Homogenization based model of flows in piezoelectric porous metamaterials driven by peristaltic deformation

Abstract: The seminar talk is devoted to the multiscale modelling of an electroactive porous material intended for fluid transport. Its functionality is based on the peristaltic flow which is induced by deforming pore walls. This phenomenon is of a great importance in physiology and biomechanics, however, as a driving mechanism of fluid transport, it presents and important and challenging issue in the design of smart ``bio-inspired'' materials. We consider locally periodic porous structures saturated by a Newtonian fluid. The peristaltic deformation wave of the microchannels is induced by a convenient local control of piezoelectric segments. Several issues related to the construction of a computationally efficient two-scale metamaterial model within the homogenization framework will be presented. We consider relatively small deformation which enables to use the linear kinematic framework. The poro-piezoelectric model derived in [1] is extended for the viscous fluid flow while respecting the inertia effects in both the phases. Using the homogenization based on the classic asymptotic analysis, cell problems (at the microlevel) are obtained which provide characteristic responses of the microstructures with respect to macroscopic strains, fluid pressure and electric potentials. These responses are needed to compute the effective (homogenized) parameters of the macroscopic problem which depend on the microconfiguration. The numerical studies demonstrate that such a linear model cannot capture the desired pumping effect of the homogenized continuum. To achieve this functionality of the model, it is necessary to account for the nonlinearity associated with deformation-dependent microconfigurations. To avoid hurdles associated with a fully nonlinear two-scale model, we apply a linearization procedure based on the sensitivity analysis of the local characteristic responses with respect to the deformation induced by the macroscopic quantities. In this way, by virtue of the methodology introduced in [2], we get first-order expansions of all the homogenized coefficients. The dynamic effects lead to the macroscopic flow model in a convolution form. For this option, a special treatment of the deformation-dependent dynamic permeability is needed. Numerical examples illustrate efficiency of the proposed computational approach [3].

[1] E. Rohan, V. Lukeš. On modelling nonlinear phenomena in deforming heterogeneous media using homogenization and sensitivity analysis concepts. Applied Mathematics and Computation (2015) 267:583-595.

[2] E. Rohan, V. Lukeš. Homogenization of the fluid-saturated piezoelectric porous media. Int. Jour. Solids and Structures (2018) 147:110-125.

[3] E. Rohan, V. Lukeš. Homogenization of peristaltic flows in piezoelectric porous media. (2023) arXiv:2304.05393v1, doi.org/10.48550/arXiv.2304.05393

MathematicsPhysics

Audience: researchers in the topic

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Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)

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