Wide Range Of Relative Densities Research Articles

Stiffness, strength, anisotropy, and buckling of lattices derived from TPMS and Platonic and Archimedean solids

Lattice metamaterials have gained considerable attention due to their distinctive topological structures and multifunctional properties. In this work, the effect of topology, loading conditions, and relative density on the effective mechanical properties of various novel lattice architectures is investigated numerically and experimentally. Thirteen strut-based lattices derived from triply periodic minimal surfaces (five lattices) as well as Platonic (three lattices) and Archimedean (five lattices) solids are considered for the first time, and their anisotropic mechanical properties, including uniaxial, shear, and bulk moduli and strengths as well as their total stiffness, buckling strengths, Poisson’s ratio, and anisotropy are investigated as a function of a wide range of relative densities (0.1% to 37%). Finite element analysis is employed to capture the full effective behavior of these lattices using periodic boundary conditions. Bifurcation analysis is performed to predict the threshold relative density governing their buckling vs yielding deformation behavior. Selected lattice structures of various relative densities are 3D printed using polymer selective laser sintering additive manufacturing technique and tested under quasi-static uniaxial compression where the experimental and numerical results are compared. The numerical results indicate that the deformation behavior can be altered between stretching and bending dominated mode of deformation as function of loading. Archimedean lattices are shown to outperform a wide range of strut-based lattices. This work opens the doors for more investigations of the multifunctional properties of these novel types of lattices and their engineering applications. Furthermore, the generated comprehensive data are useful in optimizing latticed structures using topology optimization techniques.

Compression properties of cellular iron lattice structures used to mimic bone characteristics

Recently, cellular materials made by the repetition of unit cells, that is, iron lattices have become appealing to mimic the structure of bone. The aim of the study is to choose the most adequate lattice structures, which have the compressive mechanical properties closer to the ones of bone, in the perspective of their use as temporary implants. Five types of unit cells were selected, such as, cubic (C), truncated octahedron (TO), truncated cubic (TC), rhombicuboctahedron (RCO), and rhombitrucated cuboctahedron (RTCO). The mechanical properties were assessed by numerical simulations with a finite-element analysis. The size effect was studied with the comparison of results among samples with different numbers of unit cells. Simulations covered a wide range of relative densities. Graded dense-in and dense-out configurations were constructed with lattices of types RTCO and TO, being the unit cells, themselves graded. Lattice structures RTCO and TO were found to be stable at every relative density studied, while C, TC and RCO lattices are unstable at low densities. The evaluation of size effects was not conclusive, which could be biased by other factors. The Young's modulus of RTCO and TO lattices enable to reproduce the properties of both trabecular and cortical bone, with an appropriate choice of the relative density. To mimic trabecular bone, only RTCO and TO structures with low relative densities, can be used, while arrangements of C, TC and RCO cells can only replicate the properties of cortical bone. Graded cells may have the same properties as non-graded with lower density.

Novel Design Charts for Anisotropic Effective Elastic Properties of Pyramidal Lattice Materials

Novel design charts for predicting the anisotropic effective elastic properties of pyramidal lattices are proposed for a wide range of relative density and various struts shape through finite element (FE) simulations. Pyramidal lattices are 3D printed using digital light processing (DLP) and are subsequently subjected to uniaxial compression tests to provide a partial experimental validation for the presented design charts. Regarding strut shape, the presented results uncover that using hollow-tapered instead of solid-uniform struts leads significant improvements for effective Young's and shear moduli. In addition, this study has paved the way towards enhancing our understanding of how the anisotropy of pyramidal lattices can be tailored by tuning the relative density and strut architecture. Resorting to an analytical framework, results indicate that controlling the void volume fraction of struts can lead the same effective Young's modulus for all three principal directions of pyramidal lattices with low relative densities.

