Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials

We have studied the average magnetoelectroelastic field in a multi-inclusion or inhomogeneity embedded in an infinite matrix. The magnetoelectroelastic inclusion and inhomogeneity problems are discussed [1], and a numerical algorithm to evaluate the magnetoelectroelastic Eshelby’s tensors for the general material symmetry and ellipsoidal inclusion shape is developed. The solutions for the magnetoelectroelastic inclusion and inhomogeneity problems are applied to study the multi-inclusion and inhomogeneity problems. It is shown that the average field in an annulus surrounding an inclusion embedded in an infinite magnetoelectroelastic medium only depends on the shapes and orientations of two ellipsoids, which generalizes Tanaka and Mori's observation in elasticity [2]. The average field in a multi-inclusion is then determined exactly, from which the average field in a multi-inhomogeneity is obtained, using the equivalent-inclusion concept [3]. The solutions of multi-inclusion and inhomogeneity problems serve as basis for an averaging scheme to model the effective magnetoelectroelastic moduli of heterogeneous materials, which generalizes Nemat-Nasser and Hori's multi-inclusion model in elasticity [4]. The model is further extended to predict the effective thermal moduli of the heterogeneous magnetoelectroelastic solids, generalizing the recent work of Li on the thermal expansion coefficients of elastic composites [5]. The proposed model recovers Mori–Tanaka and self-consistent approaches as special cases. Finally, some numerical results are given to demonstrate the applicability of the model. The potential techniques to enhance the magnetoelectric effect in practical composites are also discussed.