Isotropic Porous Materials Research Articles

Optimization and imputation of acoustic absorption sequence prediction for transversely isotropic porous materials: A MultiScaleCNN-Transformer-PSO model approach

To address the limitations of traditional methods in real-time prediction and adaptive optimization of sound absorption coefficients for transversely isotropic porous materials. This study introduces a method combining a Multi-Scale Convolutional Neural Network (MultiScaleCNN) and a Transformer model to improve real-time prediction and optimization of sound absorption coefficients in transversely isotropic porous materials. Using a validated transfer matrix method based on the Biot model and acoustic analysis via COMSOL 6.2, a database of sound absorption curves was created. MultiScaleCNN extracts multi-scale features, which the Transformer model uses for sequence-to-sequence modeling with a self-attention mechanism, effectively managing complex dependencies. The model achieves high accuracy in full-mask prediction, closely aligning with actual values. Additionally, Particle Swarm Optimization (PSO) optimizes sound absorption coefficients in the 1000–2000 Hz range, meeting the fitness function’s criteria. For partial-mask imputation, the model uses adjacent frequency data and features to enhance accuracy. Results show that the MultiScaleCNN-Transformer-PSO model offers a robust, data-driven approach for predicting and optimizing sound absorption coefficients, advancing the field.

Analytical investigation of porous medium effects on the flow of two micropolar fluids in a rotating annulus

Fluids with microstructures and microinertia play a vital role in microfluidics and nanfluidics system. One of such significant fluid is micropolar fluid. The characteristic behavior of micropolar fluid flow in conduit/pipe, etc. filled with porous medium helps us understand the flow behavior of biological fluids in porous media, groundwater flow in aquifiers, rotatory machines or viscometer. To understand such real-world problems, it is necessary to get into the mathematical model of such flow models. One such model with wide number of application is presented in this paper. This work investigated the flow of two micropolar fluids between the region formed by two concentric cylinders. Authors have considered inner cylinder to be at rest and outer cylinder rotating at a constant angular velocity. The region between two concentric cylinder is filled with an isotropic porous material. A slip condition at the outer wall and continuity conditions at interface of two fluids has been utilized to obtain an analytical solution for the proposed model. The numerical solution of the obtained solution for present problem is used to graphically analyze the motion of immisicble micropolar fluids rotating in an annulus filled with the porous medium. It is found that an outer cylinder has a notable influence on the flow behavior of immiscible micropolar fluids, contrary to the effect observed within the inner region. An analytical approach of this work not only helps us obtain precise results and analysis of the flow, but it also serves as a useful validation for future approximations within the scope of this work.

Inference of the acoustic properties of transversely isotropic porous materials

Transversely isotropic porous materials are well represented by equivalent fluid models based on semi-phenomenological models such as the Johnson-Champoux-Allard-Lafarge (JCAL) model and a set of material parameters. Direct measurements of these parameters, however, are often difficult or time consuming. As an alternative, inverse estimation methods provide a simple and fast framework to identify the JCAL model parameters, since they can be performed on single impedance tube measurements. In this work, we present a stochastic inverse identification method of the JCAL parameters for transversely isotropic materials. We consider the flow resistance and characteristic viscous length and the static tortuosity to be anisotropic and the frame to be fully rigid, resulting in nine unique parameters to be identified. The method is based on reflection factor measurements of a material in different orientations corresponding the transverse and isotropic principal axes. Hence, a priori knowledge of the orientation of the principal axes of the material is required. Results of the parameter inference are presented based on experimental data for a glass wool sample.

Thermal and hydrodynamic analysis inside a channel partially filled with porous material

AbstractIn this work, the transfer of heat and changes in fluid pressure within a rectangular channel fairly packed with porous material have been studied numerically for various Darcy numbers and dimensionless porous layers. The model was run with the following assumptions: laminar flow, forced convection, isotropic porous material, local thermodynamic equilibrium, constant wall temperature boundary condition, and no thermal dissipation. The study covers a broad range for the dimensionless porous layer, 0 ≤ hr < 1, and the Darcy number, 10−4 < Da < 10−2. The fully developed and developing flow over the channel is investigated in numerical study. It was observed that the inertia effect may be disregarded when Da < 10−4. The local dimensionless bulk temperature distribution, pressure drop, and velocity profiles were all shown to be impacted by the Darcy number and dimensionless porous layers, according to the numerical analysis results. The maximum heat transfer rate was attained when the ratio of the porous layer inside the channel was 0.8, and the pressure gradient was the highest. Partial packing of the channel with a porous material has two advantages: it increases the rate heat transmission rate and results in a much smaller pressure drop than a filled porous medium.

