Poroelastic Material Research Articles

Vegetal wools for building application: investigation of optimization approaches for the enhancement of low-frequency sound absorption

Bio-based building materials, such as vegetal wools for thermal and acoustic applications, are increasingly used in construction. Indeed, as they store atmospheric carbon dioxide, they have a lower carbon footprint than conventional materials. Despite high-level multi-functional properties, they suffer from poor low-frequency absorption for thin panels (less than 5 cm thick). Therefore, it seems relevant to investigate the optimization possibilities available, including meta-material approaches, and to adapt them to the specificities of vegetal wools, such as a low air resistivity for hemp and flax wools which are our main concern. To meet this challenge, a state-of-the-art is being carried out to identify the optimization methods best suited to the specific characteristics of vegetal wools. This preliminary work is based on the implementation of an initial optimization concept using a multilayer poroelastic material with a perforated resistive layer. The material structure is optimized using analytical modeling to target low frequencies. Experimental verifications are then carried out to determine the sound absorption coefficient of vegetal wools with optimized configurations.

Characterization and estimation of the acoustical and elastic parameters in stone wool samples

Mineral wool is widely used in acoustic applications. The properties of glass wool have been broadly investigated, thus resulting in a good knowledge of its structure and parameters. This information is used to describe mineral wool in general. Nevertheless, other types, such as stone wool, involve a different production process and therefore have a different fibre structure. e.g. stone wool is not transversally isotropic as glass wool. These differences can have important effects depending on the use of the material; therefore, assuming the same parameter values for both materials may lead to inaccurate results in simulations and calculations. Currently there are few studies that characterize both the acoustic and elastic properties of stone wool. This contribution reports on the characterization of two stone wool samples with different densities (~70 kg/m3 and ~140 kg/m3). The characterization aimed at obtaining the parameters that are required for the description of the propagation of sound in the material through the Biot poroelastic model, i.e. the acoustic and elastic parameters. The obtained knowledge enables the adequate modelling of the investigated poroelastic materials in different configurations by numerical methods such as finite elements and the transfer matrix method.

Innovative Strategies for designing acoustic encapsulations for e-motors to tackle NVH performance challenges

The automotive industry's rapid transition towards E-mobility is presenting novel challenges for NVH engineers having broadband frequency composition and tonal characteristics. The purpose of the paper is to present innovative strategies for electric motor NVH development by directly applying acoustic encapsulation made of poro-elastic materials onto the casing of the electric motor. The first strategy is a pure simulation approach with combination of finite element analysis (FEA) and statistical energy analysis (SEA). Finite Element Analysis is used to calculate radiated power of electric motor casing for Maxwell electromagnetic excitations on stator teeth. This radiated power is then applied as excitation on the SEA model of the electric motor casing for prediction of exterior noise using Statistical Energy Analysis. The second strategy is a hybrid approach of simulations and experimental measurements. Electric motor is characterized as a source in terms sound power from experimental measurements of sound pressure as per ISO Standard: ISO 3745:2003. This power is applied as excitation in the interior of SEA model of the electric motor for prediction of exterior noise. Both the strategies allow design of optimized sound package on the SEA model of electric motor using statistical energy analysis to achieve the NVH performance.

LCV Vehicle in-cab noise prediction and reduction using SEA based simulation approach

With increase in consumer demand vehicle OEMs are developing quieter vehicles at a design stage using acoustic simulation tools to reduce development cycle times avoiding costly proto builds and test iterations. Present work describes application of statistical energy analysis (SEA) simulation approach for in cab noise prediction and noise reduction through sound package optimization for LCV vehicle. In first step complete vehicle in-cab SEA model is prepared with baseline sound package concept. It consists of comprehensive definition of structural panels, interior and exterior cavities. Noise control treatment is modelled as multi-layer poro-elastic materials. Airborne noise excitations for sources engine, transmission, intake and exhaust muffler are applied. Source strengths for above sources were derived from dyno-coupled powertrain noise tests in the anechoic chamber. Load case of rated speed was considered neglecting tire and wind noise during simulation. Contribution analysis was carried out to find out sensitivity of different panels on interior noise at various frequencies. It was observed that bottom middle floor panel and rear glass panel were major noise contributors. Noise mitigation was carried out by optimizing floor panel sound package and intake air filter within given space constraints. These modifications resulted in overall 2 dB in-cab noise reduction

New Lie Symmetries and Exact Solutions of a Mathematical Model Describing Solute Transport in Poroelastic Materials

