抄録
In this paper we examine the analytical structure for the simulation of localized necking in sheet metal. The stress rate components which are not associated with the equilibrium condition on the necking plane can be assumed to be continuous, based on the verification given by Hill. This assumption makes it possible to apply the conventional constitutive equations for the study of the analytical structure. In many analyses reported in the literature the necking plane is assumed to be normal to the sheet plane a priori. In such a case the discontinuous velocity gradient vector has two components which are related with the three equations binding three components between the stress and strain rates in the necking plane. Hence, all the velocity gradient components must vanish in order to satisfy these conditions. This means that they must be continuous and then their multiplicity cannot occur. Furthermore, it is shown that the volume constancy requires the normality of the velocity gradient vector with the normal vector to necking plane.
