Random Foams Research Articles

Effect of pore size polydispersity on the acoustic properties of high-porosity solid foams

This study investigates the influence of pore size polydispersity on the acoustic behavior of high-porosity solid foams using numerical simulations. The effect of the size of the periodic unit cell (PUC) on the transport parameters is first examined. It is found that the size of the PUC required for properly estimating the acoustic properties of random foams depends on both the analyzed transport parameter(s) and level of polydispersity. Assuming identical and constant aperture ratio of membranes, the results indicate that (i) the viscous permeability is a reliable indicator regarding the size of the PUC (a more constraining property than the other transport parameters), and (ii) high-polydispersity foams require a larger number of pores in the PUC to achieve convergence with respect to morphological characteristics and acoustic properties. The influence of polydispersity on dimensionless transport parameters is then analyzed. It is found that polydispersity has a negligible effect on the high-frequency tortuosity but induces substantial variations in the remaining macroscopic parameters. Simulations further show that the ratio of the dimensionless transport parameters does not depend on membrane aperture ratio. This important result allows us to propose a fast method to estimate the acoustic properties of a random foam from the transport parameters of monodisperse foams with different pore sizes, for each studied transport parameter. The proposed method is finally employed to characterize the pore size and polydispersity in two real foams (with and without membranes), solving an inverse problem.

On the mechanical properties of dual-scale microlattice of starfish ossicles: A computational study

While engineering cellular solids, either stochastic foams or architected lattices, are usually made of polycrystalline or amorphous materials, echinoderms (e.g., sea urchins, starfish, and brittle stars) build their microporous skeletal elements with single-crystalline calcite. This class of biomineralized cellular solid, known as stereom, also exhibits a vast diversity in pore morphology, ranging from random open-cell foams to fully periodic lattices. In particular, the skeletal elements (also known as ossicles) of some starfish species are composed of a diamond-triply periodic minimal surface (diamond-TPMS) microlattice. In addition, the crystallographic symmetries at both atomic (calcite) and lattice (diamond-TPMS) levels are precisely aligned. Here we investigate the mechanical performance of this unique dual-scale microlattice and discuss the synergistic effects of atomic- and lattice-scale crystallographic coalignment. Our computational and theoretical analysis suggests that the mechanical isotropy of ossicles is enhanced due to the property compensation between the atomic-level and lattice-level architectures. Moreover, the observed 50 vol% relative density in the diamond-TPMS microlattice of ossicles may be a result of achieving overall mechanical isotropy, minimal surface curvature, and maximized surface area. We believe the methodology introduced here will be useful for understanding the mechanical behavior of natural crystalline cellular solids such as echinoderms’ stereom and designing dual-scale lattice materials.

Analysis of thermal storage behavior of composite phase change materials embedded with gradient-designed TPMS thermal conductivity enhancers: A numerical and experimental study

Phase change materials (PCMs) exhibit considerable potential for utilization in energy storage and temperature regulation applications, primarily attributed to their notable latent heat capacity. Nevertheless, the intrinsically limited thermal conductivity of PCMs necessitates the use of thermal conductivity enhancers (TCEs) that possess adjustable features to compensate for greater heat storage efficiency. Porous structures with flexible design freedom have garnered growing interest in contrast to traditional random foams, owing to their significantly larger surface areas and fully interconnected pore networks. This study fabricated three polar form-designed triply periodic minimal surfaces (TPMS) porous structures using selective laser melting (SLM) based on various radial density gradients, namely the uniform density, the linear gradient, and the Boltzmann gradient. The TPMS porous structures were incorporated as TCEs within a paraffin matrix to form composite TPMS-PCMs. The melting behavior of composite TPMS-PCMs during the charging process was investigated by employing both visual experiments and numerical methods. A thorough analysis was undertaken regarding the progression of solid-liquid phase interfaces, temperature distribution, convection distribution, and heat storage rate to elucidate the mechanisms that contribute to enhanced heat transfer. The findings indicate that the configuration of the density gradient has a notable impact on the melting behavior of composite TPMS-PCMs by tuning heat transfer paths. The heat storage rate of the linear gradient case is the highest among the three, reaching 12.1 W, 1.6 times that of the uniform density case, and twice that of the Boltzmann gradient case. Although the Boltzmann gradient case has the lowest heat storage rate, it demonstrates exceptional performance in terms of temperature uniformity. The average temperature gradient along the radius during melting is 348.6 °C/m, which is only 59% observed in the linear gradient case and 56% in the uniform density case. These findings substantiate the effectiveness of the radial gradient density design in the control of the thermal storage process of composite TPMS-PCMs. They serve as a reference for optimizing thermal storage and temperature control systems that rely on latent heat storage in the future.

