Numerical implementation of static Field Dislocation Mechanics theory for periodic media
Identifieur interne : 000527 ( PascalFrancis/Checkpoint ); précédent : 000526; suivant : 000528Numerical implementation of static Field Dislocation Mechanics theory for periodic media
Auteurs : R. Brenner [France] ; A. J. Beaudoin [États-Unis] ; P. Suquet [France] ; A. Acharya [États-Unis]Source :
- Philosophical magazine : (2003. Print) [ 1478-6435 ] ; 2014.
Descripteurs français
- Pascal (Inist)
- Implémentation, Théorie champ, Dislocation, Microstructure, Module élasticité, Champ périodique, Déformation élastique, Distorsion, Transformation Fourier, Contrainte interne, Propriété mécanique, Champ interne, Distribution contrainte, Répartition spatiale, Matériau hétérogène, Effet contrainte, Solution analytique, Méthode analytique, 6172L, 6220D, 6860B, 4335N.
English descriptors
- KwdEn :
- Analytical method, Analytical solution, Dislocations, Distortion, Elastic deformation, Elastic modulus, Field theories, Fourier transformation, Implementation, Inhomogeneous materials, Internal field, Internal stresses, Mechanical properties, Microstructure, Periodic field, Spatial distribution, Stress distribution, Stress effects.
Abstract
This paper investigates the implementation of Field Dislocation Mechanics (FDM) theory for media with a periodic microstructure (i.e. the Nye dislocation tensor and the elastic moduli tensor are considered as spatially periodic continuous fields). In this context, the uniqueness of the stress and elastic distortion fields is established. This allows to propose an efficient numerical scheme based on Fourier transform to compute the internal stress field, for a given spatial distribution of dislocations and applied macroscopic stress. This numerical implementation is assessed by comparison with analytical solutions for homogeneous as well as heterogeneous elastic media. A particular insight is given to the critical case of stress-free dislocation microstructures which represent equilibrium solutions of the FDM theory.
Affiliations:
- France, États-Unis
- Pennsylvanie, Provence-Alpes-Côte d'Azur, Île-de-France
- Marseille, Paris, Pittsburgh
- Université Carnegie-Mellon
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Acharya</name><affiliation wicri:level="4"><inist:fA14 i1="04"><s1>Department of Civil and Environmental Engineering, Carnegie Mellon University, 103 Porter Hall</s1><s2>Pittsburgh, PA 15213</s2><s3>USA</s3><sZ>4 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Pittsburgh, PA 15213</wicri:noRegion><orgName type="university">Université Carnegie-Mellon</orgName><placeName><settlement type="city">Pittsburgh</settlement><region type="state">Pennsylvanie</region></placeName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">14-0164782</idno><date when="2014">2014</date><idno type="stanalyst">PASCAL 14-0164782 INIST</idno><idno type="RBID">Pascal:14-0164782</idno><idno type="wicri:Area/PascalFrancis/Corpus">000960</idno><idno type="wicri:Area/PascalFrancis/Curation">003C70</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000527</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000527</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Numerical implementation of static Field Dislocation Mechanics theory for periodic media</title><author><name sortKey="Brenner, R" sort="Brenner, R" uniqKey="Brenner R" first="R." last="Brenner">R. Brenner</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean le Rond d'Alembert</s1><s2>75005, Paris</s2><s3>FRA</s3><sZ>1 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region">Île-de-France</region><region type="old region">Île-de-France</region><settlement type="city">Paris</settlement></placeName></affiliation></author><author><name sortKey="Beaudoin, A J" sort="Beaudoin, A J" uniqKey="Beaudoin A" first="A. J." last="Beaudoin">A. J. Beaudoin</name><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St.