Localization in inelastic rate dependent shearing deformations

TL;DR

This paper investigates shear band formation in metals under high strain rates, demonstrating how strain softening and rate sensitivity lead to instability and localized deformation through analytical and numerical methods.

Contribution

It introduces a nonlinear model capturing shear band formation, combining linearized analysis and self-similar solutions to explain localization phenomena.

Findings

Strain softening and rate sensitivity induce Turing instability.

Constructed explicit shear localizing solutions via heteroclinic orbits.

Numerical analysis supports the formation of shear bands in the model.

Abstract

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