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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

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  • 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 date: 2013-09-06

  Revised date: 2013-11-29

  Online 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)

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.

Cite this article

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, 2014 , 35(8) : 1005 -1028 . DOI: 10.1007/s10483-014-1846-7

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