Finite element analysis on yield surface evolution of cellular materials

The yield surface is the boundary of elastic region in the theory of plasticity, therefore the area and the shape of the yield surface can represent the capability of cellular materials in the stress space. The yield point and the yield surface of one kind of 2D cellular materials, hexagonal honeycombs, is investigated in this study via the finite element analysis with a representative block approach. All components of requisites to computationally investigate yield surface evolution of 2D cellular materials are prepared. A proper determination of yield point for the honeycombs is proposed for the detection of initial and subsequent yield surfaces in the axial-shear stress space and the yield point determination is validated by the comparison between experimental result and finite element analysis. Taking into account a wide range of relative density for honeycombs, the mesh size as well as the pattern and the size of the representative block in finite element is investigated and selected based on the analysis of the mesh convergence analysis, the boundary effect, and the size effect. After probing paths and preloading paths are designed, the initial and subsequent yield surfaces of the honeycombs with different relative density are detected and the influence of relative density on the yield surface evolution is investigated. The investigation shows a shear preloading path followed by an axial preloading path strengthens the capability of honeycombs and the honeycomb with lower relative density may exhibit different behavior of yield surface evolution than those with higher relative density. Further, phenomena of cellular materials including the Bauschinger effect and the hardening behavior (isotropic, kinematic, rotation, distortional) are observed from the yield surface evolution of honeycombs.

Cone penetration tests in dry and saturated Ticino sand

It is commonly assumed that dry and saturated sands exhibit similar cone resistance–relative density relationships. Some studies pointed out that partial saturation and calcareous sands with considerable fines content are potential factors affecting these relationships. However, there is experimental evidence in Shaqour Bull Eng Geol Environ 66:59-70, (2006) that clean uncemented quartz sand may exhibit lower cone resistance in saturated conditions. The present study aims on contributing towards better understanding the effect of water saturation on cone resistance in sand. For this purpose, Ticino sand samples were prepared dry and saturated in a calibration chamber and cone penetration tests were performed over a wide range of relative densities and at two consolidation stresses. Overall, it was observed that dry and saturated samples exhibited similar cone resistances. Only slightly higher cone resistances were observed for dry samples at the lower consolidation stress. Two anomalous samples, which were tested dry at medium relative density, were found to exhibit way higher cone resistances than expected from published cone resistance–relative density relationships. The Young's modulus was observed to be proportional to cone resistance and independent of whether a sample was tested dry or saturated, being therefore considered as more robust soil property for cone resistance relationships.

Influence of soil density on performance of geocell-reinforced vertical anchor in sand

Influence of soil density on the performance of geocell-reinforced vertical plate anchors was studied through a series of model tests and numerical analyses. It is observed that the geocell-induced performance improvement is present over a wide range of relative density, varying from 30% (loose) to 95% (very dense). However, increase in load bearing capacity and stiffness of the anchor bed continues to increase with increase in density of the soil mass. Moreover, compared to the unreinforced case, the increase in anchor capacity due to increase in soil density tends to be greater with geocell reinforcement. This is attributed to the dilation-induced volume expansion that tends to mobilise enhanced resistance from the geocell reinforcement. In addition, the size of the rupture surface was found to increase with the increase in density of the fill soil, which indicates that, at higher density, a larger volume of soil mass has participated in sharing the anchor load, leading to the enhanced performance of the system. Numerical analysis using the computer program Fast Lagrangian Analysis of Continua was carried out. The computed results were found to be in good agreement with the observed ones.

Additively-manufactured anisotropic and isotropic 3D plate-lattice materials for enhanced mechanical performance: Simulations & experiments

Plate-lattices are an emerging category of mechanical metamaterials with exceptional mechanical performance. In this paper, a family of half-open-cell plate-lattices is innovated with exceptional mechanical properties and additive manufacturability. The elastoplastic properties and large strain response of the novel plate-lattices are investigated both numerically and experimentally. Design maps for tailoring the anisotropic index reveal that elastically isotropic plate-lattices can be obtained for a wide range of relative densities. Numerical results reveal that the isotropic plate-lattices exhibit significantly higher elastic properties than other competing topologies such as conventional truss-lattices and isotropic smooth shell-lattices, and their bulk modulus can attain the Hashin-Shtrikman upper bound for all relative densities. Large strain simulations demonstrate the remarkable energy absorption capacity of the novel plate-lattices. The numerical findings are confirmed through the compression experiments on the anisotropic and isotropic stainless steel 316 L specimens manufactured by selective laser melting. This work proposes a novel type of plate-lattices with both exceptional mechanical performance and good additive manufacturability, which opens a new channel for the design of lightweight mechanical metamaterials.

