1 S’agissant de milieux micro poreux (c'est-à-dire de milieux dont la taille caractéristique ... more 1 S’agissant de milieux micro poreux (c'est-à-dire de milieux dont la taille caractéristique des pores est de l’ordre du micron), les modélisations « macroscopiques » usuelles (homogénéisation, prises de moyennes...) doivent être modifiées. En ce qui concerne la partie dynamique, la façon la plus simple de procéder est de recalculer une perméabilité tenant compte du glissement dynamique afin de continuer à utiliser la loi de Darcy [1]. En considérant des motifs périodiques et en supposant l’écoulement périodique ou plus exactement établi, on peut en déduire de nouvelles valeurs de la perméabilité incluant les effets du glissement. La forme « macroscopique » de l’équation de l’énergie (ou de l’équation de l’énergie pour la phase fluide si la modélisation est basée sur un modèle hors équilibre thermique local), montre que la conductivité effective – c'est-à-dire la conductivité stagnante plus la conductivité due à la dispersion (< u’T’>) – dépend du couplage entre champs...
Journal of the Mechanics and Physics of Solids, 2007
A series solution to obtain the effective properties of some elastic composites media having peri... more A series solution to obtain the effective properties of some elastic composites media having periodically located heterogeneities is described. The method uses the classical expansion along Neuman series of the solution of the periodic elasticity problem in Fourier space, based on the Green's tensor, and exact expressions of factors depending on the shape of the inclusions. Some properties of convergence of the solution are presented, more specifically concerning the elasticity tensor of the reference medium, showing that the convergence occurs even for empty fibers. The solution is extended for rigid inclusions. A comparison is made with previous exact solutions for a fiber composite made of cylindrical fibers with circular cross-sections and with previous estimates. Different examples are presented for new situations concerning the study of fiber composites: composites with elliptic cross-sections and multi-phase fibrous composites.
This article explores the applicability of numerical homogenization techniques for analyzing tran... more 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 diffusioncontrolled 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.
International Journal for Numerical Methods in Engineering, 2009
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
The purpose of this paper is to study Green functions for porous saturated media and to present a... more The purpose of this paper is to study Green functions for porous saturated media and to present an example of numerical simulation using these Green functions. In the first part the equations of the porous media are recalled and the principal results concerning the features of the waves are given. The second part is devoted to the determination of sources and Green functions. We give the analytical solution, then we study some of its properties. In the third part we focus on the construction of synthetic seismograms. We show examples of bi-dimensional computation in a semi-infinite stratified porous medium, for a double dipole or a fluid injection.
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific ... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. IFP Energies nouvelles International Conference Rencontres Scientifiques d'IFP Energies nouvelles
XI International Conference on Structural Dynamics
The paper presents the study of elastic composites acting as resonant metamaterials. The composit... more The paper presents the study of elastic composites acting as resonant metamaterials. The composites are made of long bers of elliptic cross section. The condition for obtaining resonant metamaterials is presented in the context of homogenization by using asymptotic expansion. It is shown that inner resonance occurs in the case of soft inclusions embedded within a sti er matrix, both components having mass densities of the same order of magnitude. The localization problem coming from the asymptotic expansion is solved in the case of bers with elliptic cross sections, leading to the dynamic density of the material. The dynamic density is characterized by resonance frequencies and the related eigenfunctions of the inclusions, that are obtained by using an expansion along Mathieu functions. The method allows us to obtain the (orthotropic) dynamic densityrelated to various cases of elliptic cross section, recovering the extreme cases of circular cross-sections and nearly plate inclusions.
On cherche a modeliser et a analyser le comportement dynamique d'un systeme forme par une pou... more On cherche a modeliser et a analyser le comportement dynamique d'un systeme forme par une poutre couplee a une lame mince. La poutre a un comportement suppose lineaire et on represente celui de la lame par une matrice de rigidite non-lineaire. Les equations de la dynamique sont alors obtenues a l'aide d'une methode de sous-structuration dynamique. Pour une excitation harmonique, on utilise la methode d'equilibrage harmonique pour transformer les equations differentielles en equations algebriques dependant de la frequence d'excitation qui sont resolues a l'aide d'une methode de continuation. Cette procedure est appliquee au cas d'un systeme poutre+lame reel. Les resultats obtenus sont compares a ceux obtenus par analyse ondelettes des signaux experimentaux et permettent une validation de la procedure proposee.
