ABSTRACT
Abstract The eigenanalysis of the localization tensor is essential for the analytical treatment of spatial discontinuities due to strain localization. The eigensolution character izes the direction of the spatial discontinuity surface and the mode of localization, but not the magnitude of the jump in the strain rate. This paper describes the mathematical developments for detecting the onset of discontinuous bifurcation, and in addition it addresses the post-bifurcation analysis of elastoplastic solids. To this end constitutive expressions will be developed which relate the stress rate to the strain rate on both sides of the spatial discontinuity leading to a discussion of plastic/plastic vs. elastic/plastic bifurcation based on the eigenanalysis of a generalized localization tensor. Keywords: Strain Localization, Elastoplastic Solid, Localization Tensor, Eigen analysis, Discontinuous Bifurcation, Constitutive Relation.