Random Foam Meso-Model and Mechanical Properties of Foam Concrete

Random Foam Meso-Model and Mechanical Properties of Foam Concrete

Modeling Mesoporous 3D-Printed Lattice Electrodes for Energy Storage

3D printing could offer the versatility to design and manufacture energy storage devices on demand. The precision and material flexibility of 3D printing is ideal for integrating porous electrodes that can enhance electrochemical performance[1]. This work analyzes the electrical conductivity of 3D-printed mesoscale strut lattices at the 100 μm – 1 mm scale with 40 – 90 % volumetric porosity to develop optimal electrodes for energy storage devices. We use a graph-theory-based model[2] to compute the conductivity of multiple 3D lattice types with either solid conducting struts or struts coated with conductive material. These structures show 3 – 5X higher conductivity than random conductive foams that lack an internal periodic mesostructure[3]. Using microstereolithography, we 3D print samples with high-resolution struts (< 70 µm) that maintain their shape and achieve high conductivity after carbonization at 700 ˚C. By tuning the lattice architecture, we manipulate the tradeoff between conductivity, weight, and porosity, validating our simulations with experimental measurements. These results demonstrate that that body-centered cubic (BCC) strut lattices have optimal conductivity per weight compared with other lattice types. Implementing these 3D-printed conductive lattices as supercapacitor electrodes, we see that the lattice architecture impacts the gravimetric capacitance of the devices as well as the mechanical strength, with octet structures outperforming both cubic and BCC lattices. Electrochemical impedance spectroscopy (EIS) shows that 3D-printed electrodes with higher porosity exhibit higher gravimetric double layer capacitance and lower charge transfer resistance, making them ideal candidates for use in supercapacitor electrodes as free-standing 3D hosts for active materials. CV characterization of the electrodes also illustrates how our graph theory-based model for 3D lattices can predict the optimal structure for energy storage. This model can also serve to predict electrode performance and tailor design for integration of higher surface area nanoporous materials on these conductive 3D printed scaffolds. This allows us to guide the design of 3D printed electrodes to minimize charge transfer resistance and achieve an optimal balance between gravimetric and volumetric energy density for device applications.[1] J. Zhao, Y. Zhang, X. Zhao, R. Wang, J. Xie, C. Yang, J. Wang, Q. Zhang, L. Li, C. Lu, Y. Yao, Advanced Functional Materials 2019, 29, 1900809.[2] J. E. Huddy, M. S. Rahman, A. B. Hamlin, Y. Ye, W. J. Scheideler, Cell Reports Physical Science 2022, 3, 100786.[3] F. G. Cuevas, J. M. Montes, J. Cintas, P. Urban, J Porous Mater 2008, 16, 675. Figure showing (a) designed octet (blue), cubic (orange), and BCC (red) lattice types as well as (b) SEM images of their experimental 3D-printed counterparts and (c) measured electrical resistance. Figure 1

