Wave Propagation In Porous Materials Research Articles

An Explicit D-FE2 Method for Transient Multiscale Analysis

Explicit FE (Finite Element) method offers distinct advantages for a variety of simulations, including nonlinear transient dynamics, large deformation due to buckling, and damage evolution in materials or structures. However, conventional computational homogenization techniques, such as the FE2 and direct FE2 (D-FE2) methods, have not yet been integrated with an explicit algorithm because of the implicit framework in their numerical implementation, and thus cannot be widely applied to concurrent multi-level modeling of transient dynamic issues in multiscale materials and structures. In this study, an explicit D-FE2 method was proposed by incorporating explicit integration algorithms into the numerical calculation of microscale RVEs based on the D-FE2 method proposed by Tan [1]. To facilitate this, an extended Hill–Mandel principle which considers the conservation of both kinetic and internal energies between macro- and micro-scales was derived, and the conventional D-FE2 method was modified using the explicit FE method. The proposed explicit D-FE2 method was validated using a series of experiments and numerical examples including drop-hammer impact on multiscale honeycomb, stress wave propagation in porous materials, compressive buckling of multi-stable metamaterials, damage and failure of fiber-reinforced composites, etc. It was validated that the proposed explicit D-FE2 method is feasible and efficient for transient dynamic analysis of multiscale materials and structures, which might be a new avenue of research in the field of impact dynamics.

Symplectic time-domain finite element method (STD-FEM) extended with wave propagation in porous materials for automotive interior acoustic modeling

The prediction of sound field evolving inside automotive interiors has gained significant attention in recent years, both for acoustic design purposes and virtual reality applications. Recently, a novel numerical simulation method was proposed by the present authors termed as symplectic time-domain finite element method. This paper discusses the numerical method and its application for simulating sound fields inside vehicle interiors. The presented case study includes the effect of seat absorption and non-rigid boundaries by applying either locally reacting, or elastic surface models exhibiting extended reactivity.

Imaging the shear and secondary compression wave: Ultrafast ultrasound in saturated foams reveals porous dispersion

Wave propagation in porous materials is of relevance in many fields of acoustics such as geophysics, noise cancellation, and biomedical imaging. In contrast to classical elastic materials, poroelastic materials support three types of elastic waves and exhibit a distinctive dispersion in the presence of viscous fluids. In addition to the compression and shear wave, a secondary compression wave, often named Biot slow wave, exists. Both, the slow compression wave and the shear wave are highly attenuated. This poses crucial difficulties for experimental detection. We overcome this challenge by using high frame rate ultrasound imaging for wave tracking inside saturated, highly porous melamine foams. To our knowledge, we show the first experimental speed and attenuation measurements inside a soft porous materials. In particular, experimental detection of the slow compression wave is scarce, and no direct imaging inside a porous material has been reported. Both wavespeeds are governed by the weak frame of the foam and exhibit a strong dispersion due to the fluid viscosity. Our experiments have direct implications for medical imaging: Melamine foams exhibit a similar microstructure as lung tissue. Furthermore, other organs such as the liver can be modeled as a soft porous material.Wave propagation in porous materials is of relevance in many fields of acoustics such as geophysics, noise cancellation, and biomedical imaging. In contrast to classical elastic materials, poroelastic materials support three types of elastic waves and exhibit a distinctive dispersion in the presence of viscous fluids. In addition to the compression and shear wave, a secondary compression wave, often named Biot slow wave, exists. Both, the slow compression wave and the shear wave are highly attenuated. This poses crucial difficulties for experimental detection. We overcome this challenge by using high frame rate ultrasound imaging for wave tracking inside saturated, highly porous melamine foams. To our knowledge, we show the first experimental speed and attenuation measurements inside a soft porous materials. In particular, experimental detection of the slow compression wave is scarce, and no direct imaging inside a porous material has been reported. Both wavespeeds are governed by the weak frame of the fo...

