Homogenization of the fluid-saturated piezoelectric porous media

TL;DR

This paper develops a homogenized macroscopic model for fluid-saturated piezoelectric porous media, capturing electric-mechanical interactions and pore control, validated through finite element simulations and direct numerical comparisons.

Contribution

It introduces a two-scale homogenization approach for piezoelectric porous media with fluid saturation, considering different microstructural arrangements and electrode control mechanisms.

Findings

Good agreement between homogenized models and direct numerical simulations.

Effective coefficients accurately capture microstructural responses.

Model enables control of deformation and pore volume via electrodes.

Abstract

The paper is devoted to the homogenization of porous piezoelectric materials saturated by electrically inert fluid. The solid part of a representative volume element consists of the piezoelectric skeleton with embedded conductors. The pore fluid in the periodic structure can constitute a single connected domain, or an array of inclusions. Also the conducting parts are represented by several mutually separated connected domains, or by inclusions. Two of four possible arrangements are considered for upscaling by the homogenization method. The macroscopic model of the first type involves coefficients responsible for interactions between the electric field and the pore pressure, or the pore volume. For the second type, the electrodes can be used for controlling the electric field at the pore level, so that the deformation and the pore volume can be influenced locally. Effective constitutive coefficients are computed using characteristic responses of the microstructure. The two-scale modelling procedure is implemented numerically using the finite element method. The macroscopic strain and electric fields are used to reconstruct the corresponding local responses at the pore level. For validation of the models, these are compared with results obtained by direct numerical simulations of the heterogeneous structure; a good agreement is demonstrated, showing relevance of the two-scale numerical modelling approach.