Graph Theory Design of 3D Printed Conductive Lattice Electrodes

Abstract3D printing has the promising capability to fabricate engineered lattice structures with broadly tunable surface area and optimal geometries for maximizing structural and functional properties. This study characterizes the electrical conductivity of 3D lattices of varying size, structure, and porosity to guide additively manufactured electrode design in energy storage devices. Graph theory‐based calculations and experiments comparing the conductivity of multiple strut lattice structures and illustrating the scaling laws governing architectures with either coated or solid conductive struts are presented. The lightweight lattices explored here show higher conductivity than random foams that lack a periodic mesostructure. It is experimentally demonstrated that the 3D lattice type influences the specific capacity when employed in supercapacitors, outperforming 2D supercapacitor counterparts, and other 3D printed electrodes while allowing for optimization of the design for different energy storage applications. Additionally, it is shown that tuning the physical structure of the lattices allows for precise control over the electrical response to mechanical loading, as confirmed through experimental measurements. The lattice structure programs the electrodes’ mechanical stiffness, with higher relative density samples showing higher Young's modulus. These results can serve to guide the design of 3D printed electrodes in a variety of electrochemical and electromechanical device applications.

Utilizing ANN for Predicting the Cauchy Stress and Lateral Stretch of Random Elastomeric Foams under Uniaxial Loading.

As a result of their cell structures, elastomeric foams exhibit high compressibility and are frequently used as buffer cushions in energy absorption. Foam pads between two surfaces typically withstand uniaxial loads. In this paper, we considered the effects of porosity and cell size on the mechanical behavior of random elastomeric foams, and proposed a constitutive model based on an artificial neural network (ANN). Uniform cell size distribution was used to represent monodisperse foam. The constitutive relationship between Cauchy stress and the four input variables of axial stretch λU, lateral stretch λL, porosity φ, and cell size θ was given by con-ANN. The mechanical responses of 500 different foam structures (20% < φ < 60%, 0.1 mm < θ < 0.5 mm) under compression and tension loads (0.4 < λU < 3) were simulated, and a dataset containing 100,000 samples was constructed. We also introduced a pre-ANN to predict lateral stretch to address the issue of missing lateral strain data in practical applications. By combining physical experience, we chose appropriate input forms and activation functions to improve ANN's extrapolation capability. The results showed that pre-ANN and con-ANN could provide reasonable predictions for λU outside the dataset. We can obtain accurate lateral stretch and axial stress predictions from two ANNs. The porosity affects the stress and λL, while the cell size only affects the stress during foam compression.

Review of modern ceramic cellular materials and composites used in heat engineering

THE PURPOSE. Cellular ceramic materials and composites have found application in many industries: energy, chemical industry, construction, aerospace. Due to their high thermomechanical properties, resistance to high temperatures and low density, cellular ceramic materials are widely used as heat exchangers for heat recovery from exhaust gases of gas turbine engines, combined-cycle plants, industrial furnaces, etc. The purpose of this work is to review modern cellular ceramic materials and composites used in heat engineering and having different structure, properties and chemical composition.METHODS. We have carried out a broad review of the literature on ceramic cellular materials and composites. We studied both domestic and foreign literature.RESULTS. The analysis of cellular ceramic materials with a regular (lattices) and random (foam) structure has been carried out. The main factors influencing the properties of ceramic foams and lattices are analyzed. Also, the main methods for the production of ceramic materials were studied, their advantages and disadvantages were revealed. A review of modern composite materials based on a ceramic matrix reinforced with carbon nanotubes, graphene nanoplates, and carbon fibers has been carried out.CONCLUSION. The properties of ceramic cellular materials, as well as their areas of application, depend on the production methods and the structure of the material. Open-cell foams are used as filters, heat exchangers, while closed-cell foams are used as thermal insulation. Applications for ceramic lattices are limited by the precision, resolution, and size of 3D printing. Thus, the improvement of additive manufacturing technologies will improve the characteristics of ceramic gratings and expand their areas of application.

