Multi-Scale Finite Element Modeling of Piezoelectric Materials by A Crystallographic Homogenization Method

Abstract

Polycrystalline piezoelectric materials have been used for actuators or sensors as a component of various electronic and mechanical devices. Higher performance is becoming required for piezoelectric materials as they are applied to new technological fields such as micro/nano machines. Each crystal grain in piezoelectric materials shows strong anisotropy in mechanical and electrical behaviors. Macroscopic properties of polycrystalline piezoelectric materials are dominated by microscopic inhomogeneous crystal morphology. Therefore, polycrystalline piezoelectric materials have a large possibility to exhibit higher performance in a macroscopic scale by design of crystal morphology in a microscopic scale. In this study, a multi-scale finite element modeling by “crystallographic homogenization method” is proposed to estimate macroscopic properties considering microscopic inhomogeneous crystal morphology, and to evaluate microscopic behaviors in response to macroscopic external loads as shown in Figure 1. The computational examples of homogenization and localization are presented for a typical piezoelectric material, barium titanate (BaTiO3) with various distributions of crystal orientations. And then, its crystal orientation distribution has been optimized by steepest decent method to maximize macroscopic piezoelectric strain constants. Computational results indicated that piezoelectric strain constants d33 and d31 increase 34% and 180% respectively, compared with conventional piezoelectric polycrystals. It should be emphasized that the optimized polycrystals have higher piezoelectric performance than single crystals. Open image in new window Fig. 1. Hierarchical structure of polycrystalline piezoelectric materials.