Search

This work aims at studying the mechanical and acoustic behaviours of a new bio-based porous epoxy resin obtained by a "green" adapted combination of the cationic photopolymerization and the porogen leaching technique. This new kind of material generally possesses interconnected complex morphology and it would be useful to consider this feature in a model. In this study, the effective properties of the material were estimated by using the asymptotic homogenization method. Four types of ordered pore arrangements together with systematic variations of the porosity and the pore size have been studied. Based on the results of these investigations, a subtle relation between the microstructure and mechanical/acoustic properties has been established. The estimated equivalent dynamic density and equivalent dynamic bulk modulus were compared with experimental results obtained by conducting the three-microphone impedance tube testing. The processing parameters of material elaboration could be adjusted so that the obtained porous material would possess the best sound absorption performance.

Bài báo trình bày kết quả phát triển vật liệu composite mới nguồn gốc tự nhiên trên cơ sở nhựa epoxy resorcinol sinh học – diatomite bằng quy trình xanh hai giai đoạn dựa trên đặc tính “sống” của sự trùng hợp cation. Bao gồm sự khởi đầu phản ứng bằng ánh sáng và sau đó là sự hóa rắn không cần ánh sáng dưới tác dụng nhiệt, quy trình này cho phép thu được các composite epoxy-diatomite dày và không trong suốt mà không cần dùng bất cứ dung môi hay chất hóa rắn gốc amine nguy hại nào. Các ảnh hưởng của hàm lượng diatomite đối với các tính chất cơ học và phản ứng với lửa của những composite này đã được khảo sát. Trên cơ sở đánh giá các tính chất này, composite thu được với diatomite chiếm 40% khối lượng được xem như composite tối ưu. Composite này có mô đun uốn là 3,6 MPa và ứng xử làm chậm cháy đáng chú ý với đỉnh tốc độ tỏa nhiệt (peak of Heat Release Rate - pHRR) 132 W/g và tổng lượng tỏa nhiệt 6 kJ/g ghi nhận được trong phân tích nhiệt lượng kế dòng đốt cháy nhiệt phân (Pyrolysis Combustion Flow Calorimetry - PCFC).

Thermoacoustic technology can play a significant role in the development of renewable energies. Thermoacoustic engines and heat pumps (or refrigerators) are however characterized by a low efficiency attributed to suboptimal components. The core of these devices is a porous material, named stack (or regenerator), in which thermoacoustic conversion takes place. The most frequently used stack in the literature remains the wire mesh, although there is still a lack of formulation for the corresponding thermoviscous response functions. Essentially, all the dynamic thermal and viscous behaviors of a porous structure can be derived thanks to the Johnson-Champoux-Allard-Lafarge (JCAL) semi-phenomenological model, where transport parameters provide input information on the macroscopic level to the model. Here, we report a set of structure–property correlations between the transport parameters of the stack and the geometrical features of the wire mesh obtained from first-principles calculations. Validation of the model is carried out by means of experimental measurements performed on three different specimens. Our results show that the knowledge of the termoviscous functions for the wire mesh allows drawing preliminary considerations on the thermoacoustic efficiency of the stack, without needing to consider a full numerical simulation of the entire device.

International audience; A methodology to learn acoustical responses based on limited experimental datasets is presented. From a methodological standpoint, the approach involves a multiscale-informed encoder used to cast the learning task in a finite-dimensional setting. A neural network model mapping parameters of interest to the latent variables is then constructed and calibrated using transfer learning and knowledge gained from the multiscale surrogate. The relevance of the approach is assessed by considering the prediction of the sound absorption coefficient for randomly-packed rigid spherical beads of equal diameter. A two-microphone method is used in this context to measure the absorption coefficient on a set of configurations with various monodisperse particle diameters and sample thicknesses, and a hybrid numerical approach relying on the Johnson-Champoux-Allard-Pride-Lafarge model is deployed as the multiscale-based predictor. It is shown that the strategy allows for the relationship between the micro-/structural parameters and the experimental acoustic response to be well approximated, even if a small physical dataset (comprised of ten samples) is used for training. The methodology, therefore, enables the identification and validation of acoustical models under constraints related to data limitation and parametric dependence. It also paves the way for an efficient exploration of the parameter space for acoustical materials design.

This paper presents for the first time an eco-friendly combination of cationic photopolymerization and the solid template technique to obtain macroporous epoxy resins from resorcinol diglycidyl ether (RDGE) with defined cell size and distribution. The polymerization was performed by cationic polymerization under UV irradiation in the presence of NaCl particles template sintered through the spark plasma sintering process (SPS). After removal of NaCl by water, a porous material with interconnected pores was obtained. The influence of processing parameters, i.e., reactant contents, UV irradiation time, and post-curing conditions on the reticulation achievement and the thermomechanical behavior have been pointed out. Mechanical, physical, acoustic and morphological properties were deeply investigated. For instance, the specific compressive modulus is of 50.9 MPa cm3.g−1 for a density of 0.224 g.cm−3 and the glass transition is around 137 °C, which makes this system an interesting alternative for sustainable building materials.

This study has developed novel fully bio-based resorcinol epoxy resin&ndash, diatomite composites by a green two-stage process based on the living character of the cationic polymerization. This process comprises the photoinitiation and subsequently the thermal dark curing, enabling the obtaining of thick and non-transparent epoxy-diatomite composites without any solvent and amine-based hardeners. The effects of the diatomite content and the compacting pressure on microstructural, thermal, mechanical, acoustic properties, as well as the flame behavior of such composites have been thoroughly investigated. Towards the development of sound absorbing and flame-retardant construction materials, a compromise among mechanical, acoustic and flame-retardant properties was considered. Consequently, the composite obtained with 50 wt.% diatomite and 3.9 MPa compacting pressure is considered the optimal composite in the present work. Such composite exhibits the enhanced flexural modulus of 2.9 MPa, a satisfying sound absorption performance at low frequencies with Modified Sound Absorption Average (MSAA) of 0.08 (for a sample thickness of only 5 mm), and an outstanding flame retardancy behavior with the peak of heat release rate (pHRR) of 109 W/g and the total heat release of 5 kJ/g in the pyrolysis combustion flow calorimeter (PCFC) analysis.

