An enhanced algorithm for nested surfaces plasticity using the implicit Mróz translation rule

In this paper we introduce an enhanced implicit algorithm for phenomenological plasticity based on nested surfaces for the description of multiaxial nonlinear hardening. The algorithm uses an implicit version of the Mróz translation rule. This rule is computed explicitly from the trial state and, as a result, the final stress state is obtained solving a nonlinear scalar equation. With the algorithm and the formulation introduced in this paper, there is no need for performing iterations in order to obtain the final active surface. This surface is determined in advance directly from the trial stress state and therefore the efficiency of the algorithm is greatly improved, specially when the number of surfaces describing the stress–strain curve is moderate to large. The algorithm has been implemented in the commercial code ADINA as a user subroutine.