</s1><s2>Urbana, IL 61801</s2><s3>USA</s3><sZ>2 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Urbana, IL 61801</wicri:noRegion></affiliation></author><author><name sortKey="Suquet, P" sort="Suquet, P" uniqKey="Suquet P" first="P." last="Suquet">P. Suquet</name><affiliation wicri:level="1"><inist:fA14 i1="03"><s1>Laboratoire de Mécanique et d'Acoustique, CNRS, UPR 7051, Aix Marseille University, Centrale Marseille, 31 Chemin Joseph Aiguier</s1><s2>13402 Marseille</s2><s3>FRA</s3><sZ>3 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>13402 Marseille</wicri:noRegion><placeName><settlement type="city">Marseille</settlement><region type="région" nuts="2">Provence-Alpes-Côte d'Azur</region></placeName></affiliation></author><author><name sortKey="Acharya, A" sort="Acharya, A" uniqKey="Acharya A" first="A." last="Acharya">A. Acharya</name><affiliation wicri:level="4"><inist:fA14 i1="04"><s1>Department of Civil and Environmental Engineering, Carnegie Mellon University, 103 Porter Hall</s1><s2>Pittsburgh, PA 15213</s2><s3>USA</s3><sZ>4 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Pittsburgh, PA 15213</wicri:noRegion><orgName type="university">Université Carnegie-Mellon</orgName><placeName><settlement type="city">Pittsburgh</settlement><region type="state">Pennsylvanie</region></placeName></affiliation></author></analytic><series><title level="j" type="main">Philosophical magazine : (2003. Print)</title><title level="j" type="abbreviated">Philos. mag. : (2003, Print)</title><idno type="ISSN">1478-6435</idno><imprint><date when="2014">2014</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Philosophical magazine : (2003. Print)</title><title level="j" type="abbreviated">Philos. mag. : (2003, Print)</title><idno type="ISSN">1478-6435</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Analytical method</term><term>Analytical solution</term><term>Dislocations</term><term>Distortion</term><term>Elastic deformation</term><term>Elastic modulus</term><term>Field theories</term><term>Fourier transformation</term><term>Implementation</term><term>Inhomogeneous materials</term><term>Internal field</term><term>Internal stresses</term><term>Mechanical properties</term><term>Microstructure</term><term>Periodic field</term><term>Spatial distribution</term><term>Stress distribution</term><term>Stress effects</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Implémentation</term><term>Théorie champ</term><term>Dislocation</term><term>Microstructure</term><term>Module élasticité</term><term>Champ périodique</term><term>Déformation élastique</term><term>Distorsion</term><term>Transformation Fourier</term><term>Contrainte interne</term><term>Propriété mécanique</term><term>Champ interne</term><term>Distribution contrainte</term><term>Répartition spatiale</term><term>Matériau hétérogène</term><term>Effet contrainte</term><term>Solution analytique</term><term>Méthode analytique</term><term>6172L</term><term>6220D</term><term>6860B</term><term>4335N</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">This