Effect of Thermal Softening in Shearing of Strain-Rate Dependent Materials

摘要

This document considers the adiabatic plastic shearing of a strain-rate dependent material exhibiting thermal-softening and strain-hardening, subject to prescribed tractions at the boundaries. The relevant question is whether thermal-softening is capable o destabilizing the shearing deformation. The author establishes the existence of two thresholds, related to the degree of thermal-softening and strain-hardening, such that: Above the first threshold solutions stabilize, as t approaches Limit of, to a certain asymptotic solution; and, below the second threshold the temperature, strain and strain rate blow up in finite time. Next, the focus is on materials that do not exhibit strain dependence and find that between the two thresholds a milder form of instability occurs. For this class of materials we also exhibit initial data for which the corresponding solutions look like shear bands. Keywords: shear band formation.