A note on the modelling of foams using Voronoi technique

Previous researchers have used Voronoi honeycombs to represent and predict the responses of random foams. Often, a two-dimensional Voronoi honeycomb model is used and the results are regarded as being identical to those of actual foams, which are in fact three-dimensional. The present study focuses on possible performance difference and the intrinsic relationship between Voronoi honeycombs and foams. Geometrical models of Voronoi honeycombs and foams with different cell irregularities are generated. Their relative densities are first calculated and compared. Based on the geometric models and an idealised elastic perfectly plastic property for the parent material, finite element (FE) analysis is carried out, respectively, for the block of the cellular material under quasi-static compression between two rigid platens. Consequently, stress–strain relationships are obtained, and it is shown that a two-dimensional Voronoi model cannot always be adopted to represent a three-dimensional foam in studying the behaviour of cellular solids.

Numerical analysis of compressive deformation for random closed-cell Al foam model

Most cellular solids presented random structure, while practically periodic models were often used in structure-property relations and numerical models. The finite element method was used to create a 2D random model that replicated the deformation characteristics of cellular models. The influences of porosity and strain rate on the deformation characteristic, energy dissipation mechanisms were investigated. The Poisson’s ratio evolution during compression was also studied. The simulated load-displacement curves were found to be consistent with experimental results, both containing elastic stage, plateau stage, hardening stage and densification stage. The yield load and plateau load were insensitive to the strain rate. In addition, it was also found that the generation and propagation of multiple random shear bands were responsible for the load-displacement characteristic. At the cell/membrane level, four failure modes and corresponding energy dissipation mechanisms were revealed. Moreover, the Poisson’s ratio decreased first and then increased with strain, which right manifested the compressibility of 2D foam in the initial stage and the densification in the end of compression. Meanwhile, the change of the Poisson’s ratio with porosity didn’t follow monotone function relation.

Elastic properties of Laguerre approximations of random foams

Stochastic models are valuable tools to study the mechanical behaviour of foams whose characteristic features include random cellular morphology and cells of different size (polydispersity). Random Laguerre tessellations, additively weighted generalisations of Voronoi tessellations, possess these features which makes them natural models for foams. This work studies how well a random foam can be represented by a Laguerre tessellation. For this means the Surface Evolver is used to simulate random, polydisperse soap froths which are subsequently reconstructed by Laguerre tessellations. By design, the resulting Laguerre approximations resemble the cellular morphology of the underlying froth. The Young’s modulus of low-density solid foams with open cells is then calculated for random, polydisperse foams based on Laguerre approximations and simulated soap froths. For the special case of monodisperse foams, we compare Laguerre approximated foams with the well known Kelvin and Weaire–Phelan foams.

Structure–property relations of three-dimensional nanoporous template-based graphene foams

Recently, much attention has been directed to 3D graphene structures due to their potential of retaining intrinsic 2D graphene properties, in combination with structural flexibility and tunable porosity. From a theoretical point of view, however, it is challenging to build 3D graphene foam structures that accurately represent experimental topological configurations. Here, we generate open-cell 3D graphene structures that closely reflect template-based manufacturing techniques and investigate their mechanical properties. We use all-atom molecular dynamics simulations to relate the overall stiffness, collapse stress and fracture properties to the underlying graphene microstructure represented by the graphene relative density, template relative density and number of graphene layers. We do so for four different template morphologies: gyroids, regular foam (BCC), random foam and nanoporous gold. The overall mechanical properties as a function of graphene relative density are analyzed in terms of power law relations to probe the microstructural deformation modes. Our results show that the open-cell 3D graphene structures feature bending as the dominant deformation mode, with regular graphene foams having the highest stiffness and strength and random foams the lowest. For gyroids we found that a higher template relative density leads to reduced mechanical properties but improved ductility. A similar trend was observed when the number of graphene layers was increased: enhanced ductility but at the expense of a reduced strength. Interestingly, we found that for low graphene density, the gyroids feature a strong self-stiffening response, leading to improvements in both strength as well as ductility. Our findings can be used as a guideline for the experimental design of innovate and lightweight graphene structures with strongly enhanced mechanical properties.

