A complete stress update algorithm for the non-associated Drucker-Prager model including treatment of the Apex
Résumé
Numerical techniques based on convex analysis are applied to the non-associated DruckerPrager 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 DruckerPrager 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.