An iterative solver applied to strongly coupled piezoelectric problems of porous Pb(Zr,Ti)O₃with nondestructive modelling of microstructure

Abstract

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.

Microstructural modelling of the polarization and properties of porous ferroelectrics

“…This oversimplified model geometry can lead to poor predictions compared to experimental data, since real porous materials consist of a microstructure of many pores with a randomly distributed porosity in which some pores are connected and some isolated. With the advent of larger computational powers, more sophisticated models are achievable which can lead to the development of porous piezoelectric models [16,17] which consist of a large number of randomly distributed pores within a polycrystalline PZT matrix.…”

Permeability determination of porous media using large‐scale finite elements and iterative solver

“…) using an iterative solver, the nodal block diagonal preconditioner is implemented. Similar preconditioner is reported to work well in promising stable convergence, even for indefinite coefficient systems arising from strongly coupled piezoelectric problems where the matrix has negative eigenvalues . Briefly stated, it is given by a block diagonal matrix where each block of entries contains a group of primary nodal stiffness.…”

Parallel iterative partitioned coupling procedure for multi-scale piezoelectric finite element analysis

“…In the finite element (FE) equation for the conventional piezoelectric analysis, coefficient matrix is not positive definite and strongly ill-condition because of coupling terms between mechanical and electrical fields [1], [2]. In this study, a parallel computing technique for piezoelectric FE analysis is newly developed based on the iterative partitioned coupling method with the parallel conjugate gradient (CG) solver.…”