Numerical calculation of permeability of periodic porous materials: Application to periodic arrays of spheres and 3D scaffold microstructures

In this paper, an efficient numerical method is proposed to calculate the anisotropic permeability in porous materials characterized by a periodic microstructure. This method is based on pore-scale fluid dynamic simulations using a static volume of fluid method. Unlike standard solution procedures for this type of problem, we here solve an average constitutive equation over both fluid and solid domain by use of a subgrid model to accurately capture momentum transfer from the fluid to solid interface regions. Using numerical simulations on periodic arrays of spheres, we first demonstrate that, by using the subgrid interface model, more accurate results can be produced, for the velocity and pressure fields, than via more conventional approaches. We then apply numerical upscaling over the unit cell to calculate the full anisotropic permeability from the pore-scale numerical results. The obtained permeability values for a variety of periodic arrays of spheres in different arrangements and packing orders are in good agreement with semianalytical results reported in literature. This validation allows for the permeability assessment of more complex structures such as isotropic gyroid structures, or anisotropic cases, here modeled in their simplest form, the ellipsoidal inclusion.     

Critical Assessment 18: elastic and thermal properties of porous materials – rigorous bounds and cross-property relations

A critical assessment of model relations describing the porosity dependence of elastic properties (Young's modulus) and thermal properties (thermal conductivity) is given. It is shown that there are essentially five types of admissible predictive model relations for the relative Young's modulus and thermal conductivity of isotropic porous materials. The cross-property relations resulting from the complete analogy between the model relations for the elastic moduli and thermal conductivity of isotropic porous materials are reviewed and compared. Finally, it is shown that the fact that relative Young's moduli are not equal to relative thermal conductivities except for materials with translational symmetry, i.e. the mere existence and necessity of non-trivial cross-property relations, proves so-called minimum solid area models to be wrong.     

Effect of fibre volume fraction on fatigue behaviour of glass fibre reinforced composite

The aim of this paper is to study the fatigue behavior of GFRP composites manufactured by vacuum bagging process by varying the volume fraction. Constant‐amplitude flexural fatigue tests were performed at zero mean stress, i.e. a cyclic stress ratio R=?1 by varying the frequency of the testing machine. The relationship between stiffness degradation rate and fibre volume fraction, was observed, and the influence of volume fraction on the tensile strength was also investigated. The results show that, as the volume fraction increases the stiffness degradation rate initially decreases and then increases after reaching a certain limit for the volume fraction. Graph between volume fraction and Young's modulus shows that as the volume fraction increases Young's modulus also increases and reaches a limit and then it decreases with further increase in volume fraction, due to the increase in fibre content which changes the material properties of the composite material. The obtained results are in agreement with the available results.     

Effect of porosity and stress concentration associated with pores on elastic creep by crack growth in brittle solids

The solution for the creep rate of a porous solid as a function of pore volume fraction, pore size and the radial or annular flaw size, is presented. The analysis is based on the concept of crack opening displacement which assumes that the displacement of a solid under stress is solely due to the opening of all radial or annular cracks emanating from the surface of the cavities. It is shown that the strain rate by crack growth is a strong function of pore size and preexisting flaw size. A linear relationship was found to exist between the strain rate by crack growth and the porosity volume fraction.     

Elastic behavior of composites containing Boolean random sets of inhomogeneities

The overall mechanical response as well as strain and stress field statistics of an heterogeneous material made of two randomly distributed, linear elastic phases, are investigated numerically. The Boolean model of spheres is used to generate microstructures consisting of either porous or rigid inclusions, at any volume fraction of the phases. Stress and strain field integral ranges, or equivalently the representative volume element, are computed and linked to features of the field statistics, and to the microstructure geometry.     

Young's modulus—porosity relations: an analysis based on a minimum contact area model

The Young's modulus–porosity relation of porous ceramic materials has been analysed based on a minimum solid area of contact model. The minimum solid area of contact developed during sintering of an assembly of monosized spheres stacked in simple cubic packing is calculated by approximating the neck area by two sine-wave functions. The first function represents the shape of a sphere and the second function signifies the shape of the neck between neighbouring spheres. The model shows excellent agreement with 12 sets of relative Young's modulus, E/Eo, versus pore volume fraction, P, data from literature on five different polycrystalline ceramic oxides, namely Lu2O3, Sm2O3, Yb2O3, Al2O3 and ThO2, whose porosities are reasonably represented by such idealized packing.     

A particle packing algorithm for packed beds with size distribution

A particle packing algorithm for simulating realistic packed beds of spheres with size distribution is described. The algorithm used the Monte Carlo method combined with the simulated annealing minimisation algorithm to solve the packed bed simulations. The objective function which was minimised was a combination of two functions, one describing the deviation from the target mean coordination number of the spheres in each size interval and the other the average fraction of overlapping volume of the spheres per contact. In this way a realistic bed structure was maintained while at the same time controlling the coordination number of the spheres. The algorithm used an experimentally validated model to predict the mean coordination number of the spheres in each size interval.     

