Two level homogenization of flows in deforming double porosity media: biot-darcy-brinkman model

We present the two-level homogenization of the flow in a deformable double-porous structure described at two characteristic scales: the higher level porosity associated with the mesoscopic structure is constituted by channels in an elastic skeleton which is made of a microporous material. The macroscopic model is derived by the asymptotic analysis of the viscous flow in the heterogeneous structure characterized by two small parameters. The first level upscaling yields a Biot continuum model coupled with the Stokes flow. The second step of the homogenization leads to a macroscopic flow model which attains the form of the Darcy-Brinkman flow model coupled with the deformation of the poroelastic continuum involving the effective parameters given by the microscopic and the mesoscopic porosity features

On acoustic band gaps in homogenized piezoelectric phononic materials

We consider a composite medium made of weakly piezoelectric inclusions periodically distributed in the matrix which ismade of a different piezoelectricmaterial. Themediumis subject to a periodic excitation with an incidence wave frequency independent of scale ε of the microscopic heterogeneities. Two-scale method of homogenization is applied to obtain the limit homogenized model which describes acoustic wave propagation in the piezoelectric medium when ε → 0. In analogy with the purely elastic composite, the resulting model allows existence of the acoustic band gaps. These are identified for certain frequency ranges whenever the so-called homogenized mass becomes negative. The homogenized model can be used for band gap prediction and for dispersion analysis for low wave numbers. Modeling such composite materials seems to be perspective in the context of Smart Materials design

Modeling flows in periodically heterogeneous porous media with deformation-dependent permeability

The paper proposes a non-linear model of the Biot continuum. The nonlienarity is introduced in terms of the material coefficients which are expressed as linear functions of the macroscopic response. These functions are obtained by the sensitivity analysis of the homogenized coefficients computed for a given geometry of the porous structure which transforms due to the local deformation. Linear kinematics is assumed, however, the approach can be extended to large deforming porous materials

Homogenization of the fluid-saturated piezoelectric porous metamaterials

The paper is devoted to the homogenization approach in modelling of peri- odic porous media constituted by piezoelectric porous skeleton with pores saturated by viscous fluid. The representative volume element contains the piezoelectric solid part (the matrix) and the fluid saturated pores (the channels). Both the matrix and the channels form connected subdomains. The mathematical model describing the material behaviour at the microscopic scale involves the quasi-static equilibrium equation governing the solid piezoelectric skeleton, the Stokes model of the viscous fluid flow in the channels and the coupling interface conditions on the transmission interface. The macroscopic model is derived using the unfolding method of homogenization. The effective material coefficients are computed using characteristic responses of the porous microstructure. The consti- tutive law for the upscaled piezo-poroelastic material involves a coefficient coupling the electric field and the pore pressure. A numerical example illustrates different responses of the porous medium subject to the drained and undrained loading

Modeling and estimation of the cardiac electromechanical activity

{\it Computers \& Structures}, in pressWe describe an approach that we propose to model the electromechanical behavior of the heart, and to use the model in a data assimilation procedure in order to perform an identification of the parameters and state. The modeling of the heart tissue is based on an electrically-activated contraction law formulated via multiscale considerations and is consistent with various physiological and thermomechanical key requirements. The global heart system also incorporates a simplified lumped modeling of the blood compartments. We report on numerical simulations and on validations of our model in reference and pathological conditions. Furthermore, the data assimilation procedure is intended to give access to quantities of interest for diagnosis purposes, and we present some promising results in this direction

Dynamics of a cantilever beam with piezoelectric sensor: Parameter identification

This work has been supported by the grant 23-06220S of the Czech Science Foundation within institutional support RVO:61388998

Author Correction: SciPy 1.0: fundamental algorithms for scientific computing in Python.

An amendment to this paper has been published and can be accessed via a link at the top of the paper