Mitsuteru Asai

An iterative solver applied to strongly coupled piezoelectric problems of porous Pb(Zr,Ti)O3 with nondestructive modelling of microstructure

A new preconditioned iterative solver based on the Kryrov subspace method is developed for solving large-scale finite element (FE) models of piezoelectric problems. The system matrix of piezoelectric FE analysis has negative eigenvalues because of coupling terms between mechanical and electrical fields. A general preconditioned iterative solver is ineffective for large-scale piezoelectric FE analysis due to the indefinite system matrix. A block diagonal preconditioner for the piezoelectric finite element method (FEM) is proposed by grouping nodal values as a block. Then the proposed solver is applied to the homogenization method, which can evaluate the effective macroscopic material properties by using FEM. In the FE modelling of complex microstructures, a semi-automatic technique with nondestructive observation provides reasonable 3D micrographs of porous Pb(Zr,Ti)O3 (PZT). The efficiency of the proposed solver is investigated through the homogenization analysis of real porous PZT samples.