Numerical Analysis of Compressive Deformation for Random Closed-Cell Al Foam Model

Numerical Analysis of Compressive Deformation for Random Closed-Cell Al Foam Model

Experimental study of innovative periodic cellular structures as air volumetric absorbers

This work presents an experimental thermal evaluation of new and innovative porous morphologies suitable for volumetric solar receivers. Five new morphologies, four of them based on the repetition of single unit cells: diamond, rotated cube, tetrakaidecahedron, cube shifted, and a random morphology following the Voronoi tessellation technique were tested. In addition, for emerging geometries, two different cell size configurations were evaluated: one with constant cell size dimension and one with cell's size changing with flux direction. All the lattices were analysed experimentally in a lab-scale solar simulator. The results were compared with the ones of the already established and more conventional silicon carbide honeycomb and random foams proving that a gain in performance is achievable with the Voronoi morphology, both with constant cell size and increasing cell size pattern.

Quasi-periodic lattices: Pattern matters too

Two kinds of behaviour are commonly distinguished among porous architectured materials: stretching-dominated and bending-dominated ones. One or the other is favoured depending on the mechanical application. This property has been widely studied for random foams and periodic lattices, but has not yet been considered for quasi-periodic ones. Generally speaking, few studies have investigated their mechanical behaviour, and when this has been done, the impact of the elementary pattern shape has not been considered. In this paper we propose a classification of quasi-periodic structures depending on their dominance type by performing numerical simulations on mesoscopic models, and analysing the proportions of the strain energy stored in stretching and bending. As a result, three different dominance behaviours can be distinguished: completely stretching or bending dominated and varying dominance. Belonging to one or the other category depends mainly on the elementary pattern shape, and thus so does the overall mechanical behaviour.

Microscopic and macroscopic instabilities in elastomeric foams

The present work is a thorough study on the elastic instabilities of flexible polymeric foams under compression. Tessellation-based topologies are employed to generate micromechanical models of open-cell random foams with controlled morphologies. Solid distribution on the resulting topologies is assigned based on a closed-form expression for the relative density that accounts for material overlap at the nodes. Simulations of foams with different microstructures are used to first reproduce experimentally obtained results, and subsequently to elucidate the connection between microstructure and the corresponding buckling mode. Compression of an anisotropic foam along the rise and transverse directions displays two distinct buckling modes that have previously been reported experimentally: a long-wavelength instability corresponding to a limit-load type response, and a microscopic instability that produces a monotonically increasing nonlinear response. The presence of large cell size distributions, i.e. polydispersity, is shown to also lead to a monotonic response, which is associated with the increased compaction of the largest cells that are present within the domain. The agreement between experimental and numerical responses is very favorable. The critical stresses are subsequently calculated as a function of key microstructural characteristics including foam density, anisotropy, cell-size distributions and ligament uniformity. The results indicate that a strong amount of anisotropy is needed for the transition from a microscopic instability to the macroscopic one while polydisperse foams produce a stable monotonic response, even in the presence of cell anisotropy.

On the mechanical behaviour of additively manufactured metamaterials under dynamic conditions

High-energy absorption and light-weightiness are two critical properties for impact protection in the aerospace sector. In the past, the use of periodic honeycomb structures or random porous metallic foams were the preferred route to obtain a good specific-energy absorption performance. In recent years, the use of additive manufacturing has increased the design freedom creating a new generation of reticulated and porous materials: the metamaterials or lattice materials. The internal geometries of these lattice structures can be tuned for superior optimal properties, e.g., energyabsorption and density. However, the mechanics of these materials under impact need to be understood with the purpose of mechanical optimisation, and the computational models validated. In this work, we present the experimental compressive behaviour, at room temperature, of two Ti6Al4V lattice structures under static and dynamic conditions. The quasi-static tests were performed by using a universal testing machine while the dynamic tests were conducted at 480s-1 with a split-Hopkinson bar. In all cases, the deformation process was filmed to analyse the failure. Finally, finiteelement simulations were done, employing the Johnson-Cook model, to describe the response of the alloy. The simulations were able to reflect the failure characteristics of each metamaterial but were not able to describe the macroscopic response due to the differences between the experimental and computational volume fraction.

