Abstract
This paper examines the analytical structure for simulating the localization in soil material. The three components of stress rate associated with the shear plane are related with the equilibrium condition on the plane. Other components can be assumed to be continuous, based on Hill's verification with respect to the continuity of stress on the plane where discontinuous velocity arises. This assumption makes possible application of the conventional constitutive equations to examine the structure. Consequently, all components of stress rate become continuous across the shear plane. Then, the constitutive relation between strain rate difference and stress rate difference must be linear with a constant coefficient independent upon their components. Furthermore, under such circumstances, all components of the discontinuous velocity gradient vector vanish. Hence, it means that they must be continuous under rigorous consideration, and their multiplicity does not appear.
