Persitaltic driven flows in piezoelectric porous dynamic metamaterials - homogenization based modelling

Abstract

The paper deals with the homogenization-based modelling of periodic porous structures saturated by a Newtonian fluid and locally controlable due to embedded piezoelectric segments which can induce a peristaltic deformation of the microchannels, in response to prescribed propagating voltage waves. The two-scale homogenized problem is nonlinear by the consequence deformation-dependent homogenized coefficients in the macroscopic equations. For this, a linear expansions based on the sensitivity analysis of the homogenized coefficients with respect to the deformation induced by the macroscopic quantities is employed. A special care is needed to apply this approach to the dynamic permeability which is involved in the time convolution integrals. This approximate treatment of the non-linearity is justified as far as the deformations are moderate. As an advantage, it enables to reduce the computational cost not exceeding much the one of linear problems. At the same time, the nonlinearity is important to capture the pumping effect of the porous material in a case of time periodic actuation by electric field.