Developing a homogenization approach for estimation of in-plan effective elastic moduli of hexagonal honeycombs

In this research, a computational technique is developed for determining effective in-plane properties of hexagonal core honeycombs utilizing homogenization multi-scale technique based on averaging theorems. Purposely associated with engineering constants, specialized unit cells under appropriate boundary conditions are elaborated for two well-known configurations of uniform cell wall thickness and doubled thickness vertical cell walls hexagonal honeycombs. Constant boundary element method (CBEM) are employed for discretizing the boundary integral form of equivalent stress and strain equations and avoiding dependency to the mesh density and elements type selection challenges at cell walls intersection. Comparing with available experimental data for uniform cell wall thickness hexagonal honeycombs, the proposed method validated for a wide range of relative densities. Then comparing with well-defined existing analytical methods which have been previously validated experimentally, the verification of proposed method is done for uniform cell wall thickness and double thickness vertical cell walls. The results show that the proposed methods can present a well approximation of in-plane engineering constants for relative densities lower than 0.3 and also can be applied to higher relative densities by defining proper unit cells where available analytical methods encounter with significant inability.

Re-entrant auxetic lattices with enhanced stiffness: A numerical study

Traditional auxetic lattices are featured with negative Poisson's ratio but weak stiffness. In this work, a set of auxetic lattices with enhanced stiffness are proposed by adding a strengthening rib into conventional auxetic unit cells in a direction perpendicular to the re-entrant direction. The effective mechanical properties of these variants are calculated using the fast Fourier transform-based homogenization method, which show that their Young's modulus in 2D can be improved by approximately 200% along the strengthening direction without significant sacrifice of auxetic property. However, such an enhancement is weakened in 3D as the variant of a tetrahedral cell has an approximate 100% improvement of Young's modulus only at low relative density. Though the stiffness of a variant hexahedral cell can be doubled in 3D at a wide range of relative density, its Poisson's ratio remains negative only in a narrow range of relative density. The findings in this work will offer new opportunities for the applications of auxetic materials which not only need negative Poisson's ratio but also high stiffness.

Three dimensional modelling of closed-cell aluminium foams with predictive macroscopic behaviour

This study presents an efficient approach to generate a realistic micromechanical model for closed-cell foams using irregular Voronoi models. Starting with a reference microstructure consisting of regular Kelvin cells, the nucleating points underlying each reference unit cell is subjected to a random displacement, the magnitude of which depends on the pore size and a misalignment parameter. For convenience, the misalignment parameter is calibrated from available statistical data on unit cell geometries for the commercially available closed-cell aluminium foam, and a common value is utilised for all cases considered. Numerical analyses with the irregular 3D micromechanical models are done using ABAQUS/Explicit. Considering both uniaxial and hydrostatic compressive loading cases, the numerical responses compare well with the experimental data in literature, over a wide range of relative densities. The deformation mechanism is next elaborated. In uniaxial compression, the deformation initiates at the weaker regions induced by the geometrical irregularities, before evolving into a localized deformation band through the coalescence between neighbouring regions of local weakness. This localized deformation band forms an irregular 3D relief in space, a phenomenon which cannot be captured by regular periodic microstructures. In hydrostatic compression, the irregular geometry also induces deformation through cell wall bending. In tension, a stretching mode induces a shift in the yield surface towards the positive mean stress quadrant, which is consistent with experimental observations. The proposed approach thus generates the irregular 3D microstructures efficiently through a single calibrated misalignment parameter, leading to realistic deformation mechanisms, with good predictions on the macroscopic behaviour, over a wide range of relative densities and different loading conditions.

Effective property evaluation and analysis of three-dimensional periodic lattices and composites through Bloch-wave homogenization.

