Internal-variable constitutive model for rate-independent plasticity with hardening saturation surface

An elastic-plastic material model with internal variables and thermodynamic potential, not admitting hardening states out of a saturation surface, is presented. The existence of such a saturation surface in the internal variables space - a consequence of the boundedness of the energy that can be stored in the material's internal micro-structure - encompasses, in case of general kinematic/isotropic hardening, a one-parameter family of envelope surfaces in the stress space, which in turn is enveloped by a limit surface. In contrast to a multi-surface model, no ad hoc rules are required to avoid the intersection between the yield and bounding/envelope surface. The flow laws of the proposed model are studied in case of associative plasticity with the aid of the maximum intrinsic dissipation theorem. It is shown that the material behaves like a standard one as long as its hardening state either is not saturated, or undergoes a desaturation from a saturated hardening state, whereas, for saturated hardening states not followed by desaturation, it conforms to a combined yielding law in which the static internal variable rates obey a nonlinear hardening rule similar to that of analogous models of the literature. Additionally, the material is shown to behave as a perfectly plastic material for a class of(critical) saturated hardening states for which the stress state is on the limit surface. For nonassociative material models, it is shown that, under a special choice of the plastic: and saturation potentials and through a suitable parameter identification, the well-known Chaboche model is reproduced. A few numerical examples are presented to illustrate the associative material response under monotonic and cyclic loadings.