Simulations of a stretching bar using a plasticity model from the shear transformation zone theory

An Eulerian simulation framework is developed to study an elastoplastic model of amorphous materials that is based upon the shear transformation zone (STZ) theory developed by Langer and coworkers [1]. In this theory, plastic deformation is controlled by an effective temperature that measures the amount of configurational disorder in the material. The simulation is used to model ductile fracture in a stretching bar that initially contains a small notch, and the effects of many of the model parameters are examined. The simulation tracks the shape of the bar using the level set method. Within the bar, a finite difference discretization is employed that makes use of the essentially non-oscillatory (ENO) scheme. The system of equations is moderately stiff due to the presence of large elastic constants, and one of the key numerical challenges is to accurately track the level set and construct extrapolated field values for use in boundary conditions. A new approach to field extrapolation is discussed that is second-order accurate and requires a constant amount of work per grid point.