DOES A SHEAR-BAND RESULT FROM A THERMAL-EXPLOSION

Based on results of computer simulations using the numerical method of lines, a simplified one-dimensional reaction-diffusion type of model, with an Arrhenius-type model for the plastic flow surface, is present ed for the localization of thermoelastic-plastic shear in ductile soli ds into an adiabatic shear band at high strain rate. This model is sho wn to share a number of similarities with a model of thermal reaction in a rigid solid explosive. Using small strain-rate-sensitivity asympt otics, which is analogous to high activation-energy asymptotics in the mathematical theory of combustion, it is shown there is an analogue i n the mathematical theory of plasticity of the ignition problem in che mical combustion. This raises the interesting question: Does an adiaba tic shear band result from a thermal explosion?