Crushing behavior and deformation mechanism of additively manufactured Voronoi-based random open-cell polymer foams

The macroscopic mechanical performances and the mesostructural deformation mechanisms of random open-cell polymer foams subjected to quasi-static loading were investigated. Three typical materials, namely, polyamide 6 (PA6), polyamide 12 (PA12), and polylactide (PLA), used in the additive manufacturing techniques, were considered as the base materials of open-cell polymer foams. Polymer foam specimens with predesigned mesostructural configurations and different relative densities were examined under quasi-static compression. The experimental results showed that the deformation modes and mechanical responses of the polymer foams exhibited a strong dependence on the properties of bulk materials and the fabrication process. It was found that elastic buckling dominated the failure of the PA12 and PA6 foams, whereas the failure of the PLA foams was dominated by strut collapse and the debonding of the relatively weak interlayers. The PA6 and PA12 foams, with low relative densities, could significantly recover from their compacted states, whereas the PLA foams were crushed without distinct rebounding. The elastic modulus, plateau stress, and specific energy absorption of the fabricated foams were quantified by using scaling laws as a function of the relative density. A revised statistical constitutive model was proposed for the random open-cell polymer foams under compression and it was confirmed that the revised model could accurately capture the whole crushing behavior of the foams.

Influence of boundary conditions on computation of the effective thermal conductivity of foams

Accurate numerical simulation of the effective thermal conductivity (ETC) of 3D pore-scale foam models requires a judicious choice of boundary conditions, as the computational domains are often smaller than the representative volume element, giving rise to considerable edge effects. Within the finite element homogenization framework, a set of mixed boundary conditions are considered alongside the usual uniform and periodic boundary conditions. Validity criteria and order relations, demonstrated from entropy-based principles, are numerically verified on unit cell-based geometries, random virtual periodic foams, and non-periodic tomography-reconstructed foams of equivalent microstructure. A statistical treatment based on the integral range provides confidence intervals for the estimated ETC. For foam samples with random homogeneous porosity, the mixed boundary conditions are shown to fulfill the macrohomogeneity condition and thus provide thermodynamically valid ETC estimates. For periodic foams with irregular microstructure, the ETC is very slightly underestimated under the mixed boundary conditions. For non-periodic geometries, it is shown that periodic boundary conditions–commonly viewed as the reference–underestimate the ETC due to boundary geometry mismatch, while the mixed boundary conditions give a more accurate and precise estimate.

Pressure Drop and Convective Heat Transfer in Different SiSiC Structures Fabricated by Indirect Additive Manufacturing

Abstract The microstructure of porous materials has a significant effect on their transport properties. Engineered cellular ceramics can be designed to exhibit properties at will, thanks to the advances in additive manufacturing. We investigated the heat and mass transport characteristics of SiSiC lattices produced by three-dimensional (3D) printing and replication, with three different morphologies: rotated cube (RC), Weaire–Phelan (WPh), and tetrakaidecahedron (TK) lattices, and a commercially available ceramic foam. The pressure gradients were measured experimentally for various velocities. The convective heat transfer coefficients were determined through a steady-state experimental technique in combination with numerical analysis. The numerical model was a volume-averaged model based on a local thermal nonequilibrium (LTNE) assumption of the two homogeneous phases. The results showed that for TK and WPh structures, undesirable manufacturing anomalies (specifically window clogging) led to unexpectedly higher pressure drops across the samples and increased thermal dispersion. Compared to the TK and WPh structures the manufactured RC lattice and the random foam had lower heat transfer rates but also lower pressure drops. These lower values for the RC lattice and foam are also a result of their lower specific surface areas.