Two-step homogenization simulation for multidomain and multigrain structures in piezoelectric materials

In this paper, a two-step scale-up procedure based on asymptotic homogenization theory is proposed for hierarchical structures consisting of multigrains and multidomains in piezoelectric materials. Intragranular domains are modeled as a microstructure during the first-step homogenization. Then, in the second-step homogenization, an aggregate of randomly oriented grains is modeled by applying the first-step homogenized material properties of multidomains to every grain. A dual-domain structure consisting of positive and negative directional domains with a 180° orientation gap is computed for case study analysis. The three-dimensional electron backscatter diffraction-measured microstructure is employed for the multigrain structure. The effect of the domain configuration on the macroscopic homogenized material properties of polycrystalline piezoelectric materials is investigated through the two-step homogenization process. In particular, the material property changes caused by the piezoelectric effect, which cannot be estimated by the mixture law, are discussed for multigrain and multidomain structures.