Numerical solutions of shear localization in a finite slab

A straight forward numerical scheme is devised to solve the one-dimensional problem of shear localization in a finite slab. This scheme is much less computationally intensive than a full scale numerical solution. The scheme is developed by first employing asymptotic methods, based upon typical values of the material parameters, to reduce the problem. The reduced version of the problem is ultimately expressed as a coupled nonlinear system for the stress and temperature along the centerline of the slab. Since this system depends only upon the time variable, it can be discretized and solved with elementary numerical methods. The efficiency of the scheme is demonstrated by calculating the solution well into the post-localization stage for a variety of parameter values. The results illustrate the significance that elastic effects have during the late stages of shear band formation.