Characterizing geometrically necessary dislocations using an elastic-plastic decomposition of Laplace stretch
type: Item
instance of: scholarly article
title: Characterizing geometrically necessary dislocations using an elastic-plastic decomposition of Laplace stretch
zbMATH Open document ID: 1478.53013
author: Sandipan Paul
author: Alan David Freed
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2021-05-14T00:00:00Z
review text: The paper studies the geometric dislocation density tensor and Burgers vector using an elastic-plastic decomposition of Laplace stretch which arises from a QR decomposition of the deformation gradient and allows for direct experimental measurement. The geometric dislocation density tensor is obtained using the classical argument of failure of a Burgers circuit in a suitable configuration, in which the deformation of the body is solely due to the movement of dislocations. The derived dislocation tensor is used as a measure of the torsion, i.e., incompatibility in the model space and vanishes when it is compatible. A balance law for geometric dislocations is derived taking into account the effect of the dislocation flux and source dislocations. The physical meaning of the plastic Laplace stretch, and consequently, of the derived geometric dislocation tensor proves to be particularly useful in the classification of dislocations. Finally, the significance of the dislocation density tensor is discussed. The derived geometric dislocation density tensor could be specifically useful in developing a strain-gradient and size-dependent theory of plasticity. With its 22 pages and 49 references the text provides a detailed and mathematically rigorous study of the problem, begining with an introduction including exhaustive systematic review of the corresponding scientific literature. Then, the authors revise the QR kinematics in a rather pedagogical manner, after which the configuration space is defined and its geometric properties are studied. In Section 5 the Burges vector is introduced while the following sections provide a balance law for geometrically necessary dislocations and classification results, as well as assessment of the significance of the derived dislocation density tensor.
reviewed by: Danail Brezov
Mathematics Subject Classification ID: 53A17
Mathematics Subject Classification ID: 53A35
Mathematics Subject Classification ID: 53B05
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 74A05
Mathematics Subject Classification ID: 74C15
zbMATH DE Number: 7348021
zbMATH Keywords: dislocations
zbMATH Keywords: incompatibility
zbMATH Keywords: torsion
zbMATH Keywords: Gram-Schmidt factorization
zbMATH Keywords: plasticity
MaRDI profile type: Publication
full work available at URL: s00033-020-01420-7
OpenAlex ID: W3095486276
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DOI: 10.1007/S00033-020-01420-7
description: scientific article; zbMATH DE number 7348021