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

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

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

Matematicke modelovani biologickych tkani.

A mathematical which can describe various materials of a complicated microstructure, particularly smooth muscle tissue, is proposed and then tested using many numerical simulations. The model presented is a central part of a framework for biomechanical modeling further comprising sensitivity algorithms for the identification of material parameters of the model and also software where these components are being implemented in. The model is based on the classical continuum theory. Effects of microstructure are incorporated into using a phenomenological approach, where a stress-strain relationship is specified directly. A composite nature of the model is treated with help of the mixture theory, where all the components involved contribute to the overall response proportionally to their volume fractions.Summary in English, French and GermanAvailable from STL, Prague, CZ / NTK - National Technical LibrarySIGLECZCzech Republi

Dynamics of a cantilever beam with piezoelectric sensor: Finite element modeling

An elastodynamical model of a cantilever beam coupled with a piezoelectric sensor is introduced and its discretization using the finite element method is presented. The mathematical model includes additional terms that enforce the floating potential boundary condition for keeping a constant charge on an electrode of the sensor. The behaviour of the model is illustrated using a numerical example corresponding to an experimental setup, where vibrations of the beam and the potential on the sensor are measured

Domain decomposition methods for solving the Burgers equation

summary:This article presents some results of numerical tests of solving the two-dimensional non-linear unsteady viscous Burgers equation. We have compared the known convergence and parallel performance properties of the additive Schwarz domain decomposition method with or without a coarse grid for the model Poisson problem with those obtained by experiments for the Burgers problem

Fast evaluation of finite element weak forms using python tensor contraction packages

In finite element calculations, the integral forms are usually evaluated using nested loops over elements, and over quadrature points. Many such forms (e.g. linear or multi-linear) can be expressed in a compact way, without the explicit loops, using a single tensor contraction expression by employing the Einstein summation convention. To automate this process and leverage existing high performance codes, we first introduce a notation allowing trivial differentiation of multi-linear finite element forms. Based on that we propose and describe a new transpiler from Einstein summation based expressions, augmented to allow defining multi-linear finite element weak forms, to regular tensor contraction expressions. The resulting expressions are compatible with a number of Python scientific computing packages, that implement, optimize and in some cases parallelize the general tensor contractions. We assess the performance of those packages, as well as the influence of operand memory layouts and tensor contraction paths optimizations on the elapsed time and memory requirements of the finite element form evaluations. We also compare the efficiency of the transpiled weak form implementations to the C-based functions available in the finite element package SfePy