The growth of unstable thermoplastic shear with application to steady- wave shock compression in solids
type: Item
instance of: scholarly article
title: The growth of unstable thermoplastic shear with application to steady- wave shock compression in solids
zbMATH Open document ID: 0603.73042
DOI: 10.1016/0022-5096(87)90030-5
author: M. E. Kipp
author: Dennis E. Grady
published in: Journal of the Mechanics and Physics of Solids
publication date: 1987-01-01T00:00:00Z
review text: The catastrophic growth of unstable thermoplastic shear following the transition from homogeneous deformation to heterogeneous localized deformation through distributed shear banding is studied through approximate analytic and computational methods. The calculations provide expressions for shear band widths, spacing, catastrophic growth times and the rate of stress communication between shear bands. The optimum shear band width and spacing are found to be consistent with a minimum work principle. The model predicts that the product of the energy dissipated and the localization time in the shear localization process is invariant with respect to changes in the driving strain rate. Such behavior has been noted in the steady-wave shock compression of a number of solids. The calculations are applied to heterogeneous shear localization observed in the shock compression of aluminum.
Mathematics Subject Classification ID: 74C15
Mathematics Subject Classification ID: 74C20
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74A15
zbMATH DE Number: 3974427
zbMATH Keywords: Mott analysis
zbMATH Keywords: post bifurcation
zbMATH Keywords: thermal softening
zbMATH Keywords: one-dimensional Lagrangian finite difference wave propagation code
zbMATH Keywords: catastrophic growth of unstable thermoplastic shear
zbMATH Keywords: transition
zbMATH Keywords: homogeneous deformation
zbMATH Keywords: heterogeneous localized deformation
zbMATH Keywords: distributed shear banding
zbMATH Keywords: approximate analytic and computational methods
zbMATH Keywords: catastrophic growth times
zbMATH Keywords: rate of stress communication
zbMATH Keywords: optimum shear band width and spacing
zbMATH Keywords: minimum work principle
zbMATH Keywords: steady-wave shock compression
MaRDI profile type: Publication
full work available at URL: 0022-5096(87)90030-5
OpenAlex ID: W2001522502
cites work: Thermoplastic instability in simple shear
cites work: Approximate linear stability analysis of a model of adiabatic shear band formation
description: scientific article; zbMATH DE number 3974427