Development of Triple Scale Finite Element Analyses Based on Crystallographic Homogenization Methods

Abstract

Crystallographic homogenization procedure is implemented in the piezoelectric and elastic‐crystalline plastic finite element (FE) code to assess its macro‐continuum properties of piezoelectric ceramics and BCC and FCC sheet metals. Triple scale hierarchical structure consists of an atom cluster, a crystal aggregation and a macro‐ continuum. In this paper, we focus to discuss a triple scale numerical analysis for piezoelectric material, and apply to assess a macro‐continuum material property. At first, we calculate material properties of Perovskite crystal of piezoelectric material, XYO3 (such as BaTiO3 and PbTiO3) by employing ab‐initio molecular analysis code CASTEP. Next, measured results of SEM and EBSD observations of crystal orientation distributions, shapes and boundaries of a real material (BaTiO3) are employed to define an inhomogeneity of crystal aggregation, which corresponds to a unit cell of micro‐structure, and satisfies the periodicity condition. This procedure is featured as a first scaling...