Open-cell Foam Model Research Articles

A modified Lattice Boltzmann method for predicting the effective thermal conductivity of open-cell foam materials

The heat transfer in porous media have attracted wide attention in various scientific studies. The microstructure model of open-cell foam is reconstructed using the random generation method satisfying the microstructure stochastic properties. A modified Lattice Boltzmann method (LBM) is proposed to resolve the heat transport equations for predicting effective thermal conductivity (ETC). The proposed LBM simulation introduces the additional coefficient to moderate the difference in dimensionless relaxation time between solid and gas phase. The modified LBM simulation reliability is validated by comparing with numerical models and available experimental results. Simulations are conducted to evaluate the effects of a larger range of porosity, ambient pressure, temperature and intrusion mediums on heat transfer. The results indicate that the 400 K is considered as a turning point in the ETC dependence on temperature. At low porosity, the ETC fluctuates more sharply compared to high porosity. The impact of ambient pressure on the ETC is divided into three levels: P < 10 kPa, the ETC is almost insensitive to pressure fluctuation; 10 kPa < P < 100 kPa, the ETC slightly increases with the pressure increase; P > 100 kPa, the ETC significantly increases. The proposed LBM simulation combined with the random generation method is an efficient tool to predict the heat transfer for open-cell foam.

A Modified Lattice Boltzmann Method for Predicting the Effective Thermal Conductivity of Randomly Open-Cell Foam Materials

The heat transfer in porous media have attracted wide attention in various scientific studies. The microstructure model of open-cell foam is reconstructed using the random generation method satisfying the microstructure stochastic properties. A modified Lattice Boltzmann method (LBM) is proposed to resolve the heat transport equations for predicting effective thermal conductivity (ETC). The proposed LBM simulation introduces the additional coefficient to moderate the difference in dimensionless relaxation time between solid and gas phase. The modified LBM simulation reliability is validated by comparing with numerical models and available experimental results. Simulations are conducted to evaluate the effects of a larger range of porosity, ambient pressure, temperature and intrusion mediums on heat transfer. The results indicate that the 400K is considered as a turning point in the ETC dependence on temperature. At low porosity, the ETC fluctuates more sharply compared to high porosity. The impact of ambient pressure on the ETC is divided into three levels: P 100kPa, the ETC significantly increases. The proposed LBM simulation combined with the random generation method is an efficient tool to predict the heat transfer for open-cell foam.

Effect of surgical factors on the augmentation of cement-injectable cannulated pedicle screw fixation by a novel calcium phosphate-based nanocomposite.

Bone cement-augmented pedicle screw system demonstrates great efficacy in spinal disease treatments. However, the intrinsic drawbacks associated with clinically used polymethylmethacrylate (PMMA) cement demands for new bone cement formulations. On the basis of our previous studies, a novel injectable and biodegradable calcium phosphate-based nanocomposite (CPN) for the augmentation of pedicle screw fixation was systematically evaluated for its surgical feasibility and biomechanical performance by simulated and animal osteoporotic bone models, and the results were compared with those of clinical PMMA cement. ASTM-standard solid foam and open-cell foam models and decalcified sheep vertebra models were employed to evaluate the augmentation effects of CPN on bone tissue and on the cement-injected cannulated pedicle screws (CICPs) placed in osteoporotic bone. Surgical factors in CICPs application, such as injection force, tapping technique, screw diameter, and pedicle screw loosening scenarios, were studied in comparison with those in PMMA. When directly injected to the solid foam model, CPN revealed an identical augmentation effect to that of PMMA, as shown by the similar compressive strengths (0.73 ± 0.04 MPa for CPN group vs. 0.79 ± 0.02 MPa for PMMA group). The average injection force of CPN at approximately 40-50 N was higher than that of PMMA at approximately 20 N. Although both values are acceptable to surgeons, CPN revealed a more consistent injection force pattern than did PMMA. The dispersing and anti-pullout ability of CPN were not affected by the surgical factors of tapping technique and screw diameter. The axial pullout strength of CPN evaluated by the decalcified sheep vertebra model revealed a similar augmentation level as that of PMMA (1351.6 ± 324.2 N for CPN vs. 1459.7 ± 304.4 N for PMMA). The promising results of CPN clearly suggest its potential for replacing PMMA in CICPs augmentation application and the benefits of further study and development for clinical uses.