A one-dimensional model for fluid and solute transport in poroelastic materials (PEMs) is studied. Although the model was recently derived and some exact solutions, in particular steady-state solutions and their applications, were studied, special cases occurring when some parameters vanish were not analysed earlier. Since the governing equations are nonintegrable in nonstationary cases, the Lie symmetry method and modern tools for solving ODE systems are applied in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with new Lie symmetries are identified. Some of them have a highly nontrivial structure that cannot be predicted from a physical point of view or using Lie symmetries of other real-world models. Applying the symmetries obtained, multiparameter families of exact solutions are constructed, including those in terms of elementary and special functions (hypergeometric, Whittaker, Bessel and modified Bessel functions). A possible application of the solutions obtained is demonstrated, and it is shown that some exact solutions can describe (at least qualitatively) the solute transport in PEM. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate analytical and numerical methods for solving relevant boundary value problems.

The poroelastic layer with an axisymmetric cylindrical hole under different types of loading

The exact solution of the poroelastic axisymmetric problem for a layer with a cylinderical hole is constructed under assumptions of Biot's model. The calculations provided by derived explicit formulas for full stress and pore pressure allow to state some important dependencies between the poroelastic stress state of the layer and type of poroelastic materials, loading types and height of the layer.

Development of an empirical model for the prediction of the sound absorption coefficient for thin and low-density fibrous materials

Currently, FEA software such as ABAQUS uses empirical models to predict the sound absorption coefficient of poroelastic materials. However, based on a recent review of the literature it was found that the current sound absorption empirical models are inadequate for accurate prediction of thin (t < 20 mm), low-density materials (ρB < 50 kg/m3). Therefore, the predictions of the sound pressure levels in vehicle cabins, using such software, will be inaccurate since the trim materials are thin and have a low density. Thus, this research aimed to develop an empirical model that can accurately predict the sound absorption coefficient of these materials. Hence, polypropylene fibres consisting of four different diameters were manufactured and converted into nonwovens. Thereafter, airflow resistivity and impedance tube experimental testing were performed on the specimens. Subsequently, statistical analysis of the data was performed using SAS software. SAS was used to identify which independent variables should be included in the models to be developed. The empirical models were developed using the regression analysis toolbox in Microsoft Excel. Once the models were developed, various checks were performed to validate the assumptions of linear regression. The software NumXL was used to perform Cook’s distance tests. Thereafter, the models were validated against the validation dataset, where it was found that the developed exponential model performed best. Finally, the exponential model was compared to existing models using two data sets i.e. an internal dataset, and an external dataset derived from the literature. The developed model outperformed all the historic models on both datasets.

Quantification of Cartilage Poroelastic Material Properties Via Analysis of Loading-Induced Cell Death.

Articular cartilage (AC) is a load-bearing tissue that covers long bones in synovial joints. The biphasic/poroelastic mechanical properties of AC help it to protect joints by distributing loads, absorbing impact forces, and reducing friction. Unfortunately, alterations in these mechanical properties adversely impact cartilage function and precede joint degeneration in the form of osteoarthritis (OA). Thus, understanding what factors regulate the poroelastic mechanical properties of cartilage is of great scientific and clinical interest. Transgenic mouse models provide a valuable platform to delineate how specific genes contribute to cartilage mechanical properties. However, the poroelastic mechanical properties of murine articular cartilage are challenging to measure due to its small size (thickness ∼ 50 microns). In the current study, our objective was to test whether the poroelastic mechanical properties of murine articular cartilage can be determined based solely on time-dependent cell death measurements under constant loading conditions. We hypothesized that in murine articular cartilage subjected to constant, sub-impact loading from an incongruent surface, cell death area and tissue strain are closely correlated. We further hypothesized that the relationship between cell death area and tissue strain can be used-in combination with inverse finite element modeling-to compute poroelastic mechanical properties. To test these hypotheses, murine cartilage-on-bone explants from different anatomical locations were subjected to constant loading conditions by an incongruent surface in a custom device. Cell death area increased over time and scaled linearly with strain, which rose in magnitude over time due to poroelastic creep. Thus, we were able to infer tissue strain from cell death area measurements. Moreover, using tissue strain values inferred from cell death area measurements, we applied an inverse finite element modeling procedure to compute poroelastic material properties and acquired data consistent with previous studies. Collectively, our findings demonstrate in the key role poroelastic creep plays in mediating cell survival in mechanically loaded cartilage and verify that cell death area can be used as a surrogate measure of tissue strain that enables determination of murine cartilage mechanical properties.