Numerical solution of Euler equations employing enthalpy-based equation of state for simulating shock wave propagation in porous materials

Shock wave propagation through porous materials is investigated using numerical simulations of one dimensional Euler equations of inviscid fluid flow, with the basic aim to demonstrate the application of the enthalpy-based equation of state. A one dimensional hydrodynamics solution method employing the flux-corrected transport algorithm, which does not make use of artificial viscosity, is used for all simulations. Benchmark results on the Sedov-von Neumann-Taylor blast wave problem are given thereby showing the capabilities of the algorithm for capturing strong shock profiles. Next, numerical results for plate impact problems are obtained for porous Cu, Al, Fe and W, and compared with experimental data available in the literature. It is shown that shock waves attenuate very fast even in materials of small size and low porosity. Excellent agreement is also found with experimental data on pressure versus particle velocity in the four target materials for different porosities. Thus the enthalpy-based approach, using a few experimental data of solids at normal conditions, is shown to be capable of quantitative prediction of shock wave parameters of porous materials. An accurate but simple approach for in-line calculation of the enthalpy parameters is discussed in the appendix together with numerical results.

Nonlocal scale effect on Rayleigh wave propagation in porous fluid-saturated materials

In this paper, a Rayleigh wave model in fluid saturated porous materials based on a nonlocal Biot theory is proposed. The general characteristic equations expressed in terms of the Rayleigh wavenumbers are obtained. A specific fluid saturated porous material is used for numerical analysis. The present study shows that the nonlocal parameter does not have significant influence on the characteristics of Rayleigh waves within a low frequency range when comparing with the prediction of using the classical Biot theory. However, the influence of the nonlocal scale effect on the Rayleigh wave velocity and the displacement field becomes stronger as the response frequency increases. When the frequency exceeds a critical value, the Rayleigh wave velocity exhibits a negative dispersion. The displacement fields induced by the Rayleigh wave propagating in porous materials are also presented. An interesting phenomenon of the displacement fields is observed that the major axis of the displacement field ellipse will have a contra-rotation with respect to the vertical direction with increasing depth. This is different from the classical prediction in homogeneous materials. The presence of the nonlocal scale effect can also change the geometry property of displacement fields. In addition, the amplitude of the vertical displacement is attenuated along the depth, while the increment of the nonlocal parameters can strengthen the attenuation.

Nonlinear wave propagation in porous materials based on the Biot theory.

Nonlinearity must be considered with some porous granular media because of the large deformation under seismic waves. In this study, the propagation of nonlinear waves in porous media is studied based on the Biot theory and the governing equations are obtained by the Lagrangian formulation. Three new nonlinear parameters are introduced to consider the coupled nonlinearity between the solid and fluid components in porous media. It is shown that an additional nonlinear wave with a double frequency is generated by the coupling effect of linear fast and slow waves. When only a shear wave is applied at the source, no double-frequency nonlinear wave is predicted and three nonlinear longitudinal waves are generated. On the basis of the practical case studies, the effect of strong nonlinearity is computed under the influence of a one-dimensional single longitudinal wave source and a single shear wave source.

Vibro-acoustics of porous materials - waveguide modelling approach

The porous material is considered as a compound multi-layered waveguide (i.e. a fluid layer surrounded with elastic layers) with traction free boundary conditions. The attenuation of the vibro-acoustic waves in such a material is assessed. This approach is compared with a conventional Biot's model and a qualitative agreement in phase velocities as well as damping estimates is found. The waveguide model predicts four waves, out of which two are attenuated when the viscous fluid is considered (while the elastic layer being ideally lossless). One of these waves is found to be significantly controlled by the fluid viscosity, while for the other the effect of viscosity was observed for very small frequencies. The Biot's model predicts only one of these attenuated waves, where the latter one is not predicted. Thus the proposed waveguide approach provide additional information about the wave propagation in porous materials.

