Disclinations in nonlinear elasticity

被引：20

作者：

Derezin, Svyatoslav V. ^{[1
]}

Zubov, Leonid M. ^{[1
]}

机构：

[1] So Fed Univ, Rostov Na Donu 344090, Russia

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2011年 / 91卷 / 06期

基金：

俄罗斯基础研究基金会;

关键词：

Nonlinear elasticity; dislocations; disclinations; semi-linear material; CONTINUOUS DISTRIBUTIONS; DISCRETE DISCLINATIONS; DISLOCATIONS;

D O I：

10.1002/zamm.201000174

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The theory of line defects (dislocations and disclinations) in elastic bodies has been revisited. A consistent application of the formal limiting passage from isolated defects to the continuous distribution of these allows one to obtain a complete system of equations describing internal stresses in a body with distributed defects. Special emphasis is placed on disclinations in planar systems like graphene which very often demonstrate nonlinear elastic response. As a specific example an exact solution has been found for the problem of the eigenstresses in a disc of nonlinear elastic material due to a given density of continuously distributed disclinations. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：433 / 442

页数：10

共 45 条

[1]

[Anonymous], 2001, Riemannian Geometry in an Orthogonal Frame, DOI DOI 10.1142/4808

[2]

[Anonymous], 1997, Nonlinear theory of dislocations and disclinations in elastic bodies

[3] THEORY ON DISCLINATIONS [J].

ANTHONY, KH .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1970, 39 (01) :43-&

[4] CONTINUOUS DISTRIBUTIONS OF DISLOCATIONS - A NEW APPLICATION OF THE METHODS OF NON-RIEMANNIAN GEOMETRY [J].

BILBY, BA ;

BULLOUGH, R ;

SMITH, E .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1955, 231 (1185) :263-273

[5] CONTINUOUS DISTRIBUTIONS OF DISLOCATIONS .3. [J].

BILBY, BA ;

SMITH, E .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1956, 236 (1207) :481-505

[6] Nonlinear Elasticity of Monolayer Graphene [J].

Cadelano, Emiliano ;

Palla, Pier Luca ;

Giordano, Stefano ;

Colombo, Luciano .

PHYSICAL REVIEW LETTERS, 2009, 102 (23)

[7]

Cartan E., 1923, ANN SCIENT EC NORM S, V40, P325, DOI DOI 10.24033/ASENS.751

[8] On volterra dislocations of finitely deforming continua [J].

Casey, J .

MATHEMATICS AND MECHANICS OF SOLIDS, 2004, 9 (05) :473-492

[9]

Derezin SV, 1999, DOKL AKAD NAUK+, V366, P762

[10]

DEREZIN SV, 2010, P 14 INT C CONT MECH, P135

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