Criterion of Plastic Instability in Soil.

Abstract

In a critical compressive state accompanying with deviatoric strain, shear band is observed in soil. On the necking plane that forms a boundary between the shear band and its surroundings, the velocity gradient is discontinuous. This phenomenon indicates that solution is multiple on the necking plane. Plastic instability is known to result from the loss of uniqueness. Hence, the shear band should be analyzed in relation to plastic instability. However, the criterion of plastic instability in soil bas not been investigated in as much detail, as in metal, and attention has rarely been paid to it in the analysis of shear banding. In this study, the comprehensive criterion of plastic instability is discussed and its necessary and sufficient condition is investigated using Cam-clay model. Our previous study on the mode of shear banding showed that only two modes under plane strain rate are parmissible for conformation of the discontinuous velocity gradient on the necking plane. Taking this into account, the criterion consists of three cases, that is, a statical case and two kinematical cases. These cases are characterized by h=0 where h means the hardening modulus, and the plane strain rate censtraint is added to in the kinematical cases. Furthermore, it is shown that the shear band cannot make any angle other than 45 degrees from the principal compressive axis, even if the yield locus on the deviatoric plane is modified.