An Efficient Method to Compute Capillary Pressure Functions and Saturation-Dependent Permeabilities in Porous Domains Spanning Several Length Scales

A method for calculating capillary pressure functions and saturation-dependent permeabilities of geometries containing several length scales is presented. The method does not require the exact geometries of the smaller length scales. Instead, it requires the effective two-phase flow parameters. It does this by generating phase distributions that form static equilibria at a selected capillary pressure value, similar to pore-morphology methods. Within a porous material, the effective parameters are used to obtain the corresponding phase saturation. It is shown how these phase distributions can be used in geometries spanning several length scales to calculate the capillary pressure function and saturation-dependent permeabilities. The method is tested on a geometry containing a simple isotropic porous material and it is applied to a complex textile stack geometry from a liquid composite molding process. In this geometry, three different length scales can be distinguished. The effective two-phase flow parameters of the textile stack are calculated by the proposed method, avoiding expensive simulations.

Effective mechanical behaviors of transverse isotropic materials containing compressible liquid inclusions with surface effects

Porous media with fluid-saturated microchannels, prevalent in biomaterials, tissue engineering materials and flexible electronic devices, can be modelled as transverse isotropic materials. Surface effects can influence significantly the macro-mechanical responses of such materials, particularly for soft materials with micro- or nano-scale channels. In this study, we first develop constitutive laws for fluid saturated porous materials with microchannels by integrating the top-down (homogenization) approach with the bottom-up (micromechanics) approach. We then explicitly establish a connection between surface effects and macro-mechanical responses. Employing the generalized self-consistent model (GSCM), we estimate the effective parameters (i.e., coefficients in constitutive equations governing macro-mechanical responses), with fluid compressibility and surface effects accounted for. Our findings reveal that, as surface energy increases, the effective transverse shear modulus is enlarged, the effective plane strain bulk modulus, the unit uniaxial straining modulus and the cross modulus are all reduced, but the axial shear modulus remains nearly unchanged. As an application, we characterize the mechanical behaviors of the transverse isotropic fluid-saturated porous material with surface effects by connecting the classic Mandel solution with the estimated effective parameters. The pore pressure exhibits the Mandel-Cryer effect. The insights gained from this study are valuable for comprehending and exploring the intricate ways in which surface effects influence the mechanical responses of transversely isotropic fluid-saturated porous materials featuring sufficiently small channels.

Size-dependent yield criterion for single crystals containing spherical voids

A micromechanics-based yield criterion is derived for a porous single crystal containing a random distribution of spherical voids, using homogenization and limit analysis of a hollow spherical representative volume element obeying a strain gradient crystal plasticity model. The criterion captures the effect of plastic anisotropy due to crystallographic slip on a set of discrete slip systems, as well as the void size dependence of yielding. The yield criterion is formally similar to the well known Gurson model for isotropic porous materials, and reduces to existing results in the literature in the limiting case of large void sizes relative to the length scale in the gradient plasticity model. The yield criterion is validated by comparison with rigorous upper bound yield loci obtained using a numerical limit analysis procedure. Predictions for the size dependence of void growth are obtained by integrating the porous plasticity model, and shown to be consistent with the observations from lower scale discrete dislocation dynamics simulations. The loading path dependence of void growth in the size-independent limit are compared with finite element simulations of void growth in a single crystal using the unit cell model.

Local discontinuous Galerkin schemes for an ultrasonic propagation equation with fractional attenuation

The goal of this article is to develop local discontinuous Galerkin (LDG) schemes for solving a time fractional equation describing the ultrasonic wave in a homogeneous isotropic porous material. Two novel semi-discrete LDG schemes are designed for the considered model. The semi-discrete LDG schemes are constructed by splitting the original model into a coupled system. The first semi-discrete scheme follows the traditional LDG method by splitting second-order space derivative. The second one splits the original model for both time and space derivatives. The discontinuous Galerkin is used for the spatial discretization. Two kinds of fully discrete LDG schemes are presented by using the Grünwald-Letnikov and L1 approximation formulas for the time fractional derivatives. The $ L^2 $ norm stability and convergence analysis are carried out for both semi-discrete and fully discrete LDG schemes. The stability analysis reveals that the numerical schemes are unconditionally stable in $ L^2 $ norm and convergence with optimal convergence rate. Finally, numerical examples are presented to test the effectiveness of the proposed schemes and the correctness of the theoretical analysis.

