Formation and Development of Shear Bands in Granular Material

A system of equations modeling antiplane shear in a granular material is considered. The model includes the possibility of localization of strain, and the subsequent development of shear bands. This behavior is captured in our analysis of the Riemann initial value problem, in which an initial discontinuity propagates as a combination of moving waves and a stationary shear band. The analysis is verified by numerical results obtained with a Godunov method including adaptive mesh refinement. 1. Introduction We consider a model [4] for dynamic deformations of granular materials which allows for the localization of flow and the consequent development of shear bands. We focus on Riemann initial value problems in one space dimension that include a shear band. An unusual feature of the solutions is that they are not scale invariant. The overall structure of the solution (shown in Figure 1) is that the material unloads elastically between the shear band and a free boundary that propagates int..