Mathematics

The formation of shear bands in metals has important implications to a variety of technological processes. These bands are observed in very thin zones and are generally regarded as a precuror to material failure. Shear band formation is caused by the heat generated in regions with highest strain rate. With insufficient time for diffusion of this heat, a localized thermal softening of the metal occurs which enhances plastic flow in a thin zone. This adiabatic strain localization can be modelled as nonlinear thermally activated reaction-diffusion equations. This leads to a class of nonlocal parabolic problems and their associated steady states. An analysis of these problems will be presented.