A two-scale homogenization analysis of porous magneto-electric two-phase composites

A computational homogenization analysis for the simulation of porous magneto-electric composite materials is presented. These materials combine two or more ferroic states with each other enabling a coupling between magnetization and electric polarization. This magneto-electric coupling finds application in sensor technology or data storage devices. Since most single-phase multiferroics show coupling at very low temperatures beyond technically relevant applications, two-phase composites, consisting of a ferroelectric and a ferromagnetic phases, are manufactured. They generate a strain-induced magneto-electric coupling at room temperature. The performance and reliability of these materials is influenced by defects or pores, which can arise during the manufacturing process. We analyze the impact of pores on the magnitude of the magneto-electric coupling coefficient. In order to determine the effective properties of the composite, a two-scale finite element (FE2) homogenization approach is performed. It combines the macroscopic and microscopic scale by direct incorporation of the microscopic morphology. We derive the basic equations for the localization and the homogenization of the individual field variables and give an algorithmic expression for the effective tangent moduli. We discuss the influence of pores on the magneto-electric coupling in two-phase composites by analyzing numerical examples.