Elastic Wave Propagation in Open-Cell Foams

This work examines elastic wave propagation phenomena in open-cell foams with the use of the Bloch wave method and finite element analysis. Random foam topologies are generated with the Surface Evolver and subsequently meshed with Timoshenko beam elements, creating open-cell foam models. Convergence studies on band diagrams of different domain sizes indicate that a representative volume element (RVE) consists of at least 83 cells. Wave directionality and energy flow features are investigated by extracting phase and group velocity plots. Explicit dynamic simulations are performed on finite size domains of the considered foam structure to validate the RVE results. The effect of topological disorder is studied in detail, and excellent agreement is found between the wave behavior of the random foam and that of both the regular and perturbed Kelvin foams in the low-frequency regime. In higher modes and frequencies, however, as the wavelengths become smaller, disorder has a significant effect and the deviation between regular and random foam increases significantly.

THE RANDOM POROUS STRUCTURE AND MECHANICAL RESPONSE OF LIGHTWEIGHT ALUMINUM FOAMS

ABSTRACTLightweight porous foams have been of particular interest in recent years, since they have a very unique set of properties which can be significantly different from their solid parent materials. These properties arise from their random porous structure which is generated through specialized processing techniques. Their unique structure gives these materials interesting properties which allow them to be used in diverse applications. In particular, highly porous Al foams have been used in aircraft components and sound insulation; however due to the difficulty in processing and the random nature of the foams, they are not well understood and thus have not yet been utilized to their full potential. The objective of this study was to integrate experiments and simulations to determine whether a relationship exists between the relative density (porous density/bulk density) and the mechanical properties of open-cell Al foams. Compression experiments were performed using an Instron Universal Testing Machine (IUTM) on ERG Duocel open-cell Al foams with 5.8% relative density, with compressive loads ranging from 0-6 MPa. Foam models were generated using a combination of an open source code, Voro++, and MATLAB. A Finite Element Method (FEM)-based software, COMSOL Multiphysics 4.3, was used to simulate the mechanical behavior of Al foam structures under compressive loads ranging from 0-2 MPa. From these simulated structures, the maximum von Mises stress, volumetric strain, and other properties were calculated. These simulation results were compared against data from compression experiments. CES EduPack software, a materials design program, was also used to estimate the mechanical properties of open-cell foams for values not available experimentally, and for comparison purposes. This program allowed for accurate prediction of the mechanical properties for a given percent density foam, and also provided a baseline for the Al foam samples tested via the IUTM method. Predicted results from CES EduPack indicate that a 5.8% relative density foam will have a Young’s Modulus of 0.02-0.92 GPa while its compressive strength will be 0.34-3.37 MPa. Overall results revealed a relationship between pores per inch and selected mechanical properties of Al foams. The methods developed in this study can be used to efficiently generate open-cell foam models, and to combine experiments and simulations to calculate structure-property relationships and predict yielding and failure, which may help in the pursuit of simulation-based design of metallic foams. This study can help to improve the current methods of characterizing foams and porous materials, and enhance knowledge about theirproperties for novel applications.

Surface effects on the mechanical properties of nanoporous materials

In this paper, surface effects on the mechanical behaviour of nanoporous materials are investigated using the theory of surface elasticity and Timoshenko beam theory based on the tetrakaidecahedron (or Kelvin) open-cell foam model. Meanwhile, the influence of surface elasticity and residual surface stress on the mechanical properties of nanoporous materials is discussed. In addition, the results derived from the theory of Euler–Bernoulli beam model are also provided for comparison. Theoretical results show that the effective Young's modulus of the nanoporous materials increases as the diameter of the strut decreases, but in contrast Poisson's ratio and the brittle collapse strength decrease with the diameter of the strut. The contribution of shear deformation to surface effects on elastic properties is more significant, while the surface effects on brittle collapse strength are not sensitive to shear deformation, and it can even be neglected. As the strut size increases, the present results can be reduced to the cases without considering surface effects, which verifies the efficiency of the present model to a certain extent.

Simulating creep of snow based on microstructure and the anisotropic deformation of ice

It is generally agreed that the creep of low-density snow is accompanied by drastic microstructural changes, which are a major source of macroscopic strain hardening. There is, however, no agreement about the dominating mechanism which mediates structural mobility at the microscale. A widely used model of creeping snow allows for intercrystalline deformations at the grain boundaries but neglects intracrystalline deformations in the grains. Here we show that the opposite scenario, which solely uses intra-crystalline deformations, while neglecting grain boundary sliding, is in better agreement with experiments. To this end we have conducted in situ, microtomography measurements of snow microstructure during creep experiments. 3-D tomography images are used to simplify the full microstructure to a 3-D beam-network. This reduces the number of degrees of freedom drastically, which enables us to carry out creep simulations by finite-element methods. We use Glen’s law for secondary creep of ice as the material model and account for the anisotropic creep behaviour of single crystals by assigning individual network strands a random orientation of the c-axis. The results suggest a separation of time scales between creep stress relaxations and slow microstructural changes make the key contribution to snow hardening. Although open-cell foam models clearly fail in predicting the observed viscosity–density relations, they are interestingly suggested as a potential limiting behaviour in our experiments.

