On the consistency of nested surfaces models and their kinematic hardening rules

In this paper we briefly address the consistency of formulations for nested surfaces plasticity and their kinematic hardening translation rules. Some requirements for these formulations are then given. It is shown and discussed that multilayer plasticity based on nested yield surfaces present some inconveniences when modelling multiaxial cyclic loading. On the other hand, the use of hardening surfaces, instead of yield surfaces solves the problem partially. It is also shown that multilayer plasticity based on the Mróz kinematic rule yields clearly different multiaxial predictions when using the same uniaxial bilinear curve and different number of surfaces, which is a priori inconsistent since the same monotonic stress–strain curve should not result into a clearly different multiaxial behavior simply because of the discretization employed by the user. It is demonstrated that, in contrast with the Mróz translation rule, multilayer plasticity using the Prager translation rule results in the same prediction regardless of the number of surfaces in which the hardening part of the bilinear curve is discretized. This rule is also compliant with the principle of maximum dissipation. It also allows for a vanishing elastic region without falling into theoretical or numerical difficulties. Hence, it should not be discarded when developing advanced models.