A DEM-based analysis of the influence of aggregate structure on suspension shear yield stress

This study theoretically examined the effect of aggregate structure on the suspension shear yield stress. The aggregation process of colloidal particles was simulated using the discrete element model (DEM) combined with the well-known DLVO theory. The predicted aggregate structural characteristics, namely the coordination number and inter-particle forces were then used in a modified version of the Flatt and Bowen mechanistic model [6] to calculate the corresponding suspension yield stress. The effect of key parameters such as solid volume fraction, suspension pH and ionic strength on the aggregate structure and hence the yield stress of the suspension was investigated.The results showed that the yield stress increased significantly under conditions that were favourable for formation of complex net-like aggregate structures, such as high solid volume fractions, pH values near the iso-electric point, and high ionic strengths. In such cases, the mean coordination number reached a maximum value which was considered to be dependent on the particle size and size distribution. The suspension yield stress exhibited a power law dependency on the solid volume fraction. The interconnected network structure developed at high solid volume fractions was found to be the major contributing factor to the observed high suspension yield stress. As the particle–particle repulsion became significant, a decrease in both the number of bonds and the mechanical bonding strength of the aggregate structure was observed. That was considered to be responsible for the reduction in the suspension yield stress. The suspension yield stress became independent of the suspension ionic strength when the ionic strength exceeded the critical coagulation concentration. Satisfactory agreements were obtained between simulation results and the published experimental data.     

Rubber toughening of plastics

Measurements of particle size distribution, particle volume fraction?/, Young's modulus, tensile and compressive yield stress and Charpy impact strength were made on a series of 14 high-impact polystyrene (HIPS) polymers of widely varying structure. In materials throughout the series containing 8.5 wt % polybutadiene, it was found that?/ varied between 0.17 and 0.44 as the mean particle size increased from 0.2 to 1.8 μm. Modulus and yield stresses depended principally upon particle volume fraction but the ratio of polybutadiene to polystyrene within the particles also appeared to have some influence upon properties. By contrast, variations in ? provided only a partial explanation for the observed differences in Charpy impact strength. It is concluded that impact strength is affected by rubber particle size to a much greater extent than properties measured at low strain rates.     

Conventional and novel processing methods for cellular ceramics

Cellular ceramics are a class of highly porous materials that covers a wide range of structures, such as foams, honeycombs, interconnected rods, interconnected fibres, interconnected hollow spheres. Recently, there has been a surge of activity in this field, because these innovative materials have started to be used as components in special and advanced engineering applications. These include filtering liquids and particles in gas streams, porous burners, biomedical devices, lightweight load-bearing structures, etc. Improvements in conventional processing methods and the development of innovative fabrication approaches are required because of the increasing specific demands on properties and morphology (cell size, size distribution and interconnection) for these materials, which strictly depend on the application considered. This paper will cover the main fabrication methods for cellular ceramics, focusing primarily on foams, offering some insight into novel fabrication processes and recent developments.     

Crystallization of Spheres

Simplified computer models are used to gain insight into more complex real systems. In a reversion of this protocol, a colloidal suspension of submicron spherical particles, approximately hard and uniform, was recently crystallized in space and analyzed for crystal type. The objective was to establish how, and to what structure, hard spheres crystallize without gravity. Computational statistical thermodynamics predicts an equilibrium constant between fcc and hcp of order unity. The microgravity experiments, however, resulted in a random hybrid close-packed structure (rhcp) such that long-range order is two-dimensional. Here we report the mechanism from idealized computer experiments for crystallization of spheres from the metastable fluid. Model systems of up to N=64,000 spheres with infinite spatial periodicity have been crystallized in runs of up to 10 billion collisions. When the fluid, initially in a metastable supercooled state at 58% packing, is allowed to nucleate and freeze, a variety of structures emerges. There are three identifiable stages of structural growth: (i) initial nucleation of fcc, rhcp, and also bcc-like (body-centered cubic) local structures; (ii) rapid growth of all incipient nucleites to random stacked two-dimensional hexagonal (rhcp) grains, plus some fcc, to fill the volume; and (iii) relatively slow dissolution of unstable rhcp faces at grain boundaries. Eventually, stable nucleites emerge comprising hexagonal layers, arranged so as to contain predominantly either fcc arrangements of spheres or rhcp, in roughly 50% proportions.     

