Internal-variable constitutive model for rate-independent plasticity with hardening saturation surface
The paper is devoted to the associative and nonassociative models for elasto-plastic, kinematic and isotropic hardening materials, which are endowed with a continuous set of bounding surfaces and a (limit) saturation surface. Based on the experimental evidences that the hardening materials exhibit a tendency to attenuate their hardening capacity, the authors put a bound upon the stored energy density and postulate the existence of a finite hardening domain, whose boundary defines the (hardening) saturation surface. The plastic flow laws are derived by the maximum dissipation theorem for the associative plasticity. The plastic behaviour is described as that of a standard internal-variable constitutive model for hardening states below the saturation limit. For hardening states at the saturation limit with the scalar internal variable kept constant, the yield surface moves in the stress space giving rise to an envelope surface. The limit surface is defined as the surface enveloping the one-parameter family of envelope surfaces. Additional equations are derived for stress states on the limit surface, which admit only neutral change in this hardening state. The authors provide a complete set of constitutive equations describing the behaviour of such elasto-plastic materials. In the models both yield and saturation functions are supposed to be convex, and the rate of internal variables vanishes not only for zero rate of plastic deformations. A Mises-type model exemplifies the authors' approaches to elasto-plasticity and is employed to numerically illustrate the material response of a bar specimen in one-dimensional stress state, and respectively of a thin-walled tube specimen in torsion and extension. Some comparisons with models existing in the literature are also performed.
scientific article; zbMATH DE number 1207074