International audience; The acoustic properties of composite structures made of a perforated panel, an air gap, and a porous layer, can be studied numerically by a combined use of ad hoc optimization and sensitivity analysis methods. The methodology is briefly described and is systematically applied to a series of multi-layer configurations under manufacturing constraints. We specifically consider a foam layer of constant thickness presenting three different degrees of reticulations (pore opening). For each foam layer, the optimal geometrical parameters of the perforated panel and the cavity depth maximizing sound absorption under normal incidence are determined, together with the corresponding sensitivity indices. The simulation results are found in good agreement with interpretations and experimental data provided elsewhere. From a general perspective, the framework can be used to identify the most influential parameters within multiscale settings for acoustics studies, hence enabling robust design under material and microstructural uncertainties for instance.

International audience; This work presents benchmark examples related to the modelling of sound absorbing porous media with rigid frame based on the periodicgeometry of their microstructures. To this end, rigorous mathematical derivations are recalled to provide all necessary equations, useful relations, and formulas for the so-called direct multi-scale computations, as well as for the hybrid multi-scale calculations based on the numerically determined transport parameters of porous materials. The results of such direct and hybrid multi-scale calculations are not onlycross verified, but also confirmed by direct numerical simulations based on the linearised Navier-Stokes-Fourier equations. In addition, relevanttheoretical and numerical issues are discussed, and some practical hints are given.

International audience; This article presents an experimental and numerical parametric study of the acoustical properties of monodisperse open-cell solid foam. Solid foam samples are produced with very good control of both the pore size (from 0.2 to 1.0 mm) and the solid volume fraction (from 6% to 35%). Acoustical measurements are performed by the threemicrophone impedance tube method. From these measurements, the visco-thermal parameters-namely, viscous permeability, tortuosity, viscous characteristic length, thermal permeability, and thermal characteristic length-are determined for an extensive number of foam samples. By combining Surface Evolver and finite-element method calculations, the visco-thermal parameters of body centered cubic (bcc) foam numerical samples are also calculated on the whole range of solid volume fraction (from 0.5% to 32%), compared to measured values and to theoretical model predictions [Langlois et al. (2019). Phys. Rev. E 100(1), 013115]. Numerical results are then used to find approximate formulas of visco-thermal parameters. A systematic comparison between measurements and predictions of the Johnson-Champoux-Allard-Lafarge (JCAL) model using measured visco-thermal parameters as input parameters, reveals a consistent agreement between them. From this first step, a calculation of the optimal microstructures maximizing the sound absorption coefficient is performed. V

International audience; The ability of air-saturated fibrous media to mitigate sound wavesiscontrolled by their transport properties that are themselves controlled by the geometrical characteristics of their microstructure such as the open porosity,fiber radius, and fiber orientation. Here, micro-macro relationships are proposed to link these microstructural features to the macroscopic transport properties of random fiber structures. These transport properties are the tortuosity, the viscous and thermal static permeabilities, and the viscous and thermal characteristic lengths. First, representative elementary volumes (REVs)ofrandom fiber structures are generated for different triplets of porosity,fiber radius and fiber orientation. The fibers are allowed to overlap and are motionless (rigid-frame assumption). The fiber orientation is derivedf rom as econd order orientation tensor.S econd, the transport equations are numerically solved on the REVs which are seen as periodic unit cells. These solutions yield the transport properties governing the sound propagation and dissipation in the respective fibrous media. From these solutions, micro-macro relationships are derivedt oe stimate the transport properties when the geometry of the fiber structure is known. Finally,these relationships are used to study the influence of the microstructural features on the acoustic properties of random fiber structures.

International audience; Numerical and analytical methods at both micro-and mesoscales are used to study how the electrical resistivity and the high frequency tortuosity of solid foam are modied by the presence of membranes that partially or totally close the cell windows connecting neighbor pores. Finite element method (FEM) simulations are performed on two pores connected by a single-holed membrane and on well-ordered Kelvin foam. For two pores connected by a single-holed membrane, we show that the equation for pore access resistance obtained by Sahu and Zwolak (Phys. Rev. E 98, 012404, 2018) can predict, after a few modications, the electrical resistivity at the membrane scale for a large range of membrane apertures. In the second part, considering these analytical results, we build a pore-network model by using two kinds of conductances at the pore scale-inter-pore conductance and intra-pore conductance. Local inter-pore resistances govern foam electrical conductivity at small membrane aperture size, but when the membrane aperture has the same order of magnitude as the pore size, the intra-pore resistances are no longer negligible. An important success of this pore-network model is that it can be used to study the eects of percolation on the foam electrical conductivity by using pore-network simulations on larger samples containing a few thousands of pores and having dierent proportions of closed membrane randomly distributed over the sample. The tortuosity is found to be drastically larger than one in foam containing membranes with small apertures or a signicant fraction of closed membranes.

