Parametric multiphysics finite-volume theory for periodic composites with thermo-electro-elastic phases

Abstract

The zeroth-order multiphysics finite-volume micromechanics has been proposed to model coupled thermo-electro-mechanical behaviors of unidirectional composites embedded with piezoelectric phases. Parametric mapping is implemented within the multiphysics finite-volume theory’s framework, facilitating modeling of multiphase piezoelectric materials with complex microstructures with relatively coarse unit cell discretization. The resulting theory admits piezoelectric materials with complete anisotropy and arbitrary poling direction and enables rapid generation of the entire set of coupled thermo-mechanical, piezoelectric properties, figures of merits, as well as the local fluctuations of fields within the composite microstructures with greater fidelity than its predecessor. The proposed method is verified extensively by comparison with the finite-element homogenization technique, which produces an excellent agreement in a wide range of volume fractions but offers much better stability and efficiency. The contrast with the rectangular theory is also presented and discussed, demonstrating the advantage and the need for the development of parametric formulation. This extension further increases the finite-volume direct averaging micromechanics theory’s range of applicability, providing an attractive standard for investigating multiphase and multiphysics problems with different microstructural architectures and scales against which other approaches may be compared.

Fully-coupled electro-magneto-elastic behavior of unidirectional multiphased composites via finite-volume homogenization

“…(13), produces the surface-averaged quantities Û . Thus, the generalized Hill's electromagneto-elastic concentration matrices A q ( ) for the qth subvolume is generated to relate the average strain, electric field and magnetic field to the macroscopic loading vectors (Chen et al, 2018a;Chen and Wang, 2018):…”

“…In contrast with the FE-based technique wherein the minimization of global potential energy in the unit cell with sufficient mesh refinement leads to the ultimate satisfaction of the unit cell's global equilibrium, the finite-volume technique is based on the direct satisfaction of the governing differential equations for every subvolume at each level of mesh refinement (Chen and Pindera, 2020;Chen et al, 2018bChen et al, , 2018d. The finite-volume theory has been proved to be an attractive alternative to the finiteelement technique in micromechanical modeling of piezoelectric composites or magnetostrictive porous materials (Chen et al, 2018a;Chen and Wang, 2018). However, a fully coupled electro-magneto-elastic constitutive relationship has never been implemented into the FVDAM theory.…”

An Engineering-Problem-Based Short Experiment Project on Finite Element Method for Undergraduate Students

“…Students are not aware of the application process of finite element analysis in engineering [16][17][18]. How to introduce engineering reality into the teaching process of finite element analysis is still a problem [19][20][21][22][23][24].…”

Generalized locally-exact homogenization theory for evaluation of electric conductivity and resistance of multiphase materials

“…For example, monolithic piezoelectric materials have a limited range of coupled properties and pronounced directionality. Those problems may be circumvented by using the piezoelectric materials in the form of composites where optimum electromechanical coupling effects are obtained by selecting proper fiber volume fractions and poling orientations [8,9].…”