NUMERICAL COMPUTATIONS FOR SHEAR BANDS IN AN ANTIPLANE SHEAR MODEL

WE STUDY NUMERICALLY a model for shear bands that is loosely based on antiplane 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 effects within this shea r band into the model - rather at the shear band we impose a jump cond ition which includes a length parameter modeling the grain diameter. A t this level of approximation, we study in several cases the process b y which shear bands first form and subsequently develop, including the growth of the unloading region containing the shear band(s). Our comp utations use a Godunov method, based oil solving appropriate Riemann p roblems. 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.