Multi-scale finite element analysis of piezoelectric materials based on crystallographic homogenization method

Most piezoelectric ceramics have perovskite crystal structure, which can be characterized as a non-symmetry crystal lattice structure with strong anisotropy. They have large possibility to exhibit higher performance by controlling polycrystalline structures. In this study, a multi-scale finite element analytical procedure based on a crystallographic homogenization method has been developed to estimate macroscopic and microscopic piezo-electroelastic behaviors in keeping their compatibility. At first, the macroscopic dielectric, piezoelectric and elastic constants have been predicted for arbitrary microscopic crystal orientation distributions. As a result, it was made clear that the macroscopic piezoelectric constants have the maximum value at a particular crystal orientation. Consequently, it is possible to maximize the piezoelectricity of polycrystalline ceramics by controlling crystal orientation distributions. Furthermore, it was recognized that SDP enable us to characterize the fractal behaviors in microscopic inhomogeneous structures.