An acoustic foam is utilized increasingly in industrial by replacing the fibrous layer because of particularly a health reason. Its acoustic properties depend heavily on its microstructures (pore size's distribution , membrane presence). The aim of this work is to study the influence of an extended of pore size's distribution on its properties acoustic and elastic. The microstructure of the acoustic foam is created in three steps. Firstly, by using the discrete element method, a random stack of sphere is generated. After that, a tessellation of Laguerre from the center and radius of the spheres is carried out to build a foam skeleton. Finally, the Plateau borders, that have a concave triangular section of a variable thickness, is obtained by a minimizing of surface energy with the help of a Surface Evolver software. A simulation with the help of the finite elements method evaluates the properties acoustic., Les mousses acoustiques sont de plus en plus utilisées dans l'industrie en remplacement des milieux fibreux pour des raisons de santé notamment. Leurs propriétés acoustiques dépendent fortement de leurs microstructures (distribution de taille de pores, présence de membranes). L'objectif de ce travail est d'étudier l'influence d'une distribution étendue de tailles de pores sur les propriétés acoustiques et élastiques. La microstructure des mousses est reconstruite en trois étapes. La première étape consiste en la génération d'un empilement aléatoire de sphères, généré par la méthode des éléments discrets. Ensuite, une tessellation de Laguerre à partir des centres et des rayons des sphères est réalisée pour construire le squelette de la mousse. Finalement, les bords de Plateau ayant une section triangulaire concave d'épaisseur variable, sont obtenus par minimisation d'énergie de surface à l'aide du logiciel Surface Evolver. Les propriétés acoustiques sont calculées à l'aide de simulations par la méthode des éléments finis.

International audience; Significant advances have been made over the last 15 years in the field of modelling the acoustic properties of foams from the description of their microstructures. It entails a multidisciplinary work at the junction between physico-chemistry and mechanics of porous media, which involves a dialogue between different disciplines and requires the joint development of several techniques (imaging, upscaling, numerical computations, and experimental identification). It seems to be of timely interest to take stock of the methodological developments that have provided guidance on how to manufacture the new generation of foams with enhanced properties and to identify possible future methodological developments.

International audience; In this paper, we study how the permeability of solid foam is modified by the presence of membranes that close partially or totally the cell windows connecting neighboring pores. The finite element method (FEM) simulations computing the Stokes problem are performed at both pore and macroscopic scales. For foam with fully interconnected pores, we obtain a robust power-law relationship between permeability and aperture size. This result is due to the local pressure drop mechanism through the aperture as described by Sampson for fluid flow through a circular orifice in a thin plate. Based on this local law, pore-network simulation of simple flow is used and is shown to reproduce FEM results. Then this low computational cost method is used to study in detail the effect of an open window fraction on the percolation properties of the foam pore space. The results clarify the effect of membranes on foam permeability. Finally, Kirkpatrick’s model is adapted to provide analyticalexpressions that allow for our simulation results to be successfully reproduced.

International audience; This work is concerned with the multiscale prediction of the transport and sound absorption propertiesassociated with industrial glass wool samples. In the first step, an experimental characterizationis performed on various products using optical granulometry and porosity measurements. A morphological analysis, based on scanning electron imaging, is further conducted to identify the probability density functions associated with the fiber angular orientation. The key morphological characterization parameters of the microstructure, which serve as input parameters of the model, include the porosity, the weighted volume diameter accounting for both lengths and diameters of the analyzed fibers (and therefore the specific surface area of the random fibrous material), and the preferred out-of-plane fiber orientation generated by the manufacturing process. A computational framework is subsequently proposed and allows for the reconstruction of an equivalent fibrous network. A fully stochastic microstructural model, parameterized by the probability laws inferred from the database, is also proposed herein. Multiscale simulations are carried out to estimate transport properties and sound absorption. With no adjustable parameter, the results accounting for ten different samples obtained with various processing parameters are finally compared with the experimental data and used to assess the relevance of the reconstruction procedures and the multiscale computations.

International audience; In this study, we show how milli-fluidic tools can be used to elaborate polymer foams with tunable microstructural parameters, such as the size and the connectivity of the pores. We produce several samples having the same density and the same monodisperse pore size but different values of the closure rate of the windows separating the foam pores, which is estimated by measuring the proportion of closed cells and the size distribution of apertures for open-wall cells. This distribution is based on a distinction between the windows counting four or less edges from the windows counting more than four edges. Then a representative unit cell is reconstructed to mimic the main feature of microstructure information and serves as the basis to the computation of the sound absorbing parameter, using numerical homogenization techniques. Very good correspondences between numerical results and experimental measurements were observed. Our analysis reveals a significant dependence of membrane level on the sound absorption behavior of these foams.

International audience; The ability of fibrous media to mitigate sound waves is controlled by their transport properties that are themselves greatly affected by the geometrical characteristics of their microstructure such as porosity, fiber radius, and fiber orientation. Here, the influence of these geometrical characteristics on the anisotropic transport properties of random fiber structures is investigated. First, representative elementary volumes (REVs) of random fiber structures are generated for different triplets of porosity, fiber radius and fiber orientation. The fibers are allowed to overlap and are motionless (rigid-frame assumption). The fiber orientation is derived from a second order orientation tensor. Second, the transport equations are numerically solved on the REVs which are seen as periodic unit cells (PUCs). These solutions yield the transport properties governing the sound propagation and dissipation in the respective fibrous media. These transport properties are the tortuosity, the viscous and thermal static permeabilities, and the viscous characteristic length. Finally, relations are proposed to estimate the transport properties and the thermal characteristic length when the geometry of the fiber structures is known.

Copyright 2017 Acoustical Society of America. This article may be downloaded for personal use only.Any other use requires prior permission of the author and the Acoustical Society of America.The following article appeared in the Journal of the Acoustical Society of America (JASA) and may be found at http://dx.doi.org/10.1121/1.4989373.; International audience; The main purpose of this article is to present, within a unified framework, a technique based on numerical homogenization, to model the acoustical properties of real fibrous media from their geometrical characteristics and to compare numerical results with experimental data. The authors introduce a reconstruction procedure for a random fibrous medium and use it as a basis for the computation of its geometrical, transport, and sound absorbing properties. The previously ad hoc " fiber anisotropies " and " volume weighted average radii, " used to describe the experimental data on microstructure, are here measured using scanning electron microscopy. The authors show that these parameters, in conjunction with the bulk porosity, contribute to a precise description of the acoustical characteristics of fibrous absorbents. They also lead to an accurate prediction of transport parameters which can be used to predict acoustical properties. The computed values of the perme-ability and frequency-dependent sound absorption coefficient are successfully compared with per-meability and impedance-tube measurements. The authors' results indicate the important effect of fiber orientation on flow properties associated with the different physical properties of fibrous materials. A direct link is provided between three-dimensional microstructure and the sound absorbing properties of non-woven fibrous materials, without the need for any empirical formulae or fitting parameters.

