Steady-state shear-bands in thermo-plasticity. I: Vanishing yield stress (Q1205005)

This paper concerns the construction and stability properties of steady- state solutions of a system of partial differential equations that model simple shearing of a slab of thermo-plastic material. The class of constitutive laws that give rise to a variational formulation of the steady-state problem is identified, and a phase-plane argument is used to construct time-independent solutions that may be interpreted as steady- state shear-bands. Our variational framework captures several commonly adopted constitutive laws. Techniques from bifurcation theory for variational problems are applied to classify stable and unstable solutions.