Localization and Shear Bands in High Strain-rate Plasticity

This article is devoted to the explanation of the onset of localization and the formation of shear bands in high strain-rate plasticity of metals. We employ the Arrhenius constitutive model and show Hadamard instability for the linearized problem. For the nonlinear model, using an asymptotic procedure motivated by the theory of relaxation and the Chapman-Enskog expansion, we derive an effective equation for the evolution of the strain rate, which is backward parabolic with a small stabilizing fourth order correction. We construct self-similar solutions that describe the self-organization into a localized solution starting from well prepared data.