paper investigates the implementation of Field Dislocation Mechanics (FDM) theory for media with a periodic microstructure (i.e. the Nye dislocation tensor and the elastic moduli tensor are considered as spatially periodic continuous fields). In this context, the uniqueness of the stress and elastic distortion fields is established. This allows to propose an efficient numerical scheme based on Fourier transform to compute the internal stress field, for a given spatial distribution of dislocations and applied macroscopic stress. This numerical implementation is assessed by comparison with analytical solutions for homogeneous as well as heterogeneous elastic media. A particular insight is given to the critical case of stress-free dislocation microstructures which represent equilibrium solutions of the FDM theory.</div></front></TEI><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>1478-6435</s0></fA01><fA03 i2="1"><s0>Philos. mag. : (2003, Print)</s0></fA03><fA05><s2>94</s2></fA05><fA06><s2>16-18</s2></fA06><fA08 i1="01" i2="1" l="ENG"><s1>Numerical implementation of static Field Dislocation Mechanics theory for periodic media</s1></fA08><fA11 i1="01" i2="1"><s1>BRENNER (R.)</s1></fA11><fA11 i1="02" i2="1"><s1>BEAUDOIN (A. J.)</s1></fA11><fA11 i1="03" i2="1"><s1>SUQUET (P.)</s1></fA11><fA11 i1="04" i2="1"><s1>ACHARYA (A.)</s1></fA11><fA14 i1="01"><s1>Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean le Rond d'Alembert</s1><s2>75005, Paris</s2><s3>FRA</s3><sZ>1 aut.</sZ></fA14><fA14 i1="02"><s1>Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St.</s1><s2>Urbana, IL 61801</s2><s3>USA</s3><sZ>2 aut.</sZ></fA14><fA14 i1="03"><s1>Laboratoire de Mécanique et d'Acoustique, CNRS, UPR 7051, Aix Marseille University, Centrale Marseille, 31 Chemin Joseph Aiguier</s1><s2>13402 Marseille</s2><s3>FRA</s3><sZ>3 aut.</sZ></fA14><fA14 i1="04"><s1>Department of Civil and Environmental Engineering, Carnegie Mellon University, 103 Porter Hall</s1><s2>Pittsburgh, PA 15213</s2><s3>USA</s3><sZ>4 aut.</sZ></fA14><fA20><s1>1764-1787</s1></fA20><fA21><s1>2014</s1></fA21><fA23 i1="01"><s0>ENG</s0></fA23><fA43 i1="01"><s1>INIST</s1><s2>134A3</s2><s5>354000502771520030</s5></fA43><fA44><s0>0000</s0><s1>© 2014 INIST-CNRS. All rights reserved.</s1></fA44><fA45><s0>32 ref.</s0></fA45><fA47 i1="01" i2="1"><s0>14-0164782</s0></fA47><fA60><s1>P</s1></fA60><fA61><s0>A</s0></fA61><fA64 i1="01" i2="1"><s0>Philosophical magazine : (2003. 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A particular insight is given to the critical case of stress-free dislocation microstructures which represent equilibrium solutions of the FDM theory.</s0></fC01><fC02 i1="01" i2="3"><s0>001B60B20D</s0></fC02><fC02 i1="02" i2="3"><s0>001B60A72L</s0></fC02><fC02 i1="03" i2="3"><s0>001B60H60B</s0></fC02><fC03 i1="01" i2="3" l="FRE"><s0>Implémentation</s0><s5>01</s5></fC03><fC03 i1="01" i2="3" l="ENG"><s0>Implementation</s0><s5>01</s5></fC03><fC03 i1="02" i2="3" l="FRE"><s0>Théorie champ</s0><s5>02</s5></fC03><fC03 i1="02" i2="3" l="ENG"><s0>Field theories</s0><s5>02</s5></fC03><fC03 i1="03" i2="3" l="FRE"><s0>Dislocation</s0><s5>03</s5></fC03><fC03 i1="03" i2="3" l="ENG"><s0>Dislocations</s0><s5>03</s5></fC03><fC03 i1="04" i2="3" l="FRE"><s0>Microstructure</s0><s5>04</s5></fC03><fC03 i1="04" i2="3" l="ENG"><s0>Microstructure</s0><s5>04</s5></fC03><fC03 i1="05" i2="3" l="FRE"><s0>Module élasticité</s0><s5>05</s5></fC03><fC03 i1="05" i2="3" l="ENG"><s0>Elastic modulus</s0><s5>05</s5></fC03><fC03 