Shearing of materials exhibiting thermal softening or temperature dependent viscosity

Abstract

We consider the adiabatic shearing of an incompressible non-Newtonian liquid with temperature dependent viscosity, subjected to steady shearing of the boundary. Identical equations govern the plastic shearing of a solid exhibiting thermal softening and strain rate sensitivity with constitutive relation obeying a certain power law. We establish that every classical solution approaches a uniform shearing solution as t → + ∞ t \to + \infty at specific rates of convergence. Therefore, no shear bands formation is predicted for materials of this type.