Micromechanics of ferroic functional materials

This chapter introduces a range of ferroic functional materials including ferroelectrics, ferroelastics, and ferromagnets. Coupling among the different types of ferroic order results in multiferroic behavior that is of importance in transducers and memory devices. The physical laws governing each type of material are compared, noting the closely analogous governing equations. However, attention is also given to the differences in behavior that can necessitate distinct modeling approaches. The general form of the Eshelby tensor for coupled ferroics is introduced, and the methods for estimating the properties of composites, including self-consistent and Mori–Tanaka schemes, are briefly described. The chapter then focuses on the analysis of a commonly encountered arrangement of microstructure: a composite laminate comprising distinct crystal variants of the same physical phase. Rules are presented for determining how laminates can form with a minimum energy arrangement of layers, and methods are described for estimating the resulting material properties of the composite. An application to the microstructure of freestanding polycrystalline thin films is described