Micromechanical analysis of effective properties of magneto-electro-thermo-elastic multilayer composites

An exact matrix method, originally proposed for evaluating effective elastic constants of generally anisotropic multilayer composites, is further developed for a micromechanical analysis of multilayers with various coupled physical effects including piezoelectricity, piezomagnetism, thermoelasticity (in consideration of entropy), and the Biot’s poroelasticity. The results for a BaTiO3–CoFe2O4 magneto-electro-thermo-elastic (METE) multilayer coincide with those calculated using other micromechanical models based on the Mori–Tanaka method and the asymptotic homogenization method. It is shown that the present method can efficiently handle the most general type of multilayers with an arbitrary number of general anisotropic layers. Analytical expressions for effective material properties of a transversely isotropic METE multilayer composite are derived, from which those for functionally graded METE multilayers can be directly obtained. The effects of crystallographic orientations and volume fractions of constituting layers on the magnetoelectric coefficients are investigated for BaTiO3–CoFe2O4 and LiNbO3–CoFe2O4 multilayer composites. It is thus demonstrated that the present model can be used for the layout/material optimization of these METE multilayers to obtain a maximum product property such as the magnetoelectric, pyroelectric, and pyromagnetic coefficients. It is also shown that the same method can be used to predict the effective properties of poroelastic multilayers.