Copyright 2013 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The following article appeared in the Journal of the Acoustical Society of America (JASA) and may be found at http://link.aip.org/link/?JAS/134/4681.; International audience; The acoustical macro-behavior of mineral open-cell foam samples is modelled from microstructure morphology using a three-dimensional idealized periodic unit-cell (3D-PUC). The 3D-PUC is based on a regular arrangement of spheres, allowed to interpenetrate during the foaming process. Identi cation and sizing of the 3D-PUC is made from X-ray computed microtomography and manufacturing process information. In addition, the 3D-PUC used allows to account for two scales of porosity: the interconnected network of bubbles (meso-porosity) and the inter-crystalline porosity of a gypsum matrix (micro-porosity). Transport properties of the micro- and the meso- scales are calculated from fi rst principles and a hybrid micro-macro method is used in order to determine the frequency-dependent visco-thermal dissipation properties. The double porosity theory provides the visco-thermal coupling between the meso- and micro- scales [J. Acoust. Soc. Am. 114, 7389 (2003)]. Finally, the results are successfully compared with experiments for two di erent mineral foam samples. The main originality of this work is to maintain a direct link between the microstructure morphology and the acoustical macro-behavior all along the multi-scale modelling process, without any adjusted parameter.

Copyright 2017 Acoustical Society of America. This article may be downloaded for personal use only.Any other use requires prior permission of the author and the Acoustical Society of America.The following article appeared in the Journal of the Acoustical Society of America (JASA) and may be found at http://dx.doi.org/10.1121/1.4989373.; International audience; The purpose of this work is to systematically study the effect of the throat and the pore sizes on the sound absorbing properties of open-cell foams. The three-dimensional idealized unit cell used in this work enables to mimic the acoustical macro-behavior of a large class of cellular solid foams. This study is carried out for a normal incidence and also for a diffuse field excitation, with a relatively large range of sample thicknesses. The transport and sound absorbing properties are numerically studied as a function of the throat size, the pore size, and the sample thickness. The resulting diagrams show the ranges of the specific throat sizes and pore sizes where the sound absorption grading is maximized due to the pore morphology as a function of the sample thickness, and how it correlates with the corresponding transport parameters. These charts demonstrate, together with typical examples, how the morphological characteristics of foam could be modified in order to increase the visco-thermal dissipation effects.

Copyright 2014 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The following article appeared in the Journal of the Acoustical Society of America (JASA) and may be found at http://link.aip.org/link/?JAS/135/3172.; International audience; It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.

Copyright 2013 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The following article appeared in Proceedings of Meetings on Acoustics (POMA) and may be found at http://dx.doi.org/10.1121/1.4799694.; International audience; The present paper reports on the modeling of linear elastic properties of acoustically insulating foams with unit cells containing solid films or membranes at the junction between interconnected pores from a numerical homogenization technique. It combines fluid-flow inducedmicrostructure identification with simulations of the effective Young's modulus and Poisson ratio from a mixture of routinely available laboratory measurements (porosity, permeability, cell size) and finite element calculations when the boundary conditions of the periodic unit celltake particular symmetric forms. This combination results in microstructural determination of the macroscopic coefficients entering into the Biot-Allard theory of wave propagation and dissipation through porous media. Precise control over pore morphology and mechanical propertiesof the base material renders this multi-scale approach particularly suitable for various advanced applications.

Copyright 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.; International audience; We show that critical path ideas lead to the identification of two local characteristic sizes for the long wavelength acoustic properties in cellular solids, the pore and throat sizes. Application of the model to real foam samples, which may contain solid films or membranes yields quantitative agreement between a finite-element numerical homogenization approach and experimental results. From three routinely available laboratory measurements: the open porosity ϕ, the static viscous permeability k0, and the average struts length Lm obtained from microscopy analysis; asymptotic transport parameters at high-frequencies and the normal incidence sound absorption coefficient are derived with no adjustable parameters.

Copyright 2010 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.; International audience; Closed-cell metallic foams are known for their rigidity, lightness, thermal conductivity as well as their low production cost compared to open-cell metallic foams. However, they are also poor sound absorbers. Similarly to a rigid solid, a method to enhance their sound absorption is to perforate them. This method has shown good preliminary results but has not yet been analyzed from a microstructure point of view. The objective of this work is to better understand how perforations interact with closed-cell foam microstructure and how it modifies the sound absorption of the foam. A simple two-dimensional microstructural model of the perforated closed-cell metallic foam is presented and numerically solved. A rough three-dimensional conversion of the two-dimensional results is proposed. The results obtained with the calculation method show that the perforated closed-cell foam behaves similarly to a perforated solid; however, its sound absorption is modulated by the foam microstructure, and most particularly by the diameters of both perforation and pore. A comparison with measurements demonstrates that the proposed calculation method yields realistic trends. Some design guides are also proposed. (C) 2010 Acoustical Society of America. [DOI: 10.1121/1.3473696]

International audience; This paper presents recent developments in the field of micro-acoustics of porous media. The fundamental idea of the proposed approach is that it is possible to assess porous microstructure and acoustical properties from the three-dimensional implementation of micro-acoustics based scaling relations on porous materials. We illustrate this approach through results from the application of this technique to real samples of predominately open-cell polymeric foams.

