THE INFLUENCE OF MATERIAL NONUNIFORMITY PRECEDING SHEAR-BAND FORMATION IN A MODEL FOR GRANULAR FLOW

The onset of shear-banding in a deforming elastoplastic solid has been linked to change of type of the governing partial differential equati ons. If uniform material properties are assumed, then (i) deformations prior to shear-banding are uniform, and (ii) the onset of shear-bandi ng occurs simultaneously at all points in the sample. In this paper we study, in the context of a model for anti-plane shearing of a granula r material, the effect of a small variation in material properties (e. g. in yield strength) within the sample. Using matched asymptotic expa nsions, we find that (i) the deformation is extremely non-uniform in a short time period immediately preceding the formation of shear-bands; and (ii) generically, a shear-band forms at a single location in the sample.