An inverted spherical model of an open-cell foam structure

An inverted open-cell foam model based on hexagonal close packing symmetry is proposed for open-cell foams with different configuration of struts. The novel model predicts the properties of the broad spectrum of open-cell ceramic and metallic structures. According to the proposed model, the specific surface and hydraulic permeability can be derived from experimentally measurable parameters such as porosity and cell diameter. The calculated parameters are in good correlation with the experimental data even without introducing additional empirical coefficients.

Heat transfer correlation for high-porosity open-cell foam

Heat transfer correlation has been developed, assuming a simple cubic model of open-cell foam. The cross-linked porous structure is equivalent to a bundle of independent, slender tubes with protrusions. It may be presumed that the projected struts either cause an increase in heat transfer coefficient or they act as extended surfaces or fins. The effect of these protruded filaments has been judiciously integrated within the empirical correlation for cross-convective flow over the bank of smooth tubes. An augmentation in foam heat transfer coefficient has occurred due to cross-connections in struts. An excellent agreement has been observed between the predicted correlations and the existing ones which have been established through experimental data.

Mechanical characterization of collagen–glycosaminoglycan scaffolds

Tissue engineering scaffolds are used extensively as three-dimensional analogs of the extracellular matrix (ECM). However, less attention has been paid to characterizing the scaffold microstructure and mechanical properties than to the processing and bioactivity of scaffolds. Collagen–glycosaminoglycan (CG) scaffolds have long been utilized as ECM analogs for the regeneration of skin and are currently being considered for the regeneration of nerve and conjunctiva. Recently a series of CG scaffolds with a uniform pore microstructure has been developed with a range of sizes of equiaxed pores. Experimental characterization and theoretical modeling techniques have previously been used to describe the pore microstructure, specific surface area, cell attachment and permeability of these variants. The results of tensile and compressive tests on these CG scaffolds and of bending tests on the individual struts that define the scaffold network are reported here. The CG scaffold variants exhibited stress–strain behavior characteristic of low-density, open-cell foams with distinct linear elastic, collapse plateau and densification regimes. Scaffolds with equiaxed pores were found to be mechanically isotropic. The independent effects of hydration level, pore size, crosslink density and relative density on the mechanical properties was determined. Independent control over scaffold stiffness and pore size was obtained. Good agreement was observed between experimental results of scaffold mechanical characterization and low-density, open-cell foam model predictions for uniform scaffolds. The characterized scaffold variants provide a standardized framework with defined extracellular environments (microstructure, mechanics) for in vitro studies of the mechanical interactions between cells and scaffolds as well as in vivo tissue engineering studies.

Elasticity of DLCA model gels with loops

Aggregation is a common natural phenomenon, but the structure–property relationship of the resulting porous, fractal gels is not well understood. An earlier study using the diffusion-limited cluster–cluster aggregation model revealed that loop structure is lacking in the model gels to account for their mechanical properties. The dangling bond deflection model was then developed to address loop formation during the aggregation process. This article describes the finite element method implemented to measure the various moduli of the resulting gel structure, which was modeled as a network of linearly elastic beams. The well-known empirical correlation in gels––the power–law scaling of Young's modulus with relative densities––was reproduced, and the scaling exponent of about 3.6, which is consistent with the experimental results, was captured in the analysis. About 70% of the total strain energy in the network came from bending of the beams. The contrast in the scaling exponent as compared to the open-cell foam model is attributed to the change of connectivity in the gel network when the density of the aggregate is adjusted.

Effects of processing history on the modulus of silica xerogel films

Sintered xerogel films (porous SiO2) show a higher elastic modulus than other amorphous low dielectric constant (K) materials available for the same value of K. By comparing xerogels that were sintered, templated or made with ethylene glycol or ethanol as solvents, we show that process history is at least as important as the chemistry of the solid matrix or the porosity. The modulus extrapolated to zero porosity for the porous sintered and templated films is the same as those of the dense films made by chemical vapor deposition of SiO2. This suggests that the solid matrix for sintered xerogel films is close to ideal and their modulus is better because of the ordered arrangement of pores and fusion of particles making up the matrix. The modulus measured by nanoindentation on thick xerogel films (&amp;gt;0.8 μm) is well explained by the open cell foam model.

