Line-integral representations for extended displacements, stresses, and interaction energy of arbitrary dislocation loops in transversely isotropic magneto-electro-elastic bimaterials

doi:10.1007/s10483-014-1846-7

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (8): 1005-1028.doi: https://doi.org/10.1007/s10483-014-1846-7

Line-integral representations for extended displacements, stresses, and interaction energy of arbitrary dislocation loops in transversely isotropic magneto-electro-elastic bimaterials

袁江宏¹, 陈伟球², E. PAN³

1. Department of Civil Engineering, Zhejiang University, Hangzhou 310058, P. R. China;
2. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, P. R. China;
3. Department of Civil Engineering and Department of Applied Mathematics, University of Akron, Akron, OH 44325, U. S. A.

收稿日期:2013-09-06 修回日期:2013-11-29 出版日期:2014-08-01 发布日期:2014-08-01
通讯作者: E. PAN, Professor, Ph.D., E-mail: pan2@uakron.edu E-mail:pan2@uakron.edu
基金资助:
Project supported by the National Project of Scientific and Technical Supporting Programs Funded by Ministry of Science & Technology of China (No. 2009BAG12A01-A03-2) and the National Natural Science Foundation of China (Nos. 10972196, 11090333, 11172273, and 11321202)

Line-integral representations for extended displacements, stresses, and interaction energy of arbitrary dislocation loops in transversely isotropic magneto-electro-elastic bimaterials

Jiang-hong YUAN¹, Wei-qiu CHEN², E. PAN³

1. Department of Civil Engineering, Zhejiang University, Hangzhou 310058, P. R. China;
2. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, P. R. China;
3. Department of Civil Engineering and Department of Applied Mathematics, University of Akron, Akron, OH 44325, U. S. A.

Received:2013-09-06 Revised:2013-11-29 Online:2014-08-01 Published:2014-08-01
Supported by:
Project supported by the National Project of Scientific and Technical Supporting Programs Funded by Ministry of Science & Technology of China (No. 2009BAG12A01-A03-2) and the National Natural Science Foundation of China (Nos. 10972196, 11090333, 11172273, and 11321202)

摘要/Abstract

摘要： In addition to the hexagonal crystals of class 6 mm, many piezoelectric materials (e.g., BaTiO₃), piezomagnetic materials (e.g., CoFe₂O₄), and multiferroic composite materials (e.g., BaTiO₃-CoFe₂O₄ composites) also exhibit symmetry of transverse isotropy after poling, with the isotropic plane perpendicular to the poling direction. In this paper, simple and elegant line-integral expressions are derived for extended displacements, extended stresses, self-energy, and interaction energy of arbitrarily shaped, threedimensional (3D) dislocation loops with a constant extended Burgers vector in transversely isotropic magneto-electro-elastic (MEE) bimaterials (i.e., joined half-spaces). The derived solutions can also be simply reduced to those expressions for piezoelectric, piezomagnetic, or purely elastic materials. Several numerical examples are given to show both the multi-field coupling effect and the interface/surface effect in transversely isotropic MEE materials.

关键词: dislocation loop, multiferroic, transverse isotropy, bimaterial, half space, extended displacement, extended stress, interaction energy

Abstract: In addition to the hexagonal crystals of class 6 mm, many piezoelectric materials (e.g., BaTiO₃), piezomagnetic materials (e.g., CoFe₂O₄), and multiferroic composite materials (e.g., BaTiO₃-CoFe₂O₄ composites) also exhibit symmetry of transverse isotropy after poling, with the isotropic plane perpendicular to the poling direction. In this paper, simple and elegant line-integral expressions are derived for extended displacements, extended stresses, self-energy, and interaction energy of arbitrarily shaped, threedimensional (3D) dislocation loops with a constant extended Burgers vector in transversely isotropic magneto-electro-elastic (MEE) bimaterials (i.e., joined half-spaces). The derived solutions can also be simply reduced to those expressions for piezoelectric, piezomagnetic, or purely elastic materials. Several numerical examples are given to show both the multi-field coupling effect and the interface/surface effect in transversely isotropic MEE materials.

Key words: dislocation loop, multiferroic, transverse isotropy, bimaterial, half space, extended displacement, extended stress, interaction energy

中图分类号:

O343.8

袁江宏;陈伟球;E. PAN. Line-integral representations for extended displacements, stresses, and interaction energy of arbitrary dislocation loops in transversely isotropic magneto-electro-elastic bimaterials[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(8): 1005-1028.

Jiang-hong YUAN;Wei-qiu CHEN;E. PAN. Line-integral representations for extended displacements, stresses, and interaction energy of arbitrary dislocation loops in transversely isotropic magneto-electro-elastic bimaterials[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(8): 1005-1028.

参考文献

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Line-integral representations for extended displacements, stresses, and interaction energy of arbitrary dislocation loops in transversely isotropic magneto-electro-elastic bimaterials

Line-integral representations for extended displacements, stresses, and interaction energy of arbitrary dislocation loops in transversely isotropic magneto-electro-elastic bimaterials

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