Copyright 2008 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.; International audience; Is it possible to find a two-dimensional (2D) periodic unit cell representative of the dynamic viscous dissipation properties of a real porous media? This is a challenging question addressed in this paper through a review of tools and methods of experimental and computational micro(poro)mechanics. The combination of advanced experimental imaging and numerical homogenization techniques provides a unique opportunity to understand and assess the limits of two-dimensional models of microstructures, as a potential basis for the engineering prediction of macroscopic properties of acoustical materials. This is illustrated for a real sample of open-cell aluminum foam. The conclusion, based on this analysis, is that the 2D periodic foam model geometry provides a reliable estimate of the dynamic permeability, except in the low frequency range. This is not surprising because in the 2D periodic foam model geometry, ligaments are always perpendicular to the flow direction, thus decreasing artificially the static permeability of the viscous flow.

Copyright 2008 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.; International audience; Based on a direct generalization of a proof given by Torquato for symmetry property in static regime, this express letter clarifies the reasons why the dynamic permeability tensor is symmetric for spatially periodic structures having symmetrical axes which do not coincide with orthogonal pairs being perpendicular to the axis of three-, four-, and sixfold symmetry. This somewhat nonintuitive property is illustrated by providing detailed numerical examples for a hexagonal lattice of solid cylinders in the asymptotic and frequency dependent regimes. It may be practically useful for numerical implementation validation and∕or convergence assessment.

Copyright 2008 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.; International audience; Results from a numerical study examining micro-/macrorelations linking local geometry parameters to sound absorption properties are presented. For a hexagonal structure of solid fibers, the porosity ϕ, the thermal characteristic length Λ′, the static viscous permeability k0, the tortuosity α∞, the viscous characteristic length Λ, and the sound absorption coefficient are computed. Numerical solutions of the steady Stokes and electrical equations are employed to provide k0, α∞, and Λ. Hybrid estimates based on direct numerical evaluation of ϕ, Λ′, k0, α∞, Λ, and the analytical model derived by Johnson, Allard, and Champoux are used to relate varying (i) throat size, (ii) pore size, and (iii) fibers' cross-section shapes to the sound absorption spectrum. The result of this paper tends to demonstrate the important effect of throat size in the sound absorption level, cell size in the sound absorption frequency selectivity, and fibers' cross-section shape in the porous material weight reduction. In a hexagonal porous structure with solid fibers, the sound absorption level will tend to be maximized with a 48±10 μm throat size corresponding to an intermediate resistivity, a 13±8 μm fiber radius associated with relatively small interfiber distances, and convex triangular cross-section shape fibers allowing weight reduction.

Copyright 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.; International audience; This paper reports simulation results of frequency dependent heat conduction through three-dimensional reconstructed unit cells of an open-cell aluminum foam under acoustic excitations. First, a three-dimensional random walk based algorithm is proposed to calculate the dynamic thermal permeability or dynamic bulk modulus of periodic complex porous geometries. Second, the error and convergence of the implemented calculation algorithm are quantified in terms of the random walk population, normalized trapping distance, and type of geometry. Finally, the algorithm is applied to the calculation of the dynamic bulk modulus of an aluminum foam and compared to laboratory measurements. Good agreement is obtained between simulations and measurements.

The fundamental issue of determining acoustic properties of porous media from their local geometry is examined in this PhD dissertation thesis, thanks to a sample of open-cell aluminum foam analyzed by axial computed microtomography. Various geometric properties are measured to characterize the experimental sample at the cell size level. This is done in order to reconstruct a porous medium by means of idealized three- and two- dimensional unit-cells. The frequency dependant thermal and velocity fields governing the propagation and dissipation of acoustic waves through rigid porous media are computed by Brownian motion simulation and the finite element method, respectively. Macroscopic behavior is derived by spatial averaging of the local fields. Our results are compared to experimental data obtained from impedance tube measurements. Firstly, this approach leads to the identification of the macroscopic parameters involved in Pride and Lafarge semi-phenomenological models. Secondly, it yields a direct access to thermal and viscous dynamic permeabilities. However, the bi-dimensional model underestimates the static viscous permeability as well as the viscous characteristic length; what thus require a three-dimensional implementation., La question fondamentale de la détermination des propriétés acoustiques de milieux poreux à partir de leur géométrie locale est examinée dans cette thèse de doctorat, à partir d'un échantillon de mousse d'aluminium à cellules ouvertes ayant été analysé par microtomographie axiale à rayons-X. Plusieurs propriétés géométriques sont mesurées pour caractériser l'échantillon expérimental à l'échelle de la cellule. Cette information est utilisée de manière à reconstruire un milieu poreux au moyen d'unités cellulaires idéalisées tri- et bi- dimensionnelles. La dépendance en fréquences des champs de températures et de vitesses gouvernant la propagation et la dissipation des ondes acoustiques à travers un milieu poreux rigide est calculée par simulation de mouvement Brownien et par la méthode des éléments finis, respectivement. Le comportement macroscopique est obtenu par moyennes spatiales des champs locaux. Nos résultats sont comparés à des données expérimentales obtenues par des mesures au tube d'impédance. Premièrement, cette approche conduit à l'identification des paramètres macroscopiques du model semi-phénoménologique de Pride-Lafarge. Deuxièmement, elle fournit un accès direct aux perméabilités dynamiques thermique et visqueuse. Néanmoins, le modèle bidimensionnel sous-estime la perméabilité visqueuse statique ainsi que la longueur caractéristique visqueuse; ce qui requiert donc une implémentation tridimensionnelle.

