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

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 bipotential. 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 nonassociated cases are presented.