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A discrete mechanics approach to dislocation dynamics in BCC crystals

Ramasubramaniam, A. and Ariza, M. P. and Ortiz, M. (2007) A discrete mechanics approach to dislocation dynamics in BCC crystals. Journal of the Mechanics and Physics of Solids, 55 (3). pp. 615-647. ISSN 0022-5096.

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A discrete mechanics approach to modeling the dynamics of dislocations in BCC single crystals is presented. Ideas are borrowed from discrete differential calculus and algebraic topology and suitably adapted to crystal lattices. In particular, the extension of a crystal lattice to a CW complex allows for convenient manipulation of forms and fields defined over the crystal. Dislocations are treated within the theory as energy-minimizing structures that lead to locally lattice-invariant but globally incompatible eigendeformations. The discrete nature of the theory eliminates the need for regularization of the core singularity and inherently allows for dislocation reactions and complicated topological transitions. The quantization of slip to integer multiples of the Burgers’ vector leads to a large integer optimization problem. A novel approach to solving this NP-hard problem based on considerations of metastability is proposed. A numerical example that applies the method to study the emanation of dislocation loops from a point source of dilatation in a large BCC crystal is presented. The structure and energetics of BCC screw dislocation cores, as obtained via the present formulation, are also considered and shown to be in good agreement with available atomistic studies. The method thus provides a realistic avenue for mesoscale simulations of dislocation based crystal plasticity with fully atomistic resolution.

Item Type:Article
Related URLs:
URLURL TypeDescription
Ariza, M. P.0000-0003-0266-0216
Ortiz, M.0000-0001-5877-4824
Additional Information:© 2006 Elsevier. Received 18 March 2006, Revised 10 August 2006, Accepted 12 August 2006, Available online 27 October 2006. We gratefully acknowledge the support of the Department of Energy through Caltech's ASC Center for the Simulation of the Dynamic Response of Materials.
Funding AgencyGrant Number
Department of Energy (DOE)UNSPECIFIED
Subject Keywords:Dislocation dynamics; Crystal plasticity; Discrete mechanics; Computational mechanics; Multiscale modeling
Issue or Number:3
Record Number:CaltechAUTHORS:20171121-135628923
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Official Citation:A. Ramasubramaniam, M.P. Ariza, M. Ortiz, A discrete mechanics approach to dislocation dynamics in BCC crystals, In Journal of the Mechanics and Physics of Solids, Volume 55, Issue 3, 2007, Pages 615-647, ISSN 0022-5096, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83404
Deposited By: Lydia Suarez
Deposited On:22 Nov 2017 19:10
Last Modified:09 Mar 2020 13:18

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