Copyright 2001 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.; International audience; The weak-field dielectric dispersion (100 Hz-1.8 GHz) studies both of pure and Fe2+/Fe3 modified Cd2Nb2O7 ceramics over the temperature range of 90-380 K are presented and discussed from the viewpoint of relaxor and glassy properties of the system. It is revealed that Cd2Nb2O7 pyrochlore is intolerant of the addition of 25 mol % Fe2+ or Fe3+ for Cd2+. From the x-ray diffraction analysis, pure Cd2Nb2O7 forms a single-phase pyrochlore, while the compositions Cd1.5Fe0.52+Nb2O7 and Cd1.5Fe0.53+Nb2O7 give CdNb2O6 columbite doped with Fe2+ or Fe3+ on the Cd sites (

Copyright 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in J. Appl. Phys. 113, 084905 (2013); doi: 10.1063/1.4793492 and may be found at http://dx.doi.org/10.1063/1.4793492; International audience; Identifying microscopic geometric properties of and fluid flow through opened-cell and partially closed-cell solid structures is a challenge for material science, in particular for the design of porous media used as sound absorbers in building and transportation industries. We revisit recent literature data to identify the local characteristic lengths dominating the transport properties and sound absorbing behavior of polyurethane foam samples by performing numerical homogenization simulations. To determine the characteristic sizes of the model, we need porosity and permeability measurements in conjunction with ligament lengths estimates from available scanning electron microscope images. We demonstrate that this description of the porous material, consistent with the critical path picture following from the percolation arguments, is widely applicable. This is an important step towards tuning sound proofing properties of complex materials.

Copyright 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.; International audience; This article explores the applicability of numerical homogenization techniques for analyzing transport properties in real foam samples, mostly open-cell, to understand long-wavelength acoustics of rigid-frame air-saturated porous media on the basis of microstructural parameters. Experimental characterization of porosity and permeability of real foam samples are used to provide the scaling of a polyhedral unit-cell. The Stokes, Laplace, and diffusion-controlled reaction equations are numerically solved in such media by a finite element method in three-dimensions; an estimation of the materials' transport parameters is derived from these solution fields. The frequency-dependent visco-inertial and thermal response functions governing the long-wavelength acoustic wave propagation in rigid-frame porous materials are then determined from generic approximate but robust models and compared to standing wave tube measurements. With no adjustable constant, the predicted quantities were found to be in acceptable agreement with multi-scale experimental data and further analyzed in light of scanning electron micrograph observations and critical path considerations.

Copyright 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.; International audience; In this article, the issue of reconstructing an idealized periodic unit cell (PUC) to represent a porous medium is examined by means of microcomputed tomography (μCT). Using μCT, three-dimensional images of open-cell foam are collected and used to characterize the representative parameters of its cellular morphology. These parameters are used in order to reconstruct the porous medium by means of an idealized PUC: a tetrakaidecahedron with ligaments of triangular cross sections, whose characteristic dimensions have been measured on the μCT images. The proposed reconstruction of the idealized PUC is applied to four aluminum foams. The averaged macroscopic properties of the foams (open porosity and thermal characteristic length) are deduced from their respective PUC model and compared to experimental measurements and literature data. Good correlations are obtained. For each of the foams, this provides a parameterized idealized periodic unit cell on which the partial differential equations governing sound dissipation and propagation in foams can be solved with a view to studying the microphysical basis of the acoustical macrobehavior.

A research program has been initiated in 2002 in order to link microstructure of high porosity open‐cell foams to their acoustic properties. This paper is intended to highlight the main results of this study. The general objective of the research program is the determination of the acoustical macro‐behavior from the physics at the local scale. A real rigid‐framed porous media is studied. To this end, one needs first to determine the local geometry of the media, and second to solve over this geometry the partial differential equations that govern dissipation phenomena by thermal and viscous effects. The first step has been overcome by the technique of computed microtomography. This leads to experimental identification of the parameters of an idealized periodic unit‐cell. The second step, solving harmonic heat and viscous fluid equations, is performed using Brownian motion and finite element simulations, respectively. Then, macroscopic behavior is obtained by spatial averaging of the local and frequency‐dependent thermal and velocity fields. Results are presented in terms of two dynamic characteristic functions (viscous and thermal permeabilities) compared to impedance tube measurements. This computational methodology may be seen as a first step to optimize the microstructure of foams from a bottom‐up approach for better sound proofing.

Acoustic dissipation in porous media is mainly due to viscous and thermal mechanisms that occur in the pores of the microstructure. The purpose of this study is the determination of the macroscopic dynamic acoustic bulk modulus and thermal permeability of real foams from a local scale approach. To achieve this goal, two distinct steps are followed. First, the local geometry of a real foam is obtained using computed microtomography (μCT), then a periodic and regularly paving space tetrakaidecahedron cell is identified from the microstructure. Second, the heat equation is solved for the geometrical model. The paper provides a three‐dimensional application of the efficient simulation technique of Brownian motion proposed by Torquato et al. for steady state diffusion‐controlled problems [Appl. Phys. Lett. 55, 1847–1849 (1989)] and adapted by Lafarge [Poromechanics II, 708 (2002)] in a bi‐dimensional case. The influence of the model’s microstructural details (anisotropy, and struts junction and cross‐section) on the macroscopic properties are studied. The predictions of the macroscopic properties using this local scale approach are then compared to experimental measurements.

