ON THE DYNAMIC SHEARING PROBLEM FOR RATE- AND TEMPERATURE-DEPENDENT MEDIA

A dynamic shearing problem for rate-and temperature-dependent media is considered using an elastic-viscoplastic constitutive law with thermal softening and without hardening. The local existence of the solution and the lower-semicontinuous dependence of the blow-up time upon the initial data are obtained. The homogeneous solution is introduced and the finite-time evolution of the perturbations of this solution is studied. A stability parameter which depends only on the homogeneous solution is introduced in order to give criteria for strain localization. Finally some numerical examples are presented.