Mechanical structure–property relationship of aerogels

The elastic moduli ( E) of high-porosity materials (such as aerogels) exhibit power-law scaling with their relative densities ( ρ), E∝ ρ m , where 3⩽ m⩽4, but the physics responsible for this behavior is not well-understood. Computer models of aerogels were generated by diffusion-limited cluster–cluster aggregation (DLCA) algorithms, and their linear elastic properties were examined by the finite element method (FEM), assuming that the stiffness of each interparticle bond can be represented by a beam element. The simulation yields m≈3.6 for perfectly connected structures, contradicting the consensus that the dangling mass on the gel gives rise to the exponent. The results suggest that the high exponent is largely because of the reduction in the connectivity of the material with decreasing density. The open-cell foam model, which predicts m=2, is valid only when the connectivity remains unchanged upon variation of the density. The mechanical structure–property relationship in the gel can be described by the `blob-and-link' model. The bonds (links) between the fractal clusters (blobs) are more sparsely distributed than those inside the clusters, and therefore the strain energy is localized at the cluster boundaries during deformation. This model is consistent with the experimental evidence.

The Role of Prestress and Architecture of the Cytoskeleton and Deformability of Cytoskeletal Filaments in Mechanics of Adherent Cells: a Quantitative Analysis

Mechanical properties of adherent cells were investigated using methods of engineering mechanics. The cytoskeleton (CSK) was modeled as a filamentous network and key mechanisms and corresponding molecular structures which determine cell elastic behavior were identified. Three models of the CSK were considered: open-cell foam networks, prestressed cable nets, and a tensegrity model as a special case of the latter. For each model, the modulus of elasticity (i.e. an index of resistance to small deformation) was given as a function of mechanical and geometrical properties of CSK filaments whose values were determined from the data in the literature. Quantitative predictions for the elastic modulus were compared with data obtained previously from mechanical tests on adherent cells. The open-cell foam model yielded the elastic modulus (103–104Pa) which was consistent with measurements which apply a large compressive stress to the cell. This suggests that bending of CSK filaments is the key mechanism for resisting large compression. The prestressed cable net and tensegrity model yielded much lower elastic moduli (101–102Pa) which were consistent with values determined from equilibrium measurements at low applied stress. This suggests that CSK prestress and architecture are the primary determinants of the cell elastic response. The tensegrity model revealed the possibility that buckling of microtubules of the CSK also contributed to cell elasticity.

Uniaxial strength asymmetry in cellular materials: An analytical model

The ability to predict failure of cellular materials depends on the knowledge of microstructural mechanisms that contribute to macroscopic behavior. In this paper, we develop microstructural models to examine the mechanisms responsible for differences in tensile and compressive strength observed in cellular materials. We limit our analyses to those materials that fail by the same mechanism (yielding or microcracking) in tension and compression. Using both a honeycomb and an open-cell foam model, we demonstrate that density-dependent, compression-strong strength asymmetry arises when two conditions are met: the cell wall material has a higher yield strength in compression than in tension, and the cell walls are loaded simultaneously by axial forces and bending moments. Our models predict that strength asymmetry (defined as the ratio of compressive to tensile yield strength of the cellular material) increases with relative density (as observed in real materials such as rigid polyurethane foams and trabecular bone), and that strength asymmetry is more pronounced in anisotropic materials (where oblique struts are more closely aligned with the direction of loading).

Analysis of the elastic properties of open-cell foams with tetrakaidecahedral cells

The elastic constants of an open-cell foam model, having tetrakaidecahedral cells on a BCC lattice, were found. The Young's modulus, shear modulus and Poisson's ratio were derived, as functions of the edge cross section and the foam density, by considering the bending, twisting and extension of the cell edges. If edge bending were the only mechanism the moduli would vary with the square of the foam density. The other deformation mechanisms are predicted to reduce the power law exponent by 3–5%, and the effect of edge torsion on the modulus level is small. The foam bulk modulus is predicted to vary linearly with its relative density, so Poisson's ratio approaches 0.5 at low densities. The lattice model is elastically isotropic, whereas other lattice models of foams are highly anisotropic.

On the Linear Elastic Properties of Regular and Random Open-Cell Foam Models

Foams can be created from coagulation of gas bubbles in liquid. After removal of cell faces, an open-cell foam remains consisting of a strut framework. In the past, mechanical properties were estimated by a small unit cell consisting of only a few struts. However, the random geometry of the foam can be of importance for the linear elastic properties. Here, large foam unit cells are created using Voronoi techniques. A smooth transition from regular to random geometries is made, showing the strong sensitivity of the mechanical properties from the geometry of the microstructure. Uniaxial global loads are transmitted through chains of highly loaded struts. The deformation of the struts in the foam is a mixture of bending and normal deformation, the ratio of which shown here to be dependent on the magnitude of the density.