Homogenization of piezoelectric porous structures for peristalsis-driven flows

Abstract

We present a homogenized model of a piezo-poroelastic material which enables to transport fluid against small pressure slope. To explore functionality of such metamaterial structures, we develop multiscale computational tools. The computational models arise from the homogenization of the fluid-structure interaction problem. Cell problems (at the microlevel) are obtained which provide characteristic responses of the microstructures with respect to macroscopic strains, fluid pressure and electric potentials. Although the deformations are assumed to be small, the macroscopic nonlinearity of the device is captured using the first order expansions of the homogenized coefficients with respect to macroscopic variables. As an optional feature of the smart devices, distributed valves are involved which strongly influence the macroscopic permeability of the material. For this, homogenized model of the contact problem was developed. We present examples of microstructures and results of the simulations as the proof of concept aimed at designing smeared peristaltic pumps in a bulk medium.