Contact mechanics of open-cell foams with macroscopic asperities

Poroelastic materials mounted against rigid surfaces often result in partial contact between the two, affecting their mechanical interaction. The surface roughness of cellular materials introduces complexity in predicting their behavior due to the interface with partial contact. This interface exhibits a stiffness distinct from the bulk material, which is driven by the surface asperities and the preload. This study conducts compression experiments on an open-cell poroelastic melamine foam, and compares them to finite elements simulations and analytic predictions. The material’s intrinsic stress–strain nonlinearity is accounted for, and an original hyperelastic aging model is proposed to achieve accurate predictions of its compression stiffness across multiple time scales. Predicting the compression stiffness of a macroscopic pyramidal asperity demonstrates a good agreement with the simple analytic solution for an elastic pyramidal geometry. Using a Greenwood–Williamson-like model based on the distribution of asperities of different heights, we propose a method to predict the contact stiffness of a rough surface. Our findings have important implications for understanding and optimizing efficient vibration barriers, resulting from the simple stacking of layers and screens of raw poroelastic materials, a configuration widely adopted in the transportation and civil engineering industries.

Multiscale simulation for sound transmission loss of a particulate filter in an exhaust system using a homogenization method

Most vehicles have diesel or gasoline particulate filters to remove particulate matter contained in gas from internal combustion engines. On the other hand, regulations have been in effect for vehicle-noise emission, with several studies conducted on reducing noise from the exhaust systems of automobiles. Generally, mufflers with expansion chambers and sound-absorbing materials have been used to reduce noise emissions; however, diesel or gasoline particulate filters have also been observed to reduce noise transmitted through the filter. Herein, a novel approach based on a microstructure model is proposed to predict the sound transmission loss through a diesel/gasoline particulate filter, the wall of which is made of a ceramic porous material. In this approach, a homogenization method for sound-absorbing poroelastic materials based on the asymptotic expansion approach is applied. The method was originally developed by one of the authors of this study. Microscopic structural images are obtained through μX-ray computed tomography, and a pore network model that consists of spherical pores and cylindrical throats is constructed to represent the characteristics of the porous filter wall. A microscopic unit cell model is derived from the expected values of the pore- and throat-size distributions obtained using the pore network model. Homogenized properties, such as permeability, equivalent density, and equivalent bulk modulus, are obtained through microscopic calculations using the unit cell model. Finally, the sound transmission loss is predicted through macroscopic calculations using the homogenized properties. The calculated sound transmission loss agreed well with the values measured using an acoustic tube and simplified exhaust systems.

A mathematical model for two solutes transport in a poroelastic material and its applications

Using well-known mathematical foundations of the elasticity theory, a mathematical model for two solutes transport in a poroelastic material (soft tissue is a typical example) is suggested. It is assumed that molecules of essentially different sizes dissolved in fluid and are transported through pores of different sizes. The stress tensor, the main force leading to the material deformation, is taken not only in the standard linear form but also with an additional nonlinear part. The model is constructed in 1D space and consists of five nonlinear equations. It is shown that the governing equations are integrable in stationary case, therefore all steady-state solutions are constructed. The obtained solutions are used in an example for healthy and tumour tissue, in particular, tissue displacements are calculated and compared for parameters taken from experimental data in cases of the linear and nonlinear stress tensors. Since the governing equations are non-integrable in non-stationary case, the Lie symmetry analysis is used in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with non-trivial Lie symmetries are identified. As a result, multiparameter families of exact solutions are constructed including those in terms of special functions(hypergeometric and Bessel functions). A possible application of the solutions obtained is demonstrated.

Estimating the interfacial permeability for flow into a poroelastic medium.

Boundary conditions between a porous solid and a fluid has been a long-standing problem in modeling porous media. For deformable poroelastic materials such as hydrogels, the question is further complicated by the elastic stress from the solid network. Recently, an interfacial permeability condition has been developed from the principle of positive energy dissipation on the hydrogel-fluid interface. Although this boundary condition has been used in flow computations and yielded reasonable predictions, it contains an interfacial permeability η as a phenomenological parameter. In this work, we use pore-scale models of flow into a periodic array of solid cylinders or parallel holes to determine η as a function of the pore size and porosity. This provides a means to evaluate the interfacial permeability for a wide range of poroelastic materials, including hydrogels, foams and biological tissues, to enable realistic flow simulations.

