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Finite element analysis of geometrically necessary dislocations in crystal plasticity

Hurtado, Daniel E. and Ortiz, Michael (2013) Finite element analysis of geometrically necessary dislocations in crystal plasticity. International Journal for Numerical Methods in Engineering, 93 (1). pp. 66-79. ISSN 0029-5981. doi:10.1002/nme.4376. https://resolver.caltech.edu/CaltechAUTHORS:20130115-101157040

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Abstract

We present a finite element method for the analysis of ductile crystals whose energy depends on the density of geometrically necessary dislocations (GNDs). We specifically focus on models in which the energy of the GNDs is assumed to be proportional to the total variation of the slip strains. In particular, the GND energy is homogeneous of degree one in the slip strains. Such models indeed arise from rigorous multiscale analysis as the macroscopic limit of discrete dislocation models or from phenomenological considerations such as a line-tension approximation for the dislocation self-energy. The incorporation of internal variable gradients into the free energy of the system renders the constitutive model non-local. We show that an equivalent free-energy functional, which does not depend on internal variable gradients, can be obtained by exploiting the variational definition of the total variation. The reformulation of the free energy comes at the expense of auxiliary variational problems, which can be efficiently solved using finite element approximations. The addition of surface terms in the formulation of the free energy results in additional boundary conditions for the internal variables. The proposed framework is verified by way of numerical convergence tests, and simulations of three-dimensional problems are presented to showcase its applicability. A performance analysis shows that the proposed framework solves strain-gradient plasticity problems in computing times of the order of local plasticity simulations, making it a promising tool for non-local crystal plasticity three-dimensional large-scale simulations.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/nme.4376DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/nme.4376/abstractPublisherArticle
ORCID:
AuthorORCID
Ortiz, Michael0000-0001-5877-4824
Additional Information:© 2012 John Wiley & Sons, Ltd. Received 18 November 2011; Revised 22 April 2012; Accepted 18 May 2012. Article first published online: 5 Jun. 2012. The authors gratefully acknowledge the support of the US Department of Energy National Nuclear Security Administration through Caltech’s PSAAP Center for the Predictive Modeling and Simulation of High-Energy Density Dynamic Response of Materials under award number DE-FC52-08NA28613. DH also acknowledges the financial support of Conicyt Chile through their science and technology fellowship.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE) National Nuclear Security AdministrationDE-FC52-08NA28613
Comisión Nacional de Investigación Científica y Tecnológica (CONICYT)UNSPECIFIED
Subject Keywords:strain-gradient plasticity; non-local crystal plasticity; size effects; total variation; finite elements
Issue or Number:1
DOI:10.1002/nme.4376
Record Number:CaltechAUTHORS:20130115-101157040
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130115-101157040
Official Citation:Hurtado, D. E. and Ortiz, M. (2013), Finite element analysis of geometrically necessary dislocations in crystal plasticity. Int. J. Numer. Meth. Engng., 93: 66–79. doi: 10.1002/nme.4376
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36381
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:15 Jan 2013 22:01
Last Modified:09 Nov 2021 23:21

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