Numerical Computations For Shear Bands in an Antiplane Shear Model

We study numerically a model for shear bands that is loosely based on anti-plane shearing of granular material. In the model, a shear band is idealized to a jump discontinuity in the solution to the dynamic PDE. We do not explicitly incorporate small scale eeects within the shear band into the model{rather at the shear band we impose a jump condition which includes a length parameter modeling the grain diameter. At this level of approximation, we study in several cases the process by which shear bands rst form and subsequently develop, including the growth of the unloading region containing the shear band(s). Our computations use a Godunov method, based on solving appropriate Riemann problems. In some cases, depending on the size of the jump, the Riemann problems under study do not admit a similarity solution because scale invariance is violated by the jump condition at the shear band. This novel feature adds mathematical interest to the present computations.