Hydrodynamic instability of flow through a rotating channel filled with isotropic porous media

Various geophysical and engineering applications have underlying physics, comprising system rotation's effects on the dynamics and transport phenomena in porous media flows. Comprehensive knowledge of the instability in a rotating fluid-saturated porous layer is beneficial for controlling the transport phenomena and the mixing process. The present study focuses on the temporal evolution of small disturbances in a pressure-induced fluid flow through a spanwise rotating channel filled with an isotropic porous material. A Darcy–Brinkman model, including the Coriolis force term in the momentum equation, is employed to describe the developed flow. A normal mode analysis is performed, and the coupled Orr–Sommerfeld–Squire eigenvalue problem is formulated to capture the linear instability of the perturbed flow. The Chebyshev collocation technique is used to solve the fourth-order eigenvalue problem to capture the transient behavior of the finite-amplitude disturbances. The temporal growth rate and marginal stability curves related to the Coriolis force-based instabilities are investigated. The rotating porous media flow is unstable at a much lower Reynolds number than the non-rotating configuration. The analysis confirms co-existing unstable modes and mode coalescence for a specific range of parameters, which can enhance the mixing and transport inside the porous layer. The neutral stability curves show the appearance of two different unstable zones corresponding to the long and moderate waves. Moreover, the higher permeability and porosity of the porous medium have a destabilizing influence.

The effect of voids shape on hypervelocity cylindrical cavity expansion and shock waves formation in transversely isotropic porous materials

This paper investigates the steady-state dynamic radial expansion of a pressurized circular cylindrical cavity in an infinite porous medium modeled with the constitutive framework developed by Monchiet et al. (Int J Plast 24:1158–1189, 2008), which considers the material to display a periodic porous microstructure with spheroidal voids and matrix described by the orthotropic yield criterion of Hill (Proc R Soc Lond Ser A Math Phys Sci 193:281–297, 1948). For that purpose, we have extended the formulation of dos Santos et al. (Int J Impact Eng 132:103325, 2019b) to consider oblate and prolate voids, which allows to assess the role of the initial voids shape on the elastoplastic–anisotropic fields that develop near the cavity. The theoretical development follows the cavity expansion formalism of Cohen and Durban (J Appl Mech 80:011017, 2013) and employs the artificial viscosity approach of Lew et al. (J Comput Aided Mater Des 8:213–231, 2001) to avoid singularities in the field variables due to the formation of plastic shock waves. The main outcome of this work is a relationship between the critical cavity expansion velocity for which plastic shocks emerge and the initial aspect ratio of the spheroidal voids. The results show that the formation of shocks is delayed for oblate voids, in comparison with spherical and prolate voids. These findings have been substantiated for different anisotropic behaviors and initial void volume fractions.

Boundary Value Problems of Thermoelasticity for Porous Sphere and for A Space with Spherical Cavity

This article is concerned with the coupled linear quasi-static theory of thermoelasticity for porous materials under local thermal equilibrium. The system of equations is based on the constitutive equations, Darcy's law of the flow of a fluid through a porous medium, Fourier's law of heat conduction, the equations of equilibrium, fluid mass conservation and heat transfer. The system of governing equations is expressed in terms of displacement vector field, the change of volume fraction of pores, the change of fluid pressure in pore network and the variation of temperature of porous material. The present paper is devoted to construct explicit solutions of the quasi-static boundary value problems (BVPs) of coupled theory of thermoelasticity for a porous elastic sphere and for a space with a spherical cavity. In this research the regular solution of the system of equations for an isotropic porous material is constructed by means of the elementary (harmonic, bi-harmonic and meta-harmonic) functions. The basic boundary value problems (the Dirichlet type boundary value problem for a sphere and the Neumann type boundary value problem for a space with a spherical cavity) are solved explicitly. The obtained solutions are given by means of the harmonic, bi-harmonic and meta-harmonic functions. For the harmonic functions the Poisson type formulas are obtained. The bi-harmonic and meta-harmonic functions are presented as absolutely and uniformly convergent series.

Experimental and Numerical Studies of Gas Permeability through Orthogonal Networks for Isotropic Porous Material.

