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This paper investigates the magnetoelectroelastic responses of multiferroic fibrous composites with imperfectly bonded interface under longitudinal shear. The proposed imperfect interface model is a natural generalization of the shear lag ͑or the spring layer͒ model. By virtue of the complex variable method, we first consider the case where an isolated circular multiferroic fiber is imperfectly bonded to an infinite multiferroic matrix. Very concise expressions for the complex field potentials characterizing the magnetoelectroelastic fields inside and outside the circular fiber are obtained when the matrix is subjected to the remote uniform magnetoelectroelastic loading. The Mori-Tanaka mean-field method is then employed to derive the effective moduli of the multiferroic fibrous composite made of randomly distributed fibers reinforced to the matrix. Particularly we demonstrate that the interfacial imperfection in elasticity, electricity, and magnetism will always cause a significant reduction in the magnetoelectric coefficient of the BaTiO 3-CoFe 2 O 4 fibrous composite.

The problem of two non-elliptical inclusions with internal uniform fields embedded in an infinite matrix, subjected at infinity to a uniform stress field, is discussed in detail by means of the conformal mapping technique. The introduced conformal mapping function can map the matrix region (excluding the two inclusions) onto an annulus. The problem is completely solved for anti-plane isotropic elasticity, anti-plane piezoelectricity, anti-plane anisotropic elasticity, plane elasticity and finite plane elasticity. The correctness of the solution is verified by comparison with existing solutions and by checking an extreme situation. Our results indicate that it is permissible for the two inclusions to have different material properties and different shapes. Finally, two interesting applications of the obtained results are given, and we find that when the two inclusions have different material properties, the elastic polarization tensor associated with the two non-elliptical inclusions does not lie on the lower Hashin–Shtrikman bound.

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This paper analyzes the dynamic magnetoelectroelastic behavior induced by a penny-shaped crack in a magnetoelectroelastic layer subjected to prescribed stress or prescribed displacement at the layer surfaces. Two kinds of crack surface conditions, i.e., magnetoelectrically impermeable and permeable cracks, are adopted. The Laplace and Hankel transform techniques are employed to reduce the problem to Fredholm integral equations. Field intensity factors are obtained and discussed. Numerical results of the crack opening displacement (COD) intensity factors are presented and the effects of magnetoelectromechanical loadings, crack surface conditions and crack configuration on crack propagation and growth are examined. The results indicate that among others, the fracture behaviors of magnetoelectroelastic materials are affected by the sizes and directions of the prescribed magnetic and/or electric fields, and the effects are strongly dependent on the elastic boundary conditions.