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Vestnik Samarskogo Universiteta. Estestvenno-Nauchnaya Seriya, 2022, Volume 28, Issue 1-2, Pages 55–73
DOI: https://doi.org/10.18287/2541-7525-2022-28-1-2-55-73
(Mi vsgu677)
 

This article is cited in 1 scientific paper (total in 1 paper)

Mechanics

Evolution of the field of distributed defects in a crystal during contact interaction with a system of rigid stamps

T. N. Lycheva, S. A. Lychev

Ishlinsky Institute for Problems in Mechanics RAS, Moscow, Russian Federation (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: The article discusses the mathematical modeling for the evolution of the stress-strain state and fields of defects in crystals during their contact interaction with a system of rigid punches. From a macroscopic point of view, the redistribution of defects is characterized by inelastic (viscoplastic) deformation, and therefore the processes under study can be classified as elastic-viscoplastic. Elastic and inelastic deformations are assumed to be finite. To take into account inelastic deformations, it is proposed to use a differential-geometric approach, in which the evolution of the fields of distributed defects is completely characterized by measures of incompatible deformations and quantified by material connection invariants. This connection is generated by a non-Euclidean metric, which, in turn, is given by a field of symmetric linear mappings that define (inconsistent) deformations of the crystal. Since the development of local deformations depends both on the contact interaction at the boundary and on the distribution of defects in the bulk of the crystal, the simulation problem turns out to be coupled. It is assumed that the local change in the defect density is determined by the first-order Alexander Haasen Sumino evolutionary law, which takes into account the deviatoric part of the stress field. An iterative algorithm has been developed to find coupled fields of local deformations and defects density. The numerical analysis for the model problem was provided for a silicon crystal in the form of a parallelepiped, one face of which is rigidly fixed, and a system of rigid stamps acts on the opposite face. The three-constant Mooney Rivlin potential was used to model the local elastic response.
Keywords: distributed defects, finite strains, hyperelasticity, strain incompatibility, evolution of defect fields, contact interaction, finite elements.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00400 А
The work was supported by the RFBR grant 20-01-00400 A.
Received: 19.04.2022
Revised: 02.06.2022
Accepted: 14.11.2022
Document Type: Article
UDC: 512.531; 519.7
Language: Russian
Citation: T. N. Lycheva, S. A. Lychev, “Evolution of the field of distributed defects in a crystal during contact interaction with a system of rigid stamps”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 28:1-2 (2022), 55–73
Citation in format AMSBIB
\Bibitem{LycLyc22}
\by T.~N.~Lycheva, S.~A.~Lychev
\paper Evolution of the field of distributed defects in a crystal during contact interaction with a system of rigid stamps
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2022
\vol 28
\issue 1-2
\pages 55--73
\mathnet{http://mi.mathnet.ru/vsgu677}
\crossref{https://doi.org/10.18287/2541-7525-2022-28-1-2-55-73}
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  • https://www.mathnet.ru/eng/vsgu/v28/i1/p55
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Самарского государственного университета. Естественнонаучная серия
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    References:23
     
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