The simple shear oscillation and the restrictions to elastic-plastic constitutive relations

Based on the definitions of hardening, softening and ideal plastic behavior of elastic-plastic materials in the true stress tensor space, the phenomen a of simple shear oscillation are shown to be relative to the oscillatory o ccurrence of hardening and softening behavior of elastic-plastic materials, namely the oscillation of hardening behavior, by analyzing a simple model of rigid-plastic materials with kinematical hardening under simple shear de formation. To make the models of elastic-plastic materials realistic, must be satisfied the following conditions: for any constitutive model, its resp onse stresses to any continuous plastic deformation must be non-oscillatory , and there is no oscillation of hardening behavior during the plastic defo rmation.