i1="06" i2="X" l="FRE"><s0>Champ périodique</s0><s5>06</s5></fC03><fC03 i1="06" i2="X" l="ENG"><s0>Periodic field</s0><s5>06</s5></fC03><fC03 i1="06" i2="X" l="SPA"><s0>Campo periódico</s0><s5>06</s5></fC03><fC03 i1="07" i2="3" l="FRE"><s0>Déformation élastique</s0><s5>07</s5></fC03><fC03 i1="07" i2="3" l="ENG"><s0>Elastic deformation</s0><s5>07</s5></fC03><fC03 i1="08" i2="3" l="FRE"><s0>Distorsion</s0><s5>08</s5></fC03><fC03 i1="08" i2="3" l="ENG"><s0>Distortion</s0><s5>08</s5></fC03><fC03 i1="09" i2="3" l="FRE"><s0>Transformation Fourier</s0><s5>09</s5></fC03><fC03 i1="09" i2="3" l="ENG"><s0>Fourier transformation</s0><s5>09</s5></fC03><fC03 i1="10" i2="3" l="FRE"><s0>Contrainte interne</s0><s5>10</s5></fC03><fC03 i1="10" i2="3" l="ENG"><s0>Internal stresses</s0><s5>10</s5></fC03><fC03 i1="11" i2="3" l="FRE"><s0>Propriété mécanique</s0><s5>11</s5></fC03><fC03 i1="11" i2="3" l="ENG"><s0>Mechanical properties</s0><s5>11</s5></fC03><fC03 i1="12" i2="X" l="FRE"><s0>Champ interne</s0><s5>12</s5></fC03><fC03 i1="12" i2="X" l="ENG"><s0>Internal field</s0><s5>12</s5></fC03><fC03 i1="12" i2="X" l="SPA"><s0>Campo interno</s0><s5>12</s5></fC03><fC03 i1="13" i2="3" l="FRE"><s0>Distribution contrainte</s0><s5>13</s5></fC03><fC03 i1="13" i2="3" l="ENG"><s0>Stress distribution</s0><s5>13</s5></fC03><fC03 i1="14" i2="3" l="FRE"><s0>Répartition spatiale</s0><s5>14</s5></fC03><fC03 i1="14" i2="3" l="ENG"><s0>Spatial distribution</s0><s5>14</s5></fC03><fC03 i1="15" i2="3" l="FRE"><s0>Matériau hétérogène</s0><s5>15</s5></fC03><fC03 i1="15" i2="3" l="ENG"><s0>Inhomogeneous materials</s0><s5>15</s5></fC03><fC03 i1="16" i2="3" l="FRE"><s0>Effet contrainte</s0><s5>29</s5></fC03><fC03 i1="16" i2="3" l="ENG"><s0>Stress effects</s0><s5>29</s5></fC03><fC03 i1="17" i2="3" l="FRE"><s0>Solution analytique</s0><s5>30</s5></fC03><fC03 i1="17" i2="3" l="ENG"><s0>Analytical solution</s0><s5>30</s5></fC03><fC03 i1="18" i2="X" l="FRE"><s0>Méthode analytique</s0><s5>31</s5></fC03><fC03 i1="18" i2="X" l="ENG"><s0>Analytical method</s0><s5>31</s5></fC03><fC03 i1="18" i2="X" l="SPA"><s0>Método analítico</s0><s5>31</s5></fC03><fC03 i1="19" i2="3" l="FRE"><s0>6172L</s0><s4>INC</s4><s5>71</s5></fC03><fC03 i1="20" i2="3" l="FRE"><s0>6220D</s0><s4>INC</s4><s5>72</s5></fC03><fC03 i1="21" i2="3" l="FRE"><s0>6860B</s0><s4>INC</s4><s5>73</s5></fC03><fC03 i1="22" i2="3" l="FRE"><s0>4335N</s0><s4>INC</s4><s5>74</s5></fC03><fN21><s1>202</s1></fN21><fN44 i1="01"><s1>OTO</s1></fN44><fN82><s1>OTO</s1></fN82></pA></standard></inist><affiliations><list><country><li>France</li><li>États-Unis</li></country><region><li>Pennsylvanie</li><li>Provence-Alpes-Côte d'Azur</li><li>Île-de-France</li></region><settlement><li>Marseille</li><li>Paris</li><li>Pittsburgh</li></settlement><orgName><li>Université Carnegie-Mellon</li></orgName></list><tree><country name="France"><region name="Île-de-France"><name sortKey="Brenner, R" sort="Brenner, R" uniqKey="Brenner R" first="R." last="Brenner">R. Brenner</name></region><name sortKey="Suquet, P" sort="Suquet, P" uniqKey="Suquet P" first="P." last="Suquet">P. Suquet</name></country><country name="États-Unis"><noRegion><name sortKey="Beaudoin, A J" sort="Beaudoin, A J" uniqKey="Beaudoin A" first="A. J." last="Beaudoin">A. J. Beaudoin</name></noRegion><name sortKey="Acharya, A" sort="Acharya, A" uniqKey="Acharya A" first="A." last="Acharya">A. Acharya</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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