Image-based multi-scale analysis for porous piezoelectric materials based on the homogenization method

Abstract

This paper presents an image-based multi-scale analysis in order to evaluate macroscopic properties of heterogeneous porous piezoelectric materials by finite element calculations. The multi-scale analysis is based on the mathematical homogenization theory. Material heterogeneity is represented as a micro structure FE model that is automatically generated from the cross-sectioned images by high resolution X-ray CT. The high resolution X-ray measurement for porous PZT is compared with the digital image of SEM. Radius of pore is quantified from their images to compare these images. Nodal blocking preconditioned iterative solver is developed for piezoelectric FEM with high degree of freedom. In the numerical examples, material properties of porous PZT materials with different porosity are evaluated by the image-based multi-scale analysis to show the applicability and efficiency. Image-based multi-scale analysis with one million elements can be conducted by conventional PC with help of the proposed iterative solver.