Post-localization Analysis by the Subloading Surface Model with Tangential Stress Rate Effect

Abstract

Various constitutive models have been applied to the analyses of localized deformation of solids. However, most of them fall within the framework of the conventional plasticity premising that the interior of yield surface is an elastic domain and obeys the plastic potential theory in which the plastic stretching is independent of the stress rate component tangential to the yield surface. Therefore, they predict a stiff elastic response until the stress reaches the yield state and further a stiff elastoplastic response after yielding. On the other hand, the subloading surface model falling within the unconventional plasticity would be only the model capable of describing pertinently the plastic deformation induced by the rate of stress within the yield surface in general loading process including the unloading, reloading and inverse loading. Further, the numerical calculation by this model is quite efficient disusing the special algorism, e.g. the mean normal method and the radial return method in order to make the stress lie just on the yield surface in the plastic loading process since it contains the controlling function to make the stress approach automatically the yield surface in the plastic loading process. Further, this model is recently extended so as to describe the tangential stress rate effect, i.e. the inelastic deformation induced by the stress rate component tangential to the subloading surface. In this article the post-localized deformation of metal due to the shear band formation is analyzed by the finite element method incorporating the subloading surface model with the tangential stress rate effect. Thus, the influence of the tangential stress rate effect on the shear band formation is discussed exhibiting several examples of the deformation patterns.