Jerrold Bebernes
Department of Applied Mathematics, University of Colorado, Boulder
Many materials exhibit narrow bands of plastic deformation under extreme loading conditions. These shear bands are observed in very thin zones and are regarded as a precursor to material failure. Shear band formation is caused by the heat generated in regions with high strain-rate loading. With insufficient time for the diffusion of this heat, a localized thermal softening of the material occurs, enhancing plastic flow in thin zones. Assuming a constitutive equation for the material to be of Maxwell type, a one-dimensional thermo-viscous model for shear bands has previously been considered. The thermo-viscoelastic versions of the model lead to a highly nonlocal and nonlinear parabolic equation. This model exhibits various possibilities for shear band formation.