Homogenization of the fluid-saturated piezoelectric porous media

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.

Optimization of the porous material described by the Biot model

“…There are several extensions of the present work which are of interest in the context of smart structures and the material design. In particular, including the piezoelectric components in the microstructure will enable to control and optimize the fluid redistribution in the porous structure by the electric field; in this context, homogenization of the poro-piezoelectric materials reported in [22] can serve a suitable framework. Another important extension of the present study is by including the inertia effects in the micromodel.…”

Multiscale finite element calculations in Python using SfePy

“…As we assume given potentialsφ k in each of the electrode networks, the dielectric properties must be appropriately rescaled in order to preserve the finite electric field for the limit ε −→ 0: g ε = ε¯ g, d ε = ε 2¯ d, cf. [36].…”

“…6 right. See [36] for comparison of accuracy of the reconstructed solutions with a full, much more demanding, simulation. In the above article, the full (reference) simulation has approximately 4.5 × 10 5 degrees of freedom while the microscopic problem has only 741 DOFs and the macroscopic problem 577 DOFs.…”

Multiscale modelling of flow due to the peristaltic wave in deforming poro-piezoelectric medium

“…For this we employ a two-scale modelling Eduard Rohan and Vladimír Lukeš approach based on the homogenization method [3] combined with the sensitivity analysis. We extend the homogenized model of the fluid-saturated piezo-poroelastic medium equipped with the controlling conductor networks [13] to describe the fluid-structure interaction respecting influence of the deformation of the microconfiguration. The computational model arises from the homogenization of the fluid-saturated porous medium.…”