Field-theoretic approach for characterization the deformation of multicomponent polycrystalline materials
Most of inorganic structural materials (metallic alloys, ceramics, minerals etc.) are polycrystalline aggregates, consisted of macroscopically large quantity of single-crystal grains (crystallites). The mechanical behavior of the specimen of polycrystalline material is governed by the physical and m...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
Samara State Technical University
2013-12-01
|
Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
Online Access: | http://mi.mathnet.ru/eng/vsgtu1282 |
id |
doaj-5dec791bd4d54c59b993a07fbeb0faed |
---|---|
record_format |
Article |
spelling |
doaj-5dec791bd4d54c59b993a07fbeb0faed2020-11-25T02:02:27ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812013-12-014(33)869710.14498/vsgtu1282Field-theoretic approach for characterization the deformation of multicomponent polycrystalline materialsA. A. TashkinovV. E. ShavshukovMost of inorganic structural materials (metallic alloys, ceramics, minerals etc.) are polycrystalline aggregates, consisted of macroscopically large quantity of single-crystal grains (crystallites). The mechanical behavior of the specimen of polycrystalline material is governed by the physical and mechanical processes in the grains and interaction of the grains. Thus the deformation of polycrystalline material is a cooperative phenomenon typical for condensed matter physics and mechanics of heterogeneous materials. The passing of these processes depends on many parameters, including stress states of individual grains and its evolution during macrodeformation. In this paper we note a mathematical analogy between the equations of the mechanics of heterogeneous polycrystalline materials and the equations of quantum theory of particles scattering. This analogy allows to apply the methods of quantum field theory to solution of the equations of solid mechanics for heterogeneous media. We consider the application of Corringa-Kohn-Rostoker method, used in quantum theory for calculating wave function of electrons in metallic alloys, to elasticity of polycrystals. This approach allows, for instance, to calculate probability distribution density function for stresses in grains under arbitrary macrodeformation of polycrystal. Application of the method to classical problem of homogenization gives new formulae for the effective moduli of disordered polycrystalline medium.http://mi.mathnet.ru/eng/vsgtu1282 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
A. A. Tashkinov V. E. Shavshukov |
spellingShingle |
A. A. Tashkinov V. E. Shavshukov Field-theoretic approach for characterization the deformation of multicomponent polycrystalline materials Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
author_facet |
A. A. Tashkinov V. E. Shavshukov |
author_sort |
A. A. Tashkinov |
title |
Field-theoretic approach for characterization the deformation of multicomponent polycrystalline materials |
title_short |
Field-theoretic approach for characterization the deformation of multicomponent polycrystalline materials |
title_full |
Field-theoretic approach for characterization the deformation of multicomponent polycrystalline materials |
title_fullStr |
Field-theoretic approach for characterization the deformation of multicomponent polycrystalline materials |
title_full_unstemmed |
Field-theoretic approach for characterization the deformation of multicomponent polycrystalline materials |
title_sort |
field-theoretic approach for characterization the deformation of multicomponent polycrystalline materials |
publisher |
Samara State Technical University |
series |
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
issn |
1991-8615 2310-7081 |
publishDate |
2013-12-01 |
description |
Most of inorganic structural materials (metallic alloys, ceramics, minerals etc.) are polycrystalline aggregates, consisted of macroscopically large quantity of single-crystal grains (crystallites). The mechanical behavior of the specimen of polycrystalline material is governed by the physical and mechanical processes in the grains and interaction of the grains. Thus the deformation of polycrystalline material is a cooperative phenomenon typical for condensed matter physics and mechanics of heterogeneous materials. The passing of these processes depends on many parameters, including stress states of individual grains and its evolution during macrodeformation. In this paper we note a mathematical analogy between the equations of the mechanics of heterogeneous polycrystalline materials and the equations of quantum theory of particles scattering. This analogy allows to apply the methods of quantum field theory to solution of the equations of solid mechanics for heterogeneous media. We consider the application of Corringa-Kohn-Rostoker method, used in quantum theory for calculating wave function of electrons in metallic alloys, to elasticity of polycrystals. This approach allows, for instance, to calculate probability distribution density function for stresses in grains under arbitrary macrodeformation of polycrystal. Application of the method to classical problem of homogenization gives new formulae for the effective moduli of disordered polycrystalline medium. |
url |
http://mi.mathnet.ru/eng/vsgtu1282 |
work_keys_str_mv |
AT aatashkinov fieldtheoreticapproachforcharacterizationthedeformationofmulticomponentpolycrystallinematerials AT veshavshukov fieldtheoreticapproachforcharacterizationthedeformationofmulticomponentpolycrystallinematerials |
_version_ |
1724952899265495040 |