis for both the associated and the non-associated cases are presented.
mots clés Non-associated plasticity; Variational inequalities; stress update algorithms; Bi-potential approach
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