On presente dans cette communication un dispositif triaxial dynamique permettant de tester les so... more On presente dans cette communication un dispositif triaxial dynamique permettant de tester les sols grossiers, les graves et les materiaux granulaires tels que ballasts et micro- ballasts sous sollicitations monotones et cycliques. Apres avoir presente les caracteristiques principales du dispositif, on decrit succinctement deux types d'applications, l'une sur l'etude du comportement d'une grave sous cisaillement monotone, l'autre sur l'etude du comportement d'un microballast sous sollicitations cycliques. (A). (Voir fiche generale F101370 et fiches specifiques F101371 a F101382 et F101384 a F101397). (Titre en anglais : Large size dynamic triaxial set up for coarse-grained soils and materials).
Engineering Analysis with Boundary Elements, Mar 1, 2018
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Background: In the framework of periodic homogenization, the conduction problem can be formulated... more Background: In the framework of periodic homogenization, the conduction problem can be formulated as an integral equation whose solution can be represented by a Neumann series. From the theory, many efficient numerical computation methods and analytical estimations have been proposed to compute the effective conductivity of composites. Methods: We combine a Fast Fourier Transform (FFT) numerical method based on the Neumann series and analytical estimation based on the integral equation to solve the problem. Specifically, the analytical approximation is used to estimate the remainder of the series. Results: From some numerical examples, the coupling method have shown to improve significantly the original FFT iteration scheme and results are also superior to the analytical estimation. Conclusions: We have proposed a new efficient computation method to determine the effective conductivity of composites. This method combines the advantages of the FFT numerical methods and the analytical estimation based on integral equation.
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Abstract The microstructure of elastic composite materials can be adjusted in order to provide in... more Abstract The microstructure of elastic composite materials can be adjusted in order to provide inner resonance, leading to negative dynamic density. In a first step, the results on the process using asymptotic expansion that provides the structure of the effective behaviour and the scaling of physical parameters leading to inner resonance are recalled. The process allows to describe the dynamic localization problem that must be considered in order to provide the effective behaviour. The localization problem is solved for elastic composites containing cylindrical fibers with circular cross-section. It involves the recovering of eigenfrequencies of a cylindrical domain through Bessel functions. While there are several sets of eigenfrequencies, it will be shown that only one set of eigenfrequencies contributes to the dynamic density. The eigenfrequencies and the participation factors for each resonance are provided, leading to a full description of the dynamic density.
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
1 S’agissant de milieux micro poreux (c'est-à-dire de milieux dont la taille caractéristique ... more 1 S’agissant de milieux micro poreux (c'est-à-dire de milieux dont la taille caractéristique des pores est de l’ordre du micron), les modélisations « macroscopiques » usuelles (homogénéisation, prises de moyennes...) doivent être modifiées. En ce qui concerne la partie dynamique, la façon la plus simple de procéder est de recalculer une perméabilité tenant compte du glissement dynamique afin de continuer à utiliser la loi de Darcy [1]. En considérant des motifs périodiques et en supposant l’écoulement périodique ou plus exactement établi, on peut en déduire de nouvelles valeurs de la perméabilité incluant les effets du glissement. La forme « macroscopique » de l’équation de l’énergie (ou de l’équation de l’énergie pour la phase fluide si la modélisation est basée sur un modèle hors équilibre thermique local), montre que la conductivité effective – c'est-à-dire la conductivité stagnante plus la conductivité due à la dispersion (< u’T’>) – dépend du couplage entre champs...
Journal of the Mechanics and Physics of Solids, 2007
A series solution to obtain the effective properties of some elastic composites media having peri... more A series solution to obtain the effective properties of some elastic composites media having periodically located heterogeneities is described. The method uses the classical expansion along Neuman series of the solution of the periodic elasticity problem in Fourier space, based on the Green's tensor, and exact expressions of factors depending on the shape of the inclusions. Some properties of convergence of the solution are presented, more specifically concerning the elasticity tensor of the reference medium, showing that the convergence occurs even for empty fibers. The solution is extended for rigid inclusions. A comparison is made with previous exact solutions for a fiber composite made of cylindrical fibers with circular cross-sections and with previous estimates. Different examples are presented for new situations concerning the study of fiber composites: composites with elliptic cross-sections and multi-phase fibrous composites.
This article explores the applicability of numerical homogenization techniques for analyzing tran... more 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 diffusioncontrolled 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.
International Journal for Numerical Methods in Engineering, 2009
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
The purpose of this paper is to study Green functions for porous saturated media and to present a... more The purpose of this paper is to study Green functions for porous saturated media and to present an example of numerical simulation using these Green functions. In the first part the equations of the porous media are recalled and the principal results concerning the features of the waves are given. The second part is devoted to the determination of sources and Green functions. We give the analytical solution, then we study some of its properties. In the third part we focus on the construction of synthetic seismograms. We show examples of bi-dimensional computation in a semi-infinite stratified porous medium, for a double dipole or a fluid injection.
