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Metals deformed at high strain rates can exhibit failure through formation ofshear bands, a phenomenon often attributed to Hadamard instability andlocalization of the strain into an emerging coherent structure. We verifyformation of shear bands for a nonlinear model exhibiting strain softening andstrain rate sensitivity. The effects of strain softening and strain ratesensitivity are first assessed by linearized analysis, indicating that thecombined effect leads to Turing instability. For the nonlinear model a class ofself-similar solutions is constructed, that depicts a coherent localizingstructure and the formation of a shear band. This solution is associated to aheteroclinic orbit of a dynamical system. The orbit is constructed numericallyand yields explicit shear localizing solutions.

Localization in inelastic rate dependent shearing deformations