Shear Stability, Instability and Localization of Materials Exhibiting Thermal Softening, Strain Rate Sensitivity and Strain Hardening

We consider the test-problem of simple shearing of a thermoviscoplastic solid subject to steady or time-dependent boundary velocities or shear forces. Previously derived stability and nonlocalization criteria are presented. The influence of boundary conditions on the time-asymptotic “solution,” the role of nonuniformities and the localization of plastic deformation are discussed. Finally, a perturbation analysis of homogeneous solution under steady boundary velocities or stresses of a material with a gradient-dependent flow stress is presented and “shear-banding” criteria are derived.