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific ... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. IFP Energies nouvelles International Conference Rencontres Scientifiques d'IFP Energies nouvelles
XI International Conference on Structural Dynamics
The paper presents the study of elastic composites acting as resonant metamaterials. The composit... more The paper presents the study of elastic composites acting as resonant metamaterials. The composites are made of long bers of elliptic cross section. The condition for obtaining resonant metamaterials is presented in the context of homogenization by using asymptotic expansion. It is shown that inner resonance occurs in the case of soft inclusions embedded within a sti er matrix, both components having mass densities of the same order of magnitude. The localization problem coming from the asymptotic expansion is solved in the case of bers with elliptic cross sections, leading to the dynamic density of the material. The dynamic density is characterized by resonance frequencies and the related eigenfunctions of the inclusions, that are obtained by using an expansion along Mathieu functions. The method allows us to obtain the (orthotropic) dynamic densityrelated to various cases of elliptic cross section, recovering the extreme cases of circular cross-sections and nearly plate inclusions.
On cherche a modeliser et a analyser le comportement dynamique d'un systeme forme par une pou... more On cherche a modeliser et a analyser le comportement dynamique d'un systeme forme par une poutre couplee a une lame mince. La poutre a un comportement suppose lineaire et on represente celui de la lame par une matrice de rigidite non-lineaire. Les equations de la dynamique sont alors obtenues a l'aide d'une methode de sous-structuration dynamique. Pour une excitation harmonique, on utilise la methode d'equilibrage harmonique pour transformer les equations differentielles en equations algebriques dependant de la frequence d'excitation qui sont resolues a l'aide d'une methode de continuation. Cette procedure est appliquee au cas d'un systeme poutre+lame reel. Les resultats obtenus sont compares a ceux obtenus par analyse ondelettes des signaux experimentaux et permettent une validation de la procedure proposee.
On presente dans cette communication un dispositif triaxial dynamique permettant de tester les so... more On presente dans cette communication un dispositif triaxial dynamique permettant de tester les sols grossiers, les graves et les materiaux granulaires tels que ballasts et micro- ballasts sous sollicitations monotones et cycliques. Apres avoir presente les caracteristiques principales du dispositif, on decrit succinctement deux types d'applications, l'une sur l'etude du comportement d'une grave sous cisaillement monotone, l'autre sur l'etude du comportement d'un microballast sous sollicitations cycliques. (A). (Voir fiche generale F101370 et fiches specifiques F101371 a F101382 et F101384 a F101397). (Titre en anglais : Large size dynamic triaxial set up for coarse-grained soils and materials).
Engineering Analysis with Boundary Elements, Mar 1, 2018
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Background: In the framework of periodic homogenization, the conduction problem can be formulated... more Background: In the framework of periodic homogenization, the conduction problem can be formulated as an integral equation whose solution can be represented by a Neumann series. From the theory, many efficient numerical computation methods and analytical estimations have been proposed to compute the effective conductivity of composites. Methods: We combine a Fast Fourier Transform (FFT) numerical method based on the Neumann series and analytical estimation based on the integral equation to solve the problem. Specifically, the analytical approximation is used to estimate the remainder of the series. Results: From some numerical examples, the coupling method have shown to improve significantly the original FFT iteration scheme and results are also superior to the analytical estimation. Conclusions: We have proposed a new efficient computation method to determine the effective conductivity of composites. This method combines the advantages of the FFT numerical methods and the analytical estimation based on integral equation.
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Abstract The microstructure of elastic composite materials can be adjusted in order to provide in... more Abstract The microstructure of elastic composite materials can be adjusted in order to provide inner resonance, leading to negative dynamic density. In a first step, the results on the process using asymptotic expansion that provides the structure of the effective behaviour and the scaling of physical parameters leading to inner resonance are recalled. The process allows to describe the dynamic localization problem that must be considered in order to provide the effective behaviour. The localization problem is solved for elastic composites containing cylindrical fibers with circular cross-section. It involves the recovering of eigenfrequencies of a cylindrical domain through Bessel functions. While there are several sets of eigenfrequencies, it will be shown that only one set of eigenfrequencies contributes to the dynamic density. The eigenfrequencies and the participation factors for each resonance are provided, leading to a full description of the dynamic density.
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
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