Interaction between material length scale and imperfection size for localisation phenomena in viscoplastic media

Abstract

For the description of localised shear modes viscoplasticity theory is used to regularise the initial value problem. The viscous term in the constitutive equation has been shown to implicitly introduce a material length scale in the model. A relation between the material length scale and the width of the shear band in a perfect bar has been derived. The influence of imperfections on the viscoplastic solution has also been studied and the length scale set by the size of the imperfect zone has been related to the material length scale. The features of viscoplastic soluions in which these two length scale effects are present, have been studied for one- and two-dimensional problems.