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Incompatible strain gradient elasticity of Mindlin type: screw and edge dislocations

Lazar, Markus 1
1 Institut für Technische Mechanik (ITM), Karlsruher Institut für Technologie (KIT)

Abstract:
The fundamental problem of dislocations in incompatible isotropic strain gradient elasticity theory of Mindlin type, unsolved for more than half a century, is solved in this work. Incompatible strain gradient elasticity of Mindlin type is the generalization of Mindlin’s compatible strain gradient elasticity including plastic fields providing in this way a proper eigenstrain framework for the study of defects like dislocations. Exact analytical solutions for the displacement fields, elastic distortions, Cauchy stresses, plastic distortions and dislocation densities of screw and edge dislocations are derived. For the numerical analysis of the dislocation fields, elastic constants and gradient elastic constants have been used taken from ab initio DFT calculations. The displacement, elastic distortion, plastic distortion and Cauchy stress fields of screw and edge dislocations are non-singular, finite, and smooth. The dislocation fields of a screw dislocation depend on one characteristic length, whereas the dislocation fields of an edge dislocation depend on up to three characteristic lengths. For a screw dislocation, the dislocation fields obtained in incompatible strain gradient elasticity of Mindlin type agree with the corresponding ones in simplified incompatible strain gradient elasticity. ... mehr


Verlagsausgabe §
DOI: 10.5445/IR/1000135461
Veröffentlicht am 19.07.2021
Originalveröffentlichung
DOI: 10.1007/s00707-021-02999-2
Scopus
Zitationen: 7
Web of Science
Zitationen: 6
Dimensions
Zitationen: 6
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Technische Mechanik (ITM)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 0001-5970, 1619-6937
KITopen-ID: 1000135461
Erschienen in Acta mechanica
Verlag Springer
Vorab online veröffentlicht am 28.06.2021
Nachgewiesen in Dimensions
Web of Science
Scopus
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