Foam materials are frequently used in engineering applications, due to their absorption and sound insulation properties. At the same time, the evolution of CO2 emission goals, together with new standards for acoustic, thermal, and fire resistance performance, calls for further developments that seek to reduce the impact of acoustic treatments---while maintaining, or even improving, global performance. Fine particles are usually introduced during the foaming process to improve fire resistance. By disrupting the nucleation sites, this procedure leads to disordered microstructures where cells of very different sizes coexist locally. This thesis work deals with the construction and experimental validation of a computational multi-scale-informed framework for modeling the acoustic behavior of polydisperse foams. The main objective is to model the relationships between the local foam geometry and the acoustic behavior exhibited at macroscale, with a view towards devising foam manufacturing conditions under acoustic performance targets. Here, we restrict our attention to the case of foams which present strong local heterogeneities in terms of pore sizes and therefore cannot be described by a deterministic unit cell. Advanced imaging techniques (namely, axial X-ray microtomography and scanning electron microscopy) are first deployed to identify relevant morphological characteristics on the studied microstructures. The geometrical properties thus obtained are then used in order to reconstruct spatial partitions consistent with the observations. The viscous permeability, which is a key parameter for the determination of acoustic properties, is estimated through "Pore-Network" simulations. The numerical predictions show that the permeability of a foam is strongly influenced, not only by the presence of membranes, but also by the variation of pore sizes. The effect of membrane thickness on viscous parameters (i.e., the viscous characteristic length and the tortuosity) describing the asymptotic behavior at high frequencies is also thoroughly studied. For the calculation of the viscous characteristic length, the results show that the effect of thin-membrane thickness can equivalently be modeled by virtual membranes without thickness. Finally, the acoustic properties of a real foam sample presenting a wide pore size distribution are modeled. Good agreement with experimental data obtained from an impedance tube is observed, which supports the relevance of the proposed approach., Les mousses sont utilisées fréquemment notamment en raison de leurs propriétés d'absorption et d'isolation sonore. Les exigences accrues en matière de réductions d'émissions de CO2 combinées à des exigences de performances acoustiques, thermiques, et de tenue au feu impliquent un effort significatif tourné vers l'allègement des traitements acoustiques---à performances égales ou supérieures. L'introduction de particules fines lors du processus de moussage, réalisée afin d’améliorer la tenue au feu, perturbe les sites de nucléation, ce qui conduit à la production de microstructures désordonnées où coexistent localement des cellules de tailles très contrastées. Ce travail de thèse traite de la construction d'outils numériques pour la modélisation du comportement acoustique de mousses polydisperses à partir d’une démarche multi-échelle et multi-physique. L'objectif principal est de pouvoir développer des relations entre la géométrie locale et le macro-comportement acoustique, afin de pouvoir guider la fabrication de mousses dans le but d'optimiser leurs performances acoustiques. Nous nous intéressons plus particulièrement au cas de mousses qui, présentant une forte hétérogénéité locale de tailles de pores, ne peuvent être décrites par une cellule périodique idéalisée (modèle déterministe). Des techniques d'imagerie avancées (microtomographie axiale à rayons-X et microscopie électronique à balayage) sont utilisées, dans un premier temps, pour identifier les caractéristiques morphologiques des microstructures étudiées. Les caractéristiques géométriques obtenues sont ensuite modélisées afin de reconstruire des partitions spatiales proches de celles mesurées. La perméabilité visqueuse, paramètre clé au regard de la détermination des propriétés acoustiques, est estimée par une simulation de type "pore-network". Nous quantifions, au travers de telles simulations, que la perméabilité d'une mousse est fortement influencée, non seulement par la présence des membranes, mais aussi par la variation de la taille des pores. L'effet de l'épaisseur de membrane sur les paramètres visqueux (longueur caractéristique visqueuse et tortuosité) décrivant le comportement asymptotique haute fréquence est, de plus, finement étudié. Les résultats obtenus montrent, en particulier, qu'il est possible de modéliser l'effet de l'épaisseur de membranes minces par des membranes virtuelles sans épaisseur pour le calcul de la longueur caractéristique visqueuse. Enfin, les propriétés acoustiques d'un échantillon réel de mousse ayant une distribution étendue de tailles de pores sont modélisées. Une bonne concordance avec les données expérimentales obtenues à partir d'un tube d'impédance confirme la validité de la méthode proposée.

This work is mainly concerned with the determination of the acoustic properties of foams. This is a project carried out as part of a collaboration between a team of physicochemistry of foams in charge of the development of model materials (Navier laboratory UMR8205 CNRS) and a team of acousticians responsible for the study of their acoustic properties (MSME laboratory UMR 8208 CNRS). This thesis is structured around three main parts, the content of which is summarized below. 1) The first part deals with the generation of response surfaces by polynomial approximations, in order to have an intermediate model between the micro-macro fInite element model and the macroscopic response. Instead of calling the fInite element model systematically in an optimization work, we use the responsesurface that contains the information associated with finite element calculation points and the corresponding interpolations. This manuscript was published in the AAuA journal as a fast track publication. 2) The second part deals with a finite element calculation in whicha large number of realizations are carried out in order to take into account all the possible combinations when one has fine experimental characterization at the microstructure scale and that one seek to determine the properties of the foam with precision. The manuscriptis in preparation and a possible journal for the publication of this manuscript is the journal Materials and Design. 3) The third part focuses on the development of a semi-analytical model defined from an available formula to predict the permeability of a circular orifice in a thin plate. This model, used in an appropriate way, makes it possible to calculate the permeability of foams with a constant bubble size but a tuned membrane content. Numerical validations by finite element computations are proposed. The article has been accepted for publication in the journal Physical Review E. A general introduction (statement of the problem, theoretical and methodological framework, continuity and complementarity of the papers) and a general conclusion complete these three parts, and make it possible to discuss these contributions.; Ce travail concerne principalement la détermination des propriétés acoustiques de mousses. Il s’agit d’un projet mené dans le cadre d’une collaboration entre une équipe de physico-chimie des mousses chargée de l’élaboration de matériaux modèles (laboratoire Navier UMR 8205 CNRS) et une équipe d’acousticiens chargée de l’étude de leurs propriétés acoustiques (laboratoire MSME UMR 8208 CNRS). Cette thèse s’articule essentiellement autour de trois parties principales, dont le contenu est résumé ci-dessous. 1) La première partie porte sur la génération de surfaces de réponse par des approximations polynomiales, dans le but de disposer d'un modèle intermédiaire entre le modèle éléments finis micro-macro et la réponse macroscopique. Au lieu d'appeler le modèle éléments finis systématiquement dans un travail d'optimisation, on a recourt à la surface de réponse qui contient l'information associée aux points de calcul éléments finis ainsi que les interpolations correspondantes. Ce manuscrit a été publié dans le journal AAA sous forme de communication rapide. 2) La deuxième partie porte sur la mise au point d'un modèle semi-analytique définit à partir d'une formule disponible pour prédire la perméabilité d'une plaque infinie percée par un trou de surface connue. Ce modèle, utilisé de manière appropriée, permet de calculer la perméabilité de mousses dont la taille de bulles est constante et le taux de fermeture de membranes variable. Des validations numériques par éléments finis et expérimentales sont proposées. L'article a été accepté pour publication dans la revue Physical Review E. 3) La troisième partie, porte sur un calcul éléments finis dans lequel un grand nombre de réalisations sont menées de manière à prendre en compte l'ensemble des combinaisons possibles lorsque on dispose de caractérisation expérimentales fines à l'échelle de la microstructure et que l'on souhaite connaitre la réponse de la mousse avec précision. Le manuscrit est en préparation et la revue visée pour ce dernier manuscrit est le journal Materials and Design. Une introduction générale (problématique, cadre théorique et méthodologique, continuité et complémentarité des articles) et une discussion générale complètent ces trois parties, et permettent de mettre en perspectives ces contributions par rapport à la littérature existante sur le sujet.

