The Phenomenon of Shear Strain Localization in Dynamic Viscoplasticity

This article addresses shear flow localization during high rates of deformation of thermal viscoplastic materials. An overview of several efforts towards an improved understanding of shear band formation is given. This paper aims at extracting a unified framework towards the analysis of shear band formation for the considered class of deformations. For this purpose, we present a number of rigorous exact solutions for the one–dimensional simple shearing deformation of a general class of thermal viscoplastic material response. These solutions are used as benchmarks for the validation of both analytical and computational procedures. The interactive roles of inertia, rate–sensitivity, heat conduction, perturbation geometry, boundary conditions, thermal softening, strain hardening and constitutive description as regards the initiation and further intensification of flow localization are thoroughly addressed. We also examine the delicate questions concerning the notion of shear localization and the related mathematical characterization, length and time scales as well as the connection between localization and catastrophic failure.