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The elastoplastic stress is first defined as the stress which evolves as the actual strain rate is induced in an imaginary quasi-static process of elastoplastic deformation, while internal variables evolve with the viscoplastic strain rate calculated by the viscoplastic constitutive equation. Further, the novel variable “overstress tensor” reaching the current stress from the elastoplastic stress is defined. Then, the overstress model is extended so as to describe also the tangential viscoplastic strain rate induced by the overstress tensor component tangential to the yield surface. Furthermore, the viscoplastic strain rate due to the change of stress inside the yield surface is incorporated by adopting the concept of the subloading surface which falls within the framework of the unconventional elastoplasticity describing the smooth elastic-plastic transition fulfilling the smoothness and continuity conditions.

Overstress Model with Tangential-Viscoplastic Strain Rate by Incorporation of Overstress Tensor