Magneto-electro-elastic Eshelby tensors for a piezoelectric-piezomagnetic composite reinforced by ellipsoidal inclusions

Abstract

The magneto-electro-elastic Eshelby tensors that represent the stress, electric displacement, and magnetic induction in an inclusion resulting from the constraint of the surrounding matrix of piezomagnetic-piezoelectric composites are presented. The tensors provide the basis for analysis of the magneto-electro-elastic response of the composites and have numerous applications such as to the study of defects, overall properties of multiphase composites, and fracture mechanics, etc. For a three-dimensional transversely isotropic piezoelectric/piezomagnetic composite containing spheriodal inclusions, the number of nonzero Eshelby tensors is 41 while among them only 17 are independent. These independent tensors can be divided into three categories. The first category consists of those tensors related to the elastic response, the second involves those related to the piezomagnetic response, while the third includes elastic and magnetic interactive terms. Moreover, the magneto-electro-elastic Eshelby tensors are obtained in the closed forms when both constituents of the composite are transversely isotropic and shapes of the inclusion are elliptic, rod shaped, penny shaped, and ribbon like.

Extended displacement discontinuity method for crack analysis in three-dimensional two-phase transversely isotropic magnetoelectroelastic media

“…The piezoelectric volume fraction of the inclusion is denoted by V i . The material constants are given as follows [Huang et al 1998]: (38)…”

“…The integrity and reliability of the structures depend greatly on the defects, such as inclusion, void, crack, etc., in the materials and structures. So the study of cracks in magnetoelectroelastic materials and structures has been attracting more and more efforts [Huang and Kuo 1997;Wang and Shen 2003;Wang and Mai 2003;Gao and Noda 2004;Zhou et al 2004;Tian and Rajapakse 2005;Zhao et al 2006a;Zhao et al 2006b]. …”

Thermal effects in magnetoelectric memories with stress-mediated switching

“…They depend on the physical properties of the two phases and on the piezoelectric Eshelby tensor [47,48,49,15].…”

“…Nevertheless, we may now consider an arbitrary size of the particle. To explain this point we recall an important property of the Eshelby theory (which is valid for the case with any possible coupling): when an ellipsoidal particle is embedded in an infinite matrix and subjected to uniform external actions, the physical fields (electric, magnetic and elastic) induced within the particle itself are always uniform and they depend on the material properties of the two phases and on the ratios a 1 /a 2 and a 2 /a 3 [32,31,30,15,47,48,49]. The internal fields do not depend on the actual size of the particle: only the shape of the ellipsoid may influence the particle response.…”

Integral equation formulations in 2D inhomogeneous magnetoelectroelastic media

“…Based on the inclusion formulation, Huang and Kuo [3] presented a unified method to determine the magnetic, electric, and elastic fields in piezoelectric/piezomagnetic composite materials with the ellipsoidal inclusions. Huang et al [4] obtained the magnetoelectroelastic Eshelby tensors for piezomagnetic/piezoelectric composite matrix containing an ellipsoidal inclusion. Li [5] studied the average magnetoelectroelastic field in multi-inclusions or inhomogeneities embedded in an infinite matrix and presented a numerical method to evaluate the magnetoelectroelastic Eshelby's tensors for the general material symmetry and ellipsoidal inclusion shape.…”