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Nonconvex energy minimization and dislocation structures in ductile single crystals

Ortiz, M. and Repetto, E. A. (1999) Nonconvex energy minimization and dislocation structures in ductile single crystals. Journal of the Mechanics and Physics of Solids, 47 (2). pp. 397-462. ISSN 0022-5096. doi:10.1016/S0022-5096(97)00096-3.

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Plastically deformed crystals are often observed to develop intricate dislocation patterns such as the labyrinth, mosaic, fence and carpet structures. In this paper, such dislocation structures are given an energetic interpretation with the aid of direct methods of the calculus of variations. We formulate the theory in terms of deformation fields and regard the dislocations as manifestations of the incompatibility of the plastic deformation gradient field. Within this framework, we show that the incremental displacements of inelastic solids follow as minimizers of a suitably defined pseudoelastic energy function. In crystals exhibiting latent hardening, the energy function is nonconvex and has wells corresponding to single-slip deformations. This favors microstructures consisting locally of single slip. Deformation microstructures constructed in accordance with this prescription are shown to be in correspondence with several commonly observed dislocation structures. Finally, we show that a characteristic length scale can be built into the theory by taking into account the self energy of the dislocations. The extended theory leads to scaling laws which appear to be in good qualitative and quantitative agreement with observation.

Item Type:Article
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Ortiz, M.0000-0001-5877-4824
Additional Information:© 1999 Elsevier. Received 1 June 1997, Revised 25 November 1997, Available online 4 March 1999. The support of the Office of Naval Research under grant N00014-96-1-0068 is gratefully acknowledged. We are grateful to R. V. Kohn for helpful discussions and suggestions.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-96-1-0068
Subject Keywords:A Dislocations; B Constitutive behavior; Principles; B Crystal plasticity; C Energy methods
Issue or Number:2
Record Number:CaltechAUTHORS:20171213-092048666
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Official Citation:M. Ortiz, E.a. Repetto, Nonconvex energy minimization and dislocation structures in ductile single crystals, In Journal of the Mechanics and Physics of Solids, Volume 47, Issue 2, 1999, Pages 397-462, ISSN 0022-5096, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83863
Deposited By: Lydia Suarez
Deposited On:13 Dec 2017 22:43
Last Modified:15 Nov 2021 20:14

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