This research project was inscribed in an eco-conception approach for architected materials with high acoustic potential. In this research project, we are interested particularly in the description of dissipation and propagation phenomena of sound waves in a fibrous medium by using multi-scale and multi-physics approaches. In this work, we determine the transport and acoustic properties of fiber media based on the description of geometry at their local scale. The fiber media consist of asclepias fibers which are typically vegetable fibers adopting a long hollow cylinder. To solve this problem, the methodology consists of 4 principle steps below: (i) Characterize and model the geometry of fiber medium; (ii) Calculate the transport parameters and acoustic properties of reconstructed fiber medium; (iii) Validate the results of the transport and acoustic properties by comparing with experimental measurements; (iv) Evaluate the evolution of transport parameters as function of geometrical parameters at the local scale. For the geometrical reconstruction, isotropic model of straight lines (Poisson processes) and angular orientation tensor were used. They allow representing of principle characteristics influencing the transport and acoustic properties of material at macroscopic scale. The resolutions of principal problems governing the acoustic behavior at the macroscopic scale were then performed by using the numerical homogenization method. We firstly demonstrate that the developed method allows predicting of absorption behavior of a random fiber medium based on only their geometrical characteristic description (porosity, fibers radius, angular orientation distribution) without adjustment coefficient, and the validated by experimental measurements. Secondly, based on the reconstruction method, one can systematically study the whole transport phenomena on a wide range of porosity and angular orientation in order to provide the laws which can be applied by other user on a wide range of real fiber media. Finally, we verify more particular the hypothesis that a fibrous material can be described by a mean diameter value of their fibers, this work allows identifying the limit of this approach and their application conditions when a fiber medium is constituted of a large distribution of fiber diameters or bimodal; Ce projet de recherche s'inscrit dans une démarche d'éco-conception de matériaux architecturés à fort potentiel acoustique. On s'intéresse en particulier dans ce travail de thèse à la description des phénomènes de dissipation et de propagation des ondes acoustiques dans un milieu fibreux par une approche multi-échelle et multi-physique. Dans cette étude, il s'agit de décrire les propriétés acoustiques du milieu fibreux à partir d'une description de la géométrie à l'échelle locale de milieux fibreux. Le milieu fibreux est constitué de fibres d'asclépiades, qui sont typiquement des fibres végétales adoptant la forme de longs cylindres. Pour traiter ce problème, la méthodologie employée consiste en quatre étapes principales : (i) caractérisation et modélisation de la géométrie du milieu fibreux; (ii) calcul des paramètres de transport et acoustiques du milieu fibreux reconstruit; (iii) validation expérimentale de propriétés de transport et acoustiques; (iv) évaluation des évolutions de propriétés de transport en fonction des paramètres de la géométrie à l'échelle locale de matériau. En particulier, un modèle isotrope spatialement stationnaire de lignes droites (processus de Poisson) et le tenseur d'orientation angulaire correspondant, constituent des outils de modélisation de la géométrie aléatoire du milieu fibreux permettant de représenter les principales caractéristiques susceptibles d'influencer ses propriétés de transport. Il s'agit ensuite de résoudre les principaux problèmes aux limites gouvernant le comportement acoustique à l'échelle supérieure en appliquant une technique classique d’homogénéisation numérique. On montre dans un premier temps que la méthode développée permet de prédire le comportement en absorption d'un milieu fibreux aléatoire en se basant uniquement sur la description des caractéristiques géométriques du matériau fibreux réel (porosité, rayon de fibres, distributions des orientations angulaires) sans coefficient d'ajustement, validations expérimentales à l'appui. Sur la base de ce travail de reconstruction tridimensionnel, on étudie ensuite systématiquement l'ensemble des phénomènes de transport d'intérêt sur une large gamme de porosité et d'orientations angulaires, de manière à produire des lois qui peuvent être appliquées par la suite par d'autres utilisateurs sur une large gamme de milieux fibreux réels. Finalement, on examine plus particulièrement l'hypothèse classique selon laquelle un milieu fibreux peut être décrit à partir de la moyenne arithmétique du diamètre de ses fibres, afin de cerner les limites de cette approche et ses conditions d'applicabilité lorsque le milieu fibreux présente une distribution étendue de diamètres de fibres ou bimodale