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

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, three-dimensional (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.