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Boutin C.,National School of Public Civil Engineering | Geindreau C.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

This paper presents a study of transport parameters (diffusion, dynamic permeability, thermal permeability, trapping constant) of porous media by combining the homogenization of periodic media (HPM) and the self-consistent scheme (SCM) based on a bicomposite spherical pattern. The link between the HPM and SCM approaches is first established by using a systematic argument independent of the problem under consideration. It is shown that the periodicity condition can be replaced by zero flux and energy through the whole surface of the representative elementary volume. Consequently the SCM solution can be considered as a geometrical approximation of the local problem derived through HPM for materials such that the morphology of the period is "close" to the SCM pattern. These results are then applied to derive the estimates of the effective diffusion, the dynamic permeability, the thermal permeability and the trapping constant of porous media. These SCM estimates are compared with numerical HPM results obtained on periodic arrays of spheres and polyhedrons. It is shown that SCM estimates provide good analytical approximations of the effective parameters for periodic packings of spheres at porosities larger than 0.6, while the agreement is excellent for periodic packings of polyhedrons in the whole range of porosity. © 2010 The American Physical Society.

Boutin C.,National School of Public Civil Engineering
Journal of the Acoustical Society of America | Year: 2013

This paper deals with the acoustics of rigid porous media with inner resonators both saturated by the same gas. The aim is to define porous media microstructures in which inner resonance phenomena may occur, and to provide the modeling of acoustic waves in this situation. The first part, focuses on the design of a periodic medium consisting in damped Helmholtz resonators embedded in a porous matrix. In the second part, the macroscopic description of this system is established through the homogenization method. In the third part, the features of acoustic wave propagation are determined, and the occurrence of a broad band gap along with strongly dispersed waves is discussed according to the characteristics of the porous matrix and of the damped resonators. © 2013 Acoustical Society of America.

Auriault J.-L.,Joseph Fourier University | Boutin C.,National School of Public Civil Engineering
International Journal of Solids and Structures | Year: 2012

We revisit an ancient paper (Auriault and Bonnet, 1985) which points out the existence of cut-off frequencies for long acoustic wavelength in high-contrast elastic composite materials, i.e. when the wavelength is large with respect to the characteristic heterogeneity length. The separation of scales enables the use of the method of multiple scale expansions for periodic structures, a powerful upscaling technique from the heterogeneity scale to the wavelength scale. However, the results remain valid for non-periodic composite materials which show a Representative Elementary Volume (REV). The paper extends the previous investigations to three-component composite materials made of hard inclusions, coated with a soft material, both of arbitrary geometry, and embedded in a connected stiff material. The equivalent macroscopic models are rigorously established as well as their domains of validity. Provided that the stiffness contrast within the soft and the connected stiff materials is of the order of the squared separation of scales parameter, it is demonstrated (i) that the propagation of long wave may coincide with the resonance frequencies of the hard inclusions/soft material system and (ii) that the macroscopic model presents a series of cut-off frequencies given by an eigenvalue problem for the resonating domain in the cell. These results are illustrated in the case of stratified composites and the possible microstructures of heterogeneous media in which the inner dynamics phenomena may occur are discussed.© 2012 Elsevier Ltd. All rights reserved.

Soubestre J.,CEA DAM Ile-de-France | Boutin C.,National School of Public Civil Engineering
Mechanics of Materials | Year: 2012

This article deals with the effective dynamic behavior of elastic materials periodically reinforced by stiff linear slender elastic inclusions. By assuming a small scale ratio e between the period section size and the characteristic size of the system global strain, and by weighing the constituents stiffness contrast by powers of ε, the dynamic macroscopic behavior at the leading order is derived through the asymptotic homogenization method of periodic media considering different frequency ranges. A two order stiffness contrast (μm=μp = O(ε2)) is shown to lead to a dynamic macroscopic behavior spatially non-local in the transverse direction, where the system behaves as a generalized inner bending continuum, and temporally non-local in the axial direction, where the system behaves, at higher frequency, as a metamaterial in which internal resonance phenomena take place. The consequences of such non-localities on the reinforced medium modes are examined. The system axial and transverse modes are shown to be significantly different from those of usual composites. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction.

French Atomic Energy Commission, National School of Public Civil Engineering, INSA Lyon and French National Center for Scientific Research | Date: 2014-12-02

A method is provided for detecting a perturbation with respect to an initial state, of a device comprising at least one resonant mechanical element exhibiting a physical parameter sensitive to a perturbation such that the said perturbation modifies the resonance frequency of the said resonant mechanical element. A device is provided for detecting a perturbation by hysteretic cycle comprising at least one electromechanical resonator with nonlinear behaviour and means for actuation and for detection of the reception signal via a transducer so as to analyse the response signal implementing the method. A mass sensor and a mass spectrometer using the device are also provided.

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