Analyzing and evaluation of effective parameters on sound transmission loss of the triple-layered acoustic panels with sound-absorbing middle layer

In this research, a triple-layered acoustic panel with sound-absorbing intermediate layer materials is modeled analytically in order to calculate the sound transmission loss in the normal incidence field. This information provides an appropriate platform for optimum noise control. In this paper, porous material is used as an absorbent layer between two elastic panels. In modeling these triple-layered panels, theory of wave propagation in porous materials is used and bounded boundary condition of the first elastic layer and unbounded boundary condition of the second elastic layer is applied. To validate the model, the results of this model are compared with the results of the Bolton. Comparison of results revealed very good compatibility. Here, the effect of the length of the air gap between the elastic layers, density and the material of the elastic plate, the thickness and vibro-acoustic properties of the intermediate porous material on the values of transmission loss is investigated.In a wide range of frequencies, increasing air gap, density of elastic panels and porous layer thickness, increase the transmission loss up to 10 dB. At frequencies above 10 kHz, a reduction in porosity, static Young's modulus, the loss coefficient, increasing bulk density of the solid phase, the factor of geometrical structure and viscosity of porous material, increase the sound transmission loss up to 15 dB.

A porosity-based Biot model for acoustic waves in snow

AbstractPhase velocities and attenuation in snow cannot be explained by the widely used elastic or viscoelastic models for acoustic wave propagation. Instead, Biot’s model of wave propagation in porous materials should be used. However, the application of Biot’s model is complicated by the large property space of the underlying porous material. Here constant properties for ice and air, and empirical relationships are used to estimate unknown porous properties from snow porosity. Using this set of equations, phase velocities and plane wave attenuation of shear- and compressional waves are predicted as functions of porosity or density. For light snow the peculiarity was found that the velocity of the first compressional wave is lower than that of the second compressional wave that is commonly referred to as the ‘slow’ wave. The reversal of the velocities comes with an increase of attenuation for the first compressional wave. This is in line with the common observation that sound is strongly absorbed in light snow. The results have important implications for the use of acoustic waves to evaluate snow properties and to numerically simulate wave propagation in snow.

The wave propagation in porous material: A continuum from Biot solids to thermoacoustic heat engines.

Wave propagation in poroelastic materials has applications ranging from ground motion induced by atmospheric sound to thermoacoustic heat engines. Bass was involved with research in this entire continuum, including both basic and applied problems. This paper will especially cover the wave propagation formulation of thermoacoustics as it was applied by Bass and others to understand and predict the behavior of thermoacoustic prime movers. Some recollections of Bass as a statesman, scientist, and enjoyable character to be with will be presented. My first meeting with Bass and some of his guidance will also be discussed.

Dispersion and Nonlinearity of Plane Longitudinal Wave Propagation in Porous Materials

Dispersion and Nonlinearity of Plane Longitudinal Wave Propagation in Porous Materials

Non-contact ultrasound characterization of bread crumb: Application of the Biot–Allard model

This paper presents the application of the Biot–Allard model for characterization of the porous structure of bread crumb. This model describes the wave propagation in porous materials and is commonly used for the evaluation of sound absorbing properties of soft poroelastic foams. Two different bread types, a fine grain bread (FGB) with small cells and a coarse grain bread (CGB) with larger gas cells, were analyzed using both image analysis (IA) and ultrasonic techniques. IA figures for mean cell area, cell to total area ratio and number of cells/cm 2 were 0.25 and 0.47, 0.32 and 0.41, and 112.8 and 81.6, respectively for FGB and CGB. The ultrasonic technique used non-contact air coupled transducers at ultrasonic frequencies. The phase velocity and attenuation of ultrasonic waves were measured in transmission and reflection experiments. These measurements confirmed the structural differences between the two different bread types and the usefulness of the Biot–Allard model for description of wave propagation in bread crumb for a wide frequency range. In addition, the use of non-contact ultrasound allowed estimating flow resistivity, open porosity, a measure for the size of the intersections in the crumb cell walls, and tortuosity which can be considered as a structural form factor.