BOUNDARY ELEMENT MODELING AND ANALYSIS OF THE INTERACTION OF A VERTICAL BARRIER WITH SURFACE WAVES IN A POROELASTIC FORMULATION

The paper studies the possibility of attenuating the wave intensity on the surface of a half-space by installing a barrier based on the solution of a three-dimensional problem of the dynamic theory of partially saturated poroelasticity using the boundary element method. The basic idea of using a wave barrier is to create an obstacle to the propagation of surface waves over the territory occupied by structures or constructions. Open or unfilled trenches can be effective when organizing this method of protection. In the paper, numerical modeling is performed using the boundary element method based on the combined use of boundary integral equations of the direct approach of the three-dimensional isotropic theory of poroelasticity and the integral Laplace transform. To describe the poroelastic medium, the Biot model of a poroelastic material in the case of partial saturation is used. The solution in the time domain is obtained using a method based on quadrature formulas for calculating the convolution integral and referred to hereinafter as the step method. The problem of the action of a dynamic load on a deformable partially saturated poroelastic half-space with a vertical barrier in the form of a trench is considered. To assess the efficiency of wave damping by a barrier on the surface of a half-space, the amplitude reduction factor is calculated for different values of the saturation coefficient of the poroelastic material of the half-space, geometric dimensions of the barrier and boundary conditions. Graphs and maps of the amplitude reduction factor are provided. The simulation results show that the presence of a barrier in the form of a trench leads to a decrease in the Rayleigh wave amplitude at points located behind the trench, for all considered values of the parameters under study. It is also shown that the condition of permeability or impermeability of the trench boundary does not have a noticeable effect on its properties in reducing the intensity of surface waves. The results obtained can be useful for developing effective methods for protecting buildings and structures from dynamic effects.

Study on the poroelastic behaviors of the defected osteochondral unit.

Osteoarthritis has become a major disease threatening human health. The mechanism of injury under fluid involvement can be studied by finite element method. However, most models only model the articular cartilage to study the subchondral bone structure, which is too simplistic. In this study, a complete osteochondral unit was modeled and provided with a poroelastic material, and as osteoarthritis develops and the size, thickness, and shape of the osteochondral unit defect varies, the fluid flow behavior is altered, which may have functional consequences that feed back into the progression of the injury. The results of the study showed that interstitial fluid pressure and velocity decreased in defective osteochondral units. This trend was exacerbated as the size and thickness of the defect in the osteochondral unit increased. When the defect reached the trabeculae, pressure around the cartilage defect in the osteochondral unit was greatest, flow velocity in the subchondral cortical bone was greatest, and pressure and flow velocity around the trabecular defect were lowest. As osteoarthritis develops, the osteochondral unit becomes more permeable, and the pressure of the interstitial fluid decreases while the flow rate increases, resulting in severe nutrient loss. This may be the fluid flow mechanism behind osteochondral defects and osteoarthritis.

Indentation over a transversely isotropic, poroelastic, and layered half-space

Poroelastic materials are common in nature and have applications in many engineering fields. In this paper, we derive a general solution of indentation over a multilayered half-space consisting of transversely isotropic and poroelastic materials. The rigid disc-shaped indenter is subjected to a vertical force of Heaviside time-variation. The solution is expressed in terms of the recently introduced powerful Fourier-Bessel series (FBS) system of vector functions combined with the unconditionally stable dual-variable and position method for dealing with layering. Since the problem is a mixed boundary-value one, the Green's functions due to a vertical ring-load are first derived which are then utilized in the integral least-square formulation to derive the solution. In terms of the FBS method, the expansion coefficients, which are further called Love numbers, are discrete, and therefore can be pre-calculated and used repeatedly for different field points on the surface. As such, the solution based on the new FBS method is more efficient and accurate than previous integral-transform methods. This new FBS method is particularly attractive when dealing with mixed boundary-value problems where time-variation is further involved. Numerical examples are conducted to validate the accuracy of the proposed solution and to demonstrate the effects of material layering, geometry, and hydraulic boundary conditions on the contact performance of the material system.

Poynting effect in fluid-saturated poroelastic soft materials in torsion

This work studies the Poynting effect in fluid-saturated poroelastic soft materials in torsion. The Poynting effect is a nonlinear mechanical phenomenon commonly observed in soft solids such as biological soft tissues, gels and rubber. When sheared or twisted, such materials tend to either expand or contract in the direction perpendicular to the plane of shearing or twisting. Thus, to maintain a constant height, a compressive (positive Poynting effect) or tensile (negative Poynting effect) normal force must be applied to the material’s sheared face or twisted end. The mechanical response of fluid-saturated poroelastic soft materials can be described using mixture theory. Although both of its constituents are intrinsically incompressible, the biphasic material as a whole is compressible since it may gain or lose fluid through its pores. Our model—an extension of the single-constituent, incompressible solid models found in anterior studies—allows one to quantify the effect of the fluid and the solid on the normal force and torque required to maintain the torsion deformation and shows that the anomalous negative Poynting effect cannot be attributed to the poroelastic nature of the material alone. We use finite element simulations to predict the normal force and torque for biphasic materials with weakly-compressible and fully-compressible Mooney–Rivlin skeletons and Holmes–Mow-type hydraulic permeability. We also approximate analytical expressions for the normal force and torque for a weakly-compressible Mooney–Rivlin solid, which set a benchmark for the numerical simulations.

