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.

Predictive model of sound propagation in porous materials: Quantification of fiber nonwoven fabric by material density and fiber diameter

Predictive model of sound propagation in porous materials: Quantification of fiber nonwoven fabric by material density and fiber diameter

Influence of Higher Order Viscous and Thermal Effects on an Ultrasonic Wave Reflected from the First Interface of a Porous Material.

Ultrasound propagation in porous materials involves some higher order physical parameters whose importance depends on the acoustic characteristics of the materials. This article concerns the study of the influence of two parameters recently introduced, namely, the viscous and thermal surfaces, on the acoustic wave reflected by the first interface of a porous material with a rigid structure. These two parameters describe the fluid/structure interactions in a porous medium during the propagation of the acoustic wave in the high-frequency regime. Both viscous and thermal surfaces are involved in Laurent expansion, which is limited to the dynamic tortuosity and compressibility to a higher order and corrects the visco-thermal losses. A sensitivity study is performed on the modulus of the reflection coefficient at the first interface as a function of frequency and on the waveforms reflected by the porous material in the time domain. The results of this study show that highly absorbent porous materials are the most sensitive to viscous and thermal surfaces, which makes the consideration of these two parameters paramount for the characterization of highly absorbent porous materials using the waves reflected from the first interface.

A multiphase irreversible-compaction model for granular-porous materials

An Eulerian, hyperbolic, multiphase-flow model for dynamic and irreversible compaction of porous materials is constructed. A reversible model for elastic, compressible, porous material is derived. Classical homogenization results are obtained. The irreversible model is then derived in accordance with the following basic principles. First, the entropy inequality is satisfied by the model. Second, the stress coming from the elastic energy decreases in time (the material behaves as Maxwell-type materials). The irreversible model admits an equilibrium state corresponding to a Gurson-type limit which varies with the porosity. The sound velocity at the yield limit is smaller than that of the reversible model. Such an embedded model structure ensures a thermodynamically correct formulation of the porous-material model. The usual model used in the detonation community is recovered. The model is then validated on quasi-static loading–unloading experiments with HMX. The ability of the model to capture strong shock propagation in porous material as well as its ability to deal with interface between a fluid and a porous material is demonstrated and validated on Hugoniot curve of aluminium with various porosities for a unique set of empirical parameters.

Voronoi cell finite element model to simulate crack propagation in porous materials

Voronoi cell finite element models (VCFEM) containing pores and various cracks were developed in this study to simulate crack propagation in porous materials. In addition to polynomial terms, singular items were inserted into the stress function to capture the stress concentration at the tip of the crack. During crack propagation, the Voronoi element type changes such that an element may contain an internal crack, an edge crack, a bridge crack, or other types of cracks in addition to a pore. Functional of the element containing both bridge crack and external crack were derived, and a crack propagation program was developed to execute a mesh division algorithm for crack propagation from one element to another. The results of the tests showed that the proposed method could effectively be used to mitigate crack propagation.

Sound propagation in porous materials containing rough tubes

A theoretical model is developed to quantify the influence of surface roughness on sound propagation in porous materials containing rough tubes by extending the Johnson–Champoux–Allard–Lafarge (JCAL) model. The five transport parameters of the JCAL model, including the viscous permeability, thermal permeability, tortuosity, viscous characteristic length, and thermal characteristic length, are calculated by modeling the rough tubes in the porous material as parallel rough tubes having idealized sinusoidal morphologies. The transport parameters obtained using the proposed model are validated by full finite element simulations. Based on these transport parameters, the sound absorption coefficient of the porous material containing idealized rough tubes is calculated, which agrees well with the FE result. The roughness effect is investigated by comparing sound absorption performance between parallel smooth tubes and parallel rough tubes. The existence of tube roughness weakens the thermal effect but dramatically strengthens the viscous effect in sound energy dissipation, resulting in enhanced sound absorption. This work provides fundamental insights on how surface roughness affects the acoustic performance of sound-absorbing porous materials.

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.

Two-dimensional finite-difference time-domain analysis of sound propagation in rigid-frame porous material based on equivalent fluid model

An equivalent fluid model based finite-difference time-domain algorithm is proposed to simulate the frequency characteristic of rigid-frame porous material in 2-dimensional sound field. Two study cases are simulated at oblique incidence of sound, and the calculated surface impedance agree well with the theoretical value in broad frequency range. The errors are also discussed when simulating a porous material with shape with the staircase approximation. As an example, sound propagation in a porous material with triangular shape is simulated using the algorithm.

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.

An equivalent fluid model based finite-difference time-domain algorithm for sound propagation in porous material with rigid frame.

An equivalent fluid model based finite-difference time-domain algorithm is proposed to simulate the frequency characteristic of porous material with rigid frame. The rigid-frame porous material is replaced by an equivalent fluid characterized by the effective density and the effective bulk modulus, which reflect the viscous effects and thermal effects in the porous material, respectively. The effective density and the effective bulk modulus are frequency-dependent complex values, which are designed in the form of infinite impulse response filters in the frequency domain. The Z transform theory is used to discretize the frequency-domain wave equations. The accuracy of the proposed algorithm is preliminarily validated by good agreement between the calculated and measured normal-incidence sound absorption coefficients of two samples composed of different multiple-layered materials in a wide frequency range.

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.

Sound propagation in porous materials with annular pores.

Long-wavelength sound propagation in porous materials with annular pores is investigated in this paper. Closed-form analytical expressions for the effective acoustical properties of this type of material were obtained. These are compared with both direct numerical calculations of the effective properties and their calculations obtained by using semi-phenomenological models. Analytical expressions for the input parameters of the latter, i.e., static viscous and thermal permeabilities, viscous and thermal characteristic lengths, and tortuosity, are also provided. The introduced model is successfully validated by comparing its predictions with measured data taken from literature. A parametric analysis that allows highlighting the influence of the different geometrical parameters of porous materials with annular pores on their sound absorptive properties is also presented.

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.

Wave theoretical study on viscous damping and thermal conduction damping of sound propagation in porous materials

Wave theoretical study on viscous damping and thermal conduction damping of sound 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.

A design of an impedance tube for teaching acoustic material properties and laboratory techniques

The design and implementation of an adaptable acoustic impedance tube for instructional use will be presented. This system, which was designed for use in a graduate-level laboratory environment, is in accordance with ASTM standard E1050-98. The system is configurable for both horizontal and vertical measurements. Vertical use enables acoustic property measurement of granular materials, allowing characterization of a wide variety of media. The academic content is delivered by engaging students in measurements using the impedance tube. Specific acoustics content objectives include modeling of sound propagation in porous materials and the role of acoustic parameters such as porosity, tortuosity, and flow resistivity in quantifying acoustic behavior of materials. Instructional goals also include mastery of computer based data acquisition and processing. This aspect of modern laboratory practice is a critical part of our graduate acoustics curriculum. Students participated actively in the development of the software used to collect data and calibrate the impedance tube. The system design required the students to solve practical problems such as cutting and positioning of the sample as well as more demanding tasks such as design of a multilayer porous medium with desired acoustic properties.

Extended Finite Element Method for hygro‐mechanical analysis of crack propagation in porous materials

AbstractIn computational structural analyses, strong discontinuities, such as propagating cracks in concrete structures, joints in rocks or shear bands in soft soils, the highly accelerated moisture transport in the opening discontinuities has to be taken into account. The paper is concerned with an Extended Finite Element model for the numerical representation of crack propagation in partially saturated porous materials. Based on an extended variational formulation for the simulation of moisture transport in cracks, enhanced approximations of the displacement field and the moisture flux across the discontinuity are adopted. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)