With regard to the problem of gas flow through isotropic porous deposits, the issues were considered in the category of description of gas movement mechanisms for structural models of the skeleton. As part of experimental tests of gas permeability through porous material in the form of polyamide, the numerical simulation method was used, using the k–ε turbulence model. The analysis of hydrodynamic phenomena occurring in the porous material made it possible to confront experimental research with numerical calculations. The analysis shows that, for a porous polyamide bed, there is a certain limit range of gas velocity (10−4–1) ms−1 at which flow resistance is the lowest. On the other hand, the highest value of the flow resistance is gradually achieved in the range of gas velocity (1–10) ms−1. This is due to the different structure of the isotropic polyamide material. The validation of the numerical model with experimental data indicates the validity of the adopted research methodology. It was found that the permeability characteristics of the tested porous material practically did not depend on the direction of gas flow. For porous polyamide, the permeability characteristic is non-linear, which, from the point of view of the measurements carried out, indicates the advantage of turbulent gas flow over its laminar movement. The novelty of the article is a proprietary method of measuring gas permeability for a cube-shaped sample made of a material constituting a sinter of spherical particles of equal dimensions. The method enables the determination of gas flow (in each flow direction) in microchannels forming an orthogonal network, characteristic of isotropic materials.

Quantifying the effect of two-point correlations on the effective elasticity of specific classes of random porous materials with and without connectivity

It is well-known by now that the Hashin–Shtrikman bounds imply that the two-point correlation functions are not in general sufficient to estimate accurately the response of composites, especially when their underlying phases exhibit infinite contrast, e.g., porous materials. Starting from this longstanding, albeit qualitative result, this work investigates quantitatively the relevance of using two-point correlations to model the effective elastic properties of specific isotropic porous materials with and without connectivity. To achieve this in an unambiguous manner, we propose three different microstructures that share almost identical two-point statistics by design but are rather different morphologically. The choice of these microstructures is driven by their wide use in several practical problems ranging from polymers to geomaterials. The first microstructure is obtained by a random sequential adsorption (RSA) of non-overlapping, polydisperse, spherical and ellipsoidal voids oriented randomly in a unit-cell. The second one, termed connected random sequential adsorption (CRSA), is obtained from the first one by adding controlled connectivity via cylindrical channels of circular cross-section. The porosity resulting from connectivity is compensated by reducing the size of the existing voids to have the same overall porosity. Interestingly, we find that connectivity does not affect the corresponding two-point statistics. Finally, using as an input the numerical one- and two-point correlations of the RSA, we reconstruct a thresholded Gaussian random field (TGRF) microstructure. Using FFT numerical simulations, we show that the resulting effective elastic properties are very different for the three generated microstructures, despite them sharing nearly the same two-point correlation functions. We show, further, that the introduction of connectivity, and in particular the partial volume fraction of the connected channels, even small, affects strongly the resulting effective elasticity of the composite.

Implementation of new methods for non-destructing testing of diffusion coefficient in porous material products

New methods for non-destructive testing of diffusion coefficient in thin-sheet and massive products made of isotropic and anisotropic porous materials are considered. In contrast to the rigid structure in the known methods, the represented methods are more flexible in implementing measurement procedures due to higher accuracy of measuring the desired coefficient. Flexibility is provided by calculating experimental data in the preferred sections and by choosing there the static characteristic of the transducer with a stable and noise-proof output signal and in the ranges with high sensitivity to changes in parameters. Expressions for calculating the desired diffusion coefficient for each test subject and a generalized sequence of measurement procedures are introduced. The modified version of the information and measurement system for implementing the proposed methods is described, and the results of the research are presented.

An ultra-simple universal model for the effective elastic properties of isotropic 3D closed-cell porous materials

In this paper, effective elastic properties of the isotropic 3D closed-cell porous materials are comprehensively investigated through finite element method simulations, theoretical formulations and experimental tests. 3D representative volume element models with randomly distributed non-overlapping Voronoi-structured voids of various porosities (from 0.01 to 0.99) are created to compute the effective bulk and shear moduli of the porous materials. An ultra-simple universal model (USUM) is developed to predict the effective shear modulus covering the entire porosities. The effective Young’s modulus and Poisson’s ratio of ultra-simple form are then formulated. The findings show that the theoretical estimates agree well with the numerical results for all the effective elastic properties. The uniaxial compression tests are implemented on the specimens of 3D printed porous nylon to measure the effective Young’s modulus. The results suggest that the theoretical predictions of the USUM agree very well with the effective Young’s moduli of the porous materials, covering a wide range of porosity.