Asymmetric collapse and micro-jetting in shock wave propagation in porous materials

Streak records of the observation, with a nanosecond and micrometer scale resolution, of the light emitted during the Shock Wave [SW] propagation in epoxy Syntactic Foams [SF], are presented as a function of the HGMS sizes (d 50 = 42, 92 and 135 μm), the initial density (0.64, 0.81 and 0.92 g/cm 3 ) and the loading intensity (20.0 and 9.6 GPa). The obtained streak records allowed the determination of the SW velocity, the spatial profile of the intensity of the transmitted SW and the period of light oscillations. The SW velocity was found to change with the density and with the size of the HGMS. The intensity of the transmitted wave, for the samples prepared with medium and large HGMS sizes, shows to be above the values for the samples prepared with small size HGMS. For the samples with the smallest density the values of the period of light oscillation are very close to the time for the propagation between two consecutive layers of HGMS. The experimental facts point to a pulsed propagation process where the mechanism of asymmetric collapse and jet formation is dominant.

Analytical solutions for characterizing tortuosity and characteristic lengths of porous materials using acoustical measurements: Indirect model

Under the homogenization hypothesis, wave propagation in porous materials can be described using, for example, macroscopic dynamic density and bulk modulus. These functions depend on statistical geometrical parameters. Classically, five parameters are used: porosity, static air flow resistance, tortuosity, and viscous and thermal characteristic lengths. The three last parameters are generally difficult to measure with existing direct methods, for a wide range of materials. The proposed method is based on the measurement of dynamic density and compressibility, in order to separate viscous and thermal effects. With prior knowledge of airflow resistance and porosity, it is then possible to find analytical solutions for the missing parameters, fitting Johnson–Allard–Champoux model. In the same way, we also tackle the problem of the determination of static ‘‘thermal permeability’’ introduced to improve the description of thermal dissipation effect. Experimental results, obtained with various materials, using a Kundt’s tube, are presented to show the efficiency, and relative simplicity of the method. Moreover, the relevance of using a three parameters model for describing the bulk modulus is discussed.

Dynamic response of a fluid-saturated elastic porous solid

IN THIS PAPER, the field equations governing the dynamic response of a fluid-saturated elastic porous media are analyzed and built up for the study of the consolidation problem and the one-dimensional wave propagation. The two constituents are assumed to be incompressible. A one-dimensional numerical solution is derived by means of the standard Galerkin procedure and the finite element method. As a result of the incompressibility, there is only one independent dilatational wave propagating in the solid and the fluid phase. This work can provide further understanding of the wave propagation in porous materials, not only in view of the propagation speed, but also with respect to the development of the amplitudes.

One-dimensional transient wave propagation in fluid-saturated incompressible porous media

In this investigation, the general formalism for the field equations governing the dynamic response of fluid-saturated porous media is analyzed and employed for the study of transient wave motion. The two constituents are assumed to be incompressible. A one-dimensional analytical solution is derived by means of Laplace transform technique which, as a result of the incompressibility constraint, exhibits only one independent dilatational wave propagating in the solid and the fluid phases, respectively. The fluid-saturated porous material is supplied with characteristics similar to those occuring in viscoelastic solids. This work can provide the further understanding of the characteristics of wave propagation in porous materials and may be taken for a quantitative comparision to various numerical solutions.

The influence of microstructure on propagation in porous fibrous absorbents

Parameters commonly used to describe the dependence of wave propagation in porous materials on their microstructure derive from a conceptual model of an ideal capillary pore medium. The theories which introduce these parameters are reviewed, and their limitations, when applied to propagation in flexible, fibrous media, are discussed. Alternative models and associated analyses which define the disposition of the solid rather than that of the fluid are considered. In particular, a scattering analysis, which has previously been applied to a simple model of parallel, identical fibres in air, is introduced. This approach is extended in order to deduce bulk acoustical parameters for more realistic versions of the fibre model. The theoretically predicted effects of (i) variation in fibre flexibility, (ii) distributions of fibre radii, (iii) shot content, and (iv) fibre orientation, are considered.