Periodic lattices offer enhanced mechanical and dynamic properties per unit mass, and the ability to engineer the material response by optimizing the unit cell. Characterizing the effective properties of these lattice materials through experiments can be a time consuming and costly process, so analytical and numerical methods are crucial. Specifically, the Bloch-wave homogenization approach allows one to characterize the effective static properties of the lattice while simultaneously analyzing wave propagation properties such as band gaps, propagating modes, and wave directionality. While this analysis has been used for some time, a thorough study of this approach on three-dimensional (3D) lattice materials with different symmetries and geometries is presented here. Bloch-wave homogenization is applied to extract the effective stiffness tensor of 3D periodic lattices and confirmed with elastostatic homogenization, both within a finite element framework. Multiple periodic lattices with cubic, transversely isotropic, and tetragonal symmetry, including an auxetic geometry, over a wide range of relative densities are analyzed. Further, this approach is used to analyze 3D periodic composite structures, and a way to tailor their overall anisotropy is demonstrated. This work can serve as the basis for nondestructive evaluation of metamaterials properties using ultrasonic velocity measurements.

The mechanical response of cellular materials with spinodal topologies

The mechanical response of cellular materials with spinodal topologies is numerically and experimentally investigated. Spinodal microstructures are generated by the numerical solution of the Cahn-Hilliard equation. Two different topologies are investigated: ‘solid models,’ where one of the two phases is modeled as a solid material and the remaining volume is void space; and ‘shell models,’ where the interface between the two phases is assumed to be a solid shell, with the rest of the volume modeled as void space. In both cases, a wide range of relative densities and spinodal characteristic feature sizes are investigated. The topology and morphology of all the numerically generated models are carefully characterized to extract key geometrical features and ensure that the distribution of curvatures and the aging law are consistent with the physics of spinodal decomposition. Finite element meshes are generated for each model, and the uniaxial compressive stiffness and strength are extracted. We show that while solid spinodal models in the density range of 30–70% are relatively inefficient (i.e., their strength and stiffness exhibit a high-power scaling with relative density), shell spinodal models in the density range of 0.01–1% are exceptionally stiff and strong. Spinodal shell materials are also shown to be remarkably imperfection insensitive. These findings are verified experimentally by in-situ uniaxial compression of polymeric samples printed at the microscale by Direct Laser Writing (DLW). At low relative densities, the strength and stiffness of shell spinodal models outperform those of most lattice materials and approach theoretical bounds for isotropic cellular materials. Most importantly, these materials can be produced by self-assembly techniques over a range of length scales, providing unique scalability.

Compressive Properties and Energy Absorption of Aluminum Foams with a Wide Range of Relative Densities

Quasi-static uniaxial compressive experiments were conducted on aluminum foams with a wide range of relative densities (0.134-0.472). The compressive properties and energy absorption capacity were systematically characterized and compared in a more suitable way. The compressive stress instead of compressive strain achieved during energy absorption process was taken into consideration. The results show that aluminum foam is not a kind of energy absorption materials with a stationary plateau region at the plastic deformation stage. There exists a strain hardening phenomenon which makes the stress–strain curve incline at this stage. For every aluminum foam with certain relative density, there exists an optimal stress. Under its optimal stress condition, the foam can absorb the maximum energy compared to foams with whatever different relative densities. The optimal stress and corresponding maximum energy absorption capacity increase with the increase in the foam’s relative density.

Structure and Behavior of Gasless Combustion Waves in Powders

ABSTRACTThe method of simulation of the structure of powder mixture, which allows calculating the samples with a relative density from 15% up to practically close packing, is described. The 3D model of discrete combustion wave in powder mixture, which uses the actual structure of the sample, is considered. The parametric investigations of combustion of powder mixture in the wide range of relative density and particle ignition temperature are carried out. The model predicts the steady-state combustion, oscillating combustion, and extinction depending on the parameters of powder mixture. The results of the simulation are compared with experimental data.