Numerical prediction of the sound transmission loss of double panel configurations with acoustic structured and poroelastic materials

The sound transmission loss of multilayer system assemblies made of Noise Control Treatments comprising metamaterials and poroelastic materials, sandwiched between two structural panels is of utmost importance in aerospace, automotive, building and several other engineering applications. The integration of acoustic metamaterials in these systems introduces a number of challenges at the level of numerical simulation in order to predict their acoustic and structural behavior. This paper presents a methodology for the numerical simulation of the sound transmission loss of structural configurations comprising acoustic metamaterials embedded in a glass wools layer, sandwiched between two elastic panels. The metamaterial is designed as a parallel assembly of four sub-metamaterials. Each of these sub-metamaterials is also a series assembly of a periodic unit cell having a neck + cavity + neck type configuration. The four sub-metamaterials are designed so that their first resonance frequencies are grouped together in order to improve the sound transmission loss at the first two natural frequencies of the double panel. The COMSOL Multiphysics finite element method solver is used. The normal incidence and diffuse field sound transmission loss numerical results are presented and discussed in comparison with results from literature for validation.

Cracks in tensile-contracting and tensile-dilating poroelastic materials

Fibrous gels such as cartilage, blood clots, and carbon-nanotube-based sponges with absorbed oils suffer a reduction in volume by the expulsion of liquid under uniaxial tension, and this directly affects crack-tip fields and energy release rates. A continuum model is formulated for isotropic fibrous gels that exhibit a range of behaviors from volume increasing to volume decreasing in uniaxial tension by changing the ratio of two material parameters. The motion of liquid in the pores of such gels is modeled using poroelasticity. The direction of liquid fluxes around cracks is shown to depend on whether the gel locally increases or decreases in volume. The energy release rate for cracks is computed using a surface-independent integral and it is shown to have two contributions — one from the stresses in the solid network, and another from the flow of liquid. The contribution to the integral from liquid permeation tends to be negative when the gel exhibits volume decrease, which effectively is a crack shielding mechanism.

A Novel Fiber-Reinforced Poroviscoelastic Bovine Intervertebral Disc Finite Element Model For Organ Culture Experiment Simulations.

Intervertebral disc (IVD) degeneration and methods for repair and regeneration have commonly been studied in organ cultures with animal IVDs under compressive loading. With the recent establishment of novel multiaxial organ culture systems, accurate predictions of the global and local mechanical response of the IVD are needed for control system development and to aid in experiment planning. This study aimed to establish a finite element model of bovine IVD capable of predicting IVD behavior at physiological and detrimental load levels. A finite element model was created based on the dimensions and shape of a typical bovine IVD used in organ culture. The nucleus pulposus (NP) was modelled as a neo-Hookean poroelastic material and the annulus fibrosus (AF) as a fiber-reinforced poroviscoelastic material. The AF consisted of 10 lamella layers and the material properties were distributed in radial direction. The model outcome was compared to a bovine IVD in a compressive stress-relaxation experiment. A parametric study was conducted to investigate the effect of different material parameters on the overall IVD response. The model was able to capture the equilibrium response, and the relaxation response at physiological and higher strain levels. Permeability and elastic stiffness of the AF fiber network affected the overall response most prominently. The established model can be used to evaluate the response of the bovine IVD at strain levels typical for organ culture experiments, to define relevant boundaries for such studies and to aid in the development and use of new multiaxial organ culture systems.

A study on the optimal configuration of absorbing materials of multi-layered silencers for maximizing transmission loss

This study focuses on the optimal configuration of absorbing materials of multi-layered silencers applied to seawater pipelines. Absorbing materials in silencers are made of poroelastic material, and acoustic wave propagation is analyzed using the Biot-Allard Model. Acoustic transmission loss is computed numerically using COMSOL Multiphysics. It is observed that among various standard polyurethane materials, those with lower density exhibit higher acoustic transmission loss. Finally, optimization is carried out with the objective function of maximizing the transmission loss at target frequencies. Low transmission loss values at specific frequencies of one-layer silencers can be meaningfully increased by optimizing the sequence of various standard polyurethane materials.