Abstract
Based on the definitions of hardening, softening and ideal plastic behavior of elastic-plastic materials in the true stress tensor space, the phenomena of simple shear oscillation are shown to be relative to the oscillatory occurrence 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 deformation. To make the models of elastic-plastic materials realistic, must be satisfied the following conditions: for any constitutive model, its response stresses to any continuous plastic deformation must be non-oscillatory, and there is no oscillation of hardening behavior during the plastic deformation.
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Liangsen, C., Xinghua, Z. & Minfu, F. The simple shear oscillation and the restrictions to elastic-plastic constitutive relations. Appl Math Mech 20, 593–603 (1999). https://doi.org/10.1007/BF02464931
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DOI: https://doi.org/10.1007/BF02464931