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Title: A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains

Abstract

In this study, we present a field formulation for defects that draws from the classical representation of the cores as force dipoles. We write these dipoles as singular distributions. Exploiting the key insight that the variational setting is the only appropriate one for the theory of distributions, we arrive at universally applicable weak forms for defects in nonlinear elasticity. Remarkably, the standard, Galerkin finite element method yields numerical solutions for the elastic fields of defects that, when parameterized suitably, match very well with classical, linearized elasticity solutions. The true potential of our approach, however, lies in its easy extension to generate solutions to elastic fields of defects in the regime of nonlinear elasticity, and even more notably for Toupin's theory of gradient elasticity at finite strains (Toupin Arch. Ration. Mech. Anal., 11 (1962) 385). In computing these solutions we adopt recent numerical work on an isogeometric analytic framework that enabled the first three-dimensional solutions to general boundary value problems of Toupin's theory (Rudraraju et al. Comput. Methods Appl. Mech. Eng., 278 (2014) 705). We first present exhaustive solutions to point defects, edge and screw dislocations, and a study on the energetics of interacting dislocations. Then, to demonstrate the generality andmore » potential of our treatment, we apply it to other complex dislocation configurations, including loops and low-angle grain boundaries.« less

Authors:
 [1];  [1];  [1]
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  1. Univ. of Michigan, Ann Arbor, MI (United States)
Publication Date:
Research Org.:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1332709
Alternate Identifier(s):
OSTI ID: 1432113
Grant/Contract Number:  
SC0008637; #DE-SC0008637
Resource Type:
Accepted Manuscript
Journal Name:
Journal of the Mechanics and Physics of Solids
Additional Journal Information:
Journal Volume: 94; Journal Issue: C; Journal ID: ISSN 0022-5096
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Wang, Z., Rudraraju, S., and Garikipati, K. A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains. United States: N. p., 2016. Web. doi:10.1016/j.jmps.2016.03.028.
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Wang, Z., Rudraraju, S., & Garikipati, K. A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains. United States. https://doi.org/10.1016/j.jmps.2016.03.028
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Wang, Z., Rudraraju, S., and Garikipati, K. Mon . "A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains". United States. https://doi.org/10.1016/j.jmps.2016.03.028. https://www.osti.gov/servlets/purl/1332709.
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@article{osti_1332709,
title = {A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains},
author = {Wang, Z. and Rudraraju, S. and Garikipati, K.},
abstractNote = {In this study, we present a field formulation for defects that draws from the classical representation of the cores as force dipoles. We write these dipoles as singular distributions. Exploiting the key insight that the variational setting is the only appropriate one for the theory of distributions, we arrive at universally applicable weak forms for defects in nonlinear elasticity. Remarkably, the standard, Galerkin finite element method yields numerical solutions for the elastic fields of defects that, when parameterized suitably, match very well with classical, linearized elasticity solutions. The true potential of our approach, however, lies in its easy extension to generate solutions to elastic fields of defects in the regime of nonlinear elasticity, and even more notably for Toupin's theory of gradient elasticity at finite strains (Toupin Arch. Ration. Mech. Anal., 11 (1962) 385). In computing these solutions we adopt recent numerical work on an isogeometric analytic framework that enabled the first three-dimensional solutions to general boundary value problems of Toupin's theory (Rudraraju et al. Comput. Methods Appl. Mech. Eng., 278 (2014) 705). We first present exhaustive solutions to point defects, edge and screw dislocations, and a study on the energetics of interacting dislocations. Then, to demonstrate the generality and potential of our treatment, we apply it to other complex dislocation configurations, including loops and low-angle grain boundaries.},
doi = {10.1016/j.jmps.2016.03.028},
journal = {Journal of the Mechanics and Physics of Solids},
number = C,
volume = 94,
place = {United States},
year = {Mon May 16 00:00:00 EDT 2016},
month = {Mon May 16 00:00:00 EDT 2016}
}
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https://doi.org/10.1016/j.jmps.2016.03.028
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