Structural topology optimization with positive and negative Poisson’s ratio materials

PurposeNegative Poisson’s ratio (NPR) material has huge potential applications in various industrial fields. However, lower Young’s modulus due to the porous form limits its further applications. Based on the topology optimization technique, this paper aims to optimize the structure consisting two isotropic porous materials with positive Poisson’s ratio (PPR) and NPR and void.Design/methodology/approachUnder prescribed dual-volume fraction constraints, the structural compliance is taken as the objective. Young’s modulus and Poisson’s ratio are, respectively, interpolated and expressed with Lamé’s parameters for easier programming. Accordingly, the sensitivities can be derived through the chain rule. Several two- and three-dimensional illustrative examples are presented to demonstrate the capability and effectiveness of the proposed approach. The influences of Poisson’s ratios, volume fractions and Young’s moduli on the optimized results are investigated.FindingsFor NPR materials having unique load responses, the resulting topologies of PPR and NPR materials have distinct material distributions in comparison of the results from two PPR materials. Furthermore, it is observed that higher structural stiffness can be achieved from the hybrid of PPR and NPR materials than that obtained from the structures made of individual constituent materials.Originality/valueA topology optimization methodology is proposed to design structures composed of PPR and NPR materials.

Steady vibration problems in the coupled linear theory of porous elastic solids

This paper concerns the coupled linear theory of elasticity for isotropic porous materials. In this theory the coupled phenomena of the concepts of Darcy’s law and the volume fraction is considered. The basic internal and external boundary value problems (BVPs) of steady vibrations are investigated. Indeed, the fundamental solution of the system of steady vibration equations is constructed explicitly by means of elementary functions, and its basic properties are presented. The radiation conditions are established and Green’s identities are obtained. The uniqueness theorems for the regular (classical) solutions of the BVPs are proved. The surface (single layer and double layer) and volume potentials are constructed and the basic properties of these potentials are given. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.

Finite Element Modeling of Porous Microstructures With Random Holes of Different-Shapes and -Sizes to Predict Their Effective Elastic Behavior

Porous materials are promising media for designing medical instruments, drug carriers, and bioimplants because of their excellent biocompatibility, ease of design, and large variation of elastic moduli. In this study, a computational strategy using the finite element method is developed to model the porous microstructures and to predict the relevant elastic moduli considering the actual characteristics of the micropores and their distributions. First, an element-based approach is presented to generate pores of different shapes and sizes according to the experimental observations. Then, a computational scheme to evaluate the effective moduli of macroscopically isotropic porous materials based on their micro-mechanics is introduced. Next, the accuracy of our approach is verified with the analytical solutions of the extreme bounds of the elastic isotropic moduli of a simplified model and with the experimental data available in the literature. Finally, the influence of the shape of pores and their distribution modes are assessed.

Data measuring system to determine the solvent diffusion coefficient in products from capillary-porous materials

The development of methods and means for non-destructive product testing is the current task of modern instrument-making in the study field of porous materials ability to transport the substances distributed in a solid phase. They allow one to determine the characteristics of mass transfer directly in the finished product, because they do not require the preparation of special samples of a given configuration and size, typical for most of the used methods and devices. The aim of this study is to develop data measuring system that improves the performance of studies of polar solvents diffusion in porous media. The data measuring system is designed to implement methods of the solvents diffusion coefficient control in fine and bulk products from isotropic and anisotropic porous materials with one-way access to flat surfaces of specified size products. The schematic of the data measuring system, virtual surface for experiment control, the flow chart for the measurement operations of the developed methods, the results of testing the system are given.

Random 3D-printed isotropic composites with high volume fraction of pore-like polydisperse inclusions and near-optimal elastic stiffness

Highly porous materials with random closed-cell architecture combine isotropy with high stiffness. Yet in practice, the complexity of their manufacturing limits the experimental exploration of these materials, for which studies of the elastic response remain to date mainly theoretical. In this study, we measure experimentally the elastic moduli of random closed-cell porous-like composites fabricated by 3D-printing. These materials contain a high volume fraction (up to 82 vol pct) of non-overlapping, polydisperse void-like spherical inclusions, which are randomly dispersed in a homogeneous polymer matrix. We first generate the virtual microstructures of these materials using a random sequential adsorption (RSA) algorithm, and then use numerical homogenization to compute the size of the material representative volume element (RVE). The latter is used to assemble the test samples, whereby the void-like inclusions are 3D-printed using a gel-like polymer with mechanical properties that are in high contrast with those of the base polymer thus behaving mechanically as pores. Experiments reveal that the proposed isotropic random closed-cell porous materials have bulk and shear moduli that lie very close to the theoretical Hashin-Shtrikman upper bounds for an isotropic porous solid.