Jamming in granular shear flows of frictional,polydisperse cylindrical particles

In this work, frictional, cylindrical particle shear flows with different size distributions (monodisperse, binary, Gaussian, uniform) are simulated using the Discrete Element Method (DEM). The influences of particle size distribution and interparticle friction coefficient on the solid phase stresses, bulk friction coefficient, and jamming transition are investigated. In frictional dense flows, shear stresses rise rapidly with the increasing solid volume fraction when jamming occurs. The results suggest that at the jamming volume fraction, stress fluctuation and granular temperature achieve the maximum values, and the rate of the stress increase with increasing solid volume fraction approaches the peak value. Meanwhile, the degree of cylindrical particle alignment approaches a valley value. In the polydisperse flows, the jamming volume fraction exhibits significant dependences on the fraction of the longer particles and the particle size distribution. Two models considering the effect of particle size distribution are discussed for predicting the jamming volume fractions of polydisperse flows with frictional, cylindrical particles.     

The transverse moduli of fibre-composite material

The elastic moduli of uniaxial fibre-composite material are briefly reviewed. The transverse Young's modulus and the axial-transverse shear modulus are matrix dependent. A single formula is derived for their calculation. This formula accepts the Halpin-Tsai philosophy of the need for a simple equation but presumes to improve on Halpin-Tsai by eliminating an arbitrary constant varied for the cases of direct stress and shear stress. It draws attention to the variation of packing array with fibre volume fraction and demonstrates the concentration of strain at the points of minimum clearance between fibres. The accuracy of the new formula is shown, first by comparison with the two established formulae of Halpin and Tsai, and with Hewitt and Malherbe's modification of Halpin and Tsai's formula for shear. Secondly, its accuracy is shown by verifying its trends for the extremes of fibre volume fraction.     

Morphology and linear-elastic moduli of random network solids

The effective linear-elastic moduli of disordered network solids are analyzed by voxel-based finite element calculations. We analyze network solids given by Poisson-Voronoi processes and by the structure of collagen fiber networks imaged by confocal microscopy. The solid volume fraction ? is varied by adjusting the fiber radius, while keeping the structural mesh or pore size of the underlying network fixed. For intermediate ?, the bulk and shear modulus are approximated by empirical power-laws K(phi)proptophin and G(phi)proptophim with n≈1.4 and m≈1.7. The exponents for the collagen and the Poisson-Voronoi network solids are similar, and are close to the values n=1.22 and m=2.11 found in a previous voxel-based finite element study of Poisson-Voronoi systems with different boundary conditions. However, the exponents of these empirical power-laws are at odds with the analytic values of n=1 and m=2, valid for low-density cellular structures in the limit of thin beams. We propose a functional form for K(?) that models the cross-over from a power-law at low densities to a porous solid at high densities; a fit of the data to this functional form yields the asymptotic exponent n≈1.00, as expected. Further, both the intensity of the Poisson-Voronoi process and the collagen concentration in the samples, both of which alter the typical pore or mesh size, affect the effective moduli only by the resulting change of the solid volume fraction. These findings suggest that a network solid with the structure of the collagen networks can be modeled in quantitative agreement by a Poisson-Voronoi process.     

Characterization and deformation behavior of Ti hybrid compacts with solid-to-porous gradient structure

Multiple electro-discharging of pure Ti powder under the energy of 0.58 kJ generated by a 450 μF capacitor being charged to 1.6 kV is very effective to fabricate hybrid structure consisting of central solid and outer porous structure. Increasing the number of electro-discharge treatments up to 3 causes the solid initially formed at the center of the compacts to expand gradually outwards thus increasing the volume fraction of the solid region throughout the samples. The value of compressive yield stress is enhanced up to 64 MPa with increasing the number of electro-discharging treatment. Transition of deformation mode from the vertical to shear deformation clearly indicates the mechanical property and deformation behavior of the hybrid compacts with gradient structure are strongly depending on the volume concentration ratio of the central solid and outer porous areas.     

Advanced lightweight 316L stainless steel cellular lattice structures fabricated via selective laser melting

This paper investigates the manufacturability and performance of advanced and lightweight stainless steel cellular lattice structures fabricated via selective laser melting (SLM). A unique cell type called gyroid is designed to construct periodic lattice structures and utilise its curved cell surface as a self-supported feature which avoids the building of support structures and reduces material waste and production time. The gyroid cellular lattice structures with a wide range of volume fraction were made at different orientations, showing it can reduce the constraints in design for the SLM and provide flexibility in selecting optimal manufacturing parameters. The lattice structures with different volume fraction were well manufactured by the SLM process to exhibit a good geometric agreement with the original CAD models. The strut of the SLM-manufactured lattice structures represents a rough surface and its size is slightly higher than the designed value. When the lattice structure was positioned with half of its struts at an angle of 0° with respect to the building plane, which is considered as the worst building orientation for SLM, it was manufactured with well-defined struts and no defects or broken cells. The compression strength and modulus of the lattice structures increase with the increase in the volume fraction, and two equations based on Gibson–Ashby model have been established to predict their compression properties.     

