Magneto-electro-elastic properties of multiferroic composites containing periodic distribution of general multi-coated inhomogeneities

In this paper, a homogenization scheme with several desirable features is developed to determine the overall magneto-electro-elastic behavior of multiferroic composite materials containing periodic distribution of multi-inhomogeneities. The configuration of a typical inhomogeneity system is taken to be composed of an inner ellipsoidal particle surrounded by many coating layers of ellipsoidal shape. As such, the morphology of composite is sufficiently general, and then the developed methodology can be quite robust to handle a wide range of problems. Through the present analysis, we first adopt the equivalent inclusion principle in conjunction with a superposition procedure to decompose the multi-inhomogeneity system into a series of single-inclusion problems with position-dependent eigenstrain–electric–magnetic fields. The periodic microstructure will be accounted for through the Fourier series expansion of field quantities. The local form of consistency equations are then called upon, and integrated to give the expression for the average eigenfields. Finally, considering the relation between far-field loads and the local microscopic fields in the constituent phases the overall effective moduli of composite are obtained in terms of derived average eigenfields. The accuracy and generality of proposed theory is verified through consideration of several three-phase multiferroic composites with complex microstructures. In this process, the strong dependence of overall behavior of fibrous and particulate multiferroics on the microstructure parameters, such as the interface condition, thickness, eccentricity and material properties of core inhomogeneities and their coating layers is well demonstrated.