The motion of screw dislocations in crystalline materials undergoing antiplane shear: Glide, cross-slip, fine cross-slip
type: Item
instance of: scholarly article
title: The motion of screw dislocations in crystalline materials undergoing antiplane shear: Glide, cross-slip, fine cross-slip
zbMATH Open document ID: 0941.74006
author: Paolo Cermelli
author: Morton E. Gurtin
published in: Archive for Rational Mechanics and Analysis
publication date: 2000-08-07T00:00:00Z
review text: The authors discuss the motion of dislocations within the nonlinear theory of elasticity. In particular, focussing on the kinetics of screw dislocations in the case of finite antiplane shear, they present a fairly complete theory for the initiation and kinetics of glide and cross-slip motions. The theory is based essentially on the so-called configurational forces [cf. \textit{G. A. Maugin} and \textit{C. Trimarco}, Arch. Mech. 47, No. 1, 81-99 (1995; Zbl 0822.73005)], and on the exploitation of the balance law for such configurational forces in conjunction with a mechanical version of the second law of thermodynamics that accounts for the rate at which configurational forces perform work. This requires a careful discussion of energetic changes in control volumes containing dislocations, as energy itself may become infinite. An expression is recovered for the Peach-Koehler force within this framework. The principle of maximal dissipation (Hill-Mandel) is exploited in the formulation of the initiation criteria. Although the authors have a tendency to present many ideas and arguments as original, they largely build on the works of others, including contemporaries. The paper is unnecessarily discursive and long, (e.g., the introduction-summary itself is four pages long).
Mathematics Subject Classification ID: 74A60
Mathematics Subject Classification ID: 74E15
Mathematics Subject Classification ID: 74A45
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 1356109
zbMATH Keywords: nonlinear elasticity
zbMATH Keywords: kinetics of screw dislocations
zbMATH Keywords: finite antiplane shear
zbMATH Keywords: glide
zbMATH Keywords: cross-slip
zbMATH Keywords: configurational forces
zbMATH Keywords: balance law
zbMATH Keywords: second law of thermodynamics
zbMATH Keywords: Peach-Koehler force
zbMATH Keywords: principle of maximal dissipation
zbMATH Keywords: initiation criteria
reviewed by: Gérard A. Maugin
MaRDI profile type: Publication
full work available at URL: s002050050155
OpenAlex ID: W1998962009
DOI: 10.1007/S002050050155
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description: scientific article; zbMATH DE number 1356109