Studies on phase formation,microstructure development and elastic properties of reduced NiO–8YSZ anode supported bi-layer half-cell structures of solid oxide fuel cells

Half-cell structures of solid oxide fuel cells (SOFCs) with a thin and dense electrolyte layer of 8YSZ supported by a thick and porous NiO–8YSZ anode precursor structure were reduced in a gas mixture of 5% H₂–95% Ar at 800 °C for selected time periods in order to fabricate cermets with desired microstructure and composition, and to study their effects on the elastic properties at ambient and reactive atmospheres. It appears that 2 h of exposure to the reducing conditions is enough to reduce ～80% of NiO with an enhanced porosity value of 35%. The Ni–8YSZ cermet phase formation in the anode was analyzed with X-ray diffraction (XRD) in correlation with its microstructure. The elastic properties were determined after the reduction, at room and elevated temperatures using the impulse excitation technique. At room temperature the decrease in the Young's modulus was about 44% (after 8 h of reduction) and can be attributed mainly to the changes in the microstructure, particularly the increase in porosity from ～12% to 37%. Young's moduli of the as-received precursor and reduced anodes were evaluated as a function of temperature in air and reducing atmosphere. The results were explained in correlation to the initial porosity, composition and oxidation of Ni at the elevated temperatures.     

Mechanical threshold of cementitious materials at early age

At early age, the mechanical characteristics of concrete, such as Young's modulus, follow a rapid rate of change. If strains are restricted or in the event of strain gradients, tensile stresses are generated and there is a risk of cracks occurring. Besides relaxation, change in Young's modulus as a function of the degree of hydration is a major parameter for the modeling of this phenomenon. In this evolution, a threshold of the degree of hydration has to be taken into account, below which concrete displays negligible stiffness. For cement pastes, a simplified hydration model shows that percolation of the solid phases depends on the w/c ratio, which is in accordance with experimental results. On the other hand, for mortar or concrete, the presence of aggregates means that the solid volumetric fraction is such that percolation is observed before hydration occurs. Therefore another parameter is introduced: cohesion due to hydration products. By coupling our model with a finite-element code (CAST3M), it is shown that the threshold for Young's modulus in mortar is almost independent of the w/c ratio, which is in accordance with experimental results.     

基于波浪-多孔介质海床-结构物耦合模型的单桩基础波浪力分析

为了研究波浪作用下多孔介质海床特性和结构物埋深及施工下放速度等因素对结构物所受波浪力的影响,采用修正RANS方程和Forchheimer饱和阻力模型控制流体流动,流体体积法（VOF）追踪自由液面,并采用κ-ε闭合方程进行求解,建立波浪-多孔介质海床-结构物相互作用研究的三维耦合数值分析模型。首先,进行数值模型的验证分析,包含多孔介质海床对波浪传播的衰减效应,波浪作用下结构物周围湍流流动以及海床多孔特性条件下WAVE FORCES结构物所受波浪力。然后,进行结构物所受水平波浪力影响因素的参数分析,主要包含波浪条件,多孔介质海床特性及结构物特性三个方面。结果表明:将多孔介质海床简化为刚性不可渗固体而忽视海床多孔特性,会低估结构物所受的波浪力数值;大波高长周期波浪作用下,深水结构物所受波浪力较大;海床孔隙率、颗粒直径、海床厚度显著影响结构物所受波浪力;同时,结构物直径、截面形式、埋置深度及其施工下放速度v等结构物特性对波浪力的影响同样显著。因此,工程实践中,应同时考虑波浪条件、多孔海床特性和结构物埋置深度及动态运动过程,合理计算结构物所受波浪力数值,以指导结构设计和施工。     

Numerical investigations on the mechanical properties of metallic hollow spheres structure with perforations under compression

This paper numerically investigates the compressive mechanical properties of the perforated hollow spheres structures with different geometrical and physical properties. In these structures, the metallic hollow spheres are perforated regularly with several holes, which open the inner sphere volume and surface and are bonded in simple cubic, body-centered cubic and face-centred cubic patterns. The 5×5 cells finite element models under uniaxial compression are established by ABAQUS 6.14 software for simulation. The influence of the spheres’ spatial pattern, as well as base materials for the spheres and bonding necks on the structural mechanical properties are evaluated. By changing the wall thickness, hole diameter and bonding radius in the body-centered cubic packing finite element model, the elastic modulus, Poisson's ratio and initial yield stress are calculated and discussed as functions of these geometrical parameters and their average densities.