Two-equation method for heat transfer efficiency in metal honeycombs: An analytical solution

An analytical model based on the two-equation method is proposed in this study to evaluate the heat transfer performance in sandwiched metal honeycomb heat exchangers under forced convection conditions. The local thermal non-equilibrium between a cooling fluid and solid honeycombs is considered. The validity and the accuracy of the analytical results are verified by numerical simulation. Compared with the convectional corrugated wall, effective medium, and transfer matrix models, the present analytical predictions are closer to the finite element simulation results in a wide range of relative density. According to the analytical solutions, the effects of cell wall length, relative thickness of the heat exchanger, fluid-to-solid thermal conductivity ratio on flow characteristics, and heat transfer performance are subsequently examined to obtain the optimum design for compact heat exchangers that require high heat transfer performance. Results show the mutual influence between cell wall length and relative thickness. The use of a metal honeycomb in compact heat exchangers can significantly enhance heat transfer with a low pressure drop.

3D metallic glass cellular structures

3D Metallic glass structures (3DMGs) are fabricated through thermoplastic forming (TPF)-based patterning of MG sheets combined with a parallel joining technique. To demonstrate this capability and benchmark 3DMGs, we have fabricated honeycomb-like MG architectures covering a wide range of relative densities. 3DMGs exhibit high elasticity of up to 40% loading strain, high elastic energy storability, and high energy absorption which is superior compared to those made from other materials such as conventional metals and ceramics, based on our theoretical analysis. The combination of MG properties and introduced versatile fabrication method suggest the possibility of developing a wide range of 3DMGs with excellent performance for specific applications.

Effects of graphene concentration, relative density and cellular morphology on the thermal conductivity of polycarbonate–graphene nanocomposite foams

The thermal conductivity of polycarbonate–graphene nanocomposite foams was studied as a function of relative density, developed cellular structure and graphene concentration. Two types of supercritical CO2 foaming processes were employed to obtain foams with a wide range of relative densities and cellular morphologies. The thermal conductivity of unfoamed nanocomposites increased in more than two times upon addition of 5wt% graphene. Foaming led to lowered thermal conductivity values, as low as 0.03W/(mK), with thermal conductivity being mainly controlled by relative density and in a lower extent by graphene concentration. Higher thermal conductivities were obtained with increasing relative density and cell size, as well as with increasing graphene concentration, especially in those cases where improved graphene dispersion was achieved with foaming. Thermal conductivity values displayed a better fit when using a three-phase model when compared to the two-phase model previously proposed for polymer composite foams.

Optimization and Parametrical Investigation to Assess the Reconstitution of Different Types of Indian Sand Using Portable Travelling Pluviator

By using the air pluviation technique, it is aimed to achieve the desired relative density with uniform void ratio throughout the specimen in order to maintain the homogeneity and to avoid the spatial variability. Further, in order to achieve the maximum deposition intensity, a systematic optimization study has been carried out rigorously in a test tank to determine the diameter of the orifice to be employed for the sieve plates of different porosity and the number of sieve plates to be installed in the diffuser sieve sets. The study has been conducted with four different patterns of sieves with different porosity to achieve a wide range of relative densities for four different uniformly graded Indian sands. The dynamic penetrometer which is considered to be one of the cost effective instruments has been efficiently used to determine the soil resistance at various locations of the test tank for every given height of fall in order to check the uniformity of placement density throughout the sand bed. The study reveals that the sand beds of different relative densities could be achieved using different patterns of diffuser sieves at optimum sand flow rate without compromising the uniformity. The effect of height of fall as well as porosity of diffuser sieves on the relative density of different sands has been studied in detail. The deposition intensity and the relative density obtained from the present study are compared with the values available in the literature.

Effective elastic properties of periodic hexagonal honeycombs

We investigate the elastic behavior of periodic hexagonal honeycombs over a wide range of relative densities and cell geometries, using both analytical and numerical approaches. Previous modeling approaches are reviewed and their limitations identified. More accurate estimates of all nine elastic constants are obtained by modifying the analysis of Gibson and Ashby (1997) to account for the nodes at the intersection of the vertical and inclined members. The effect of the nodes becomes significant at high relative densities. We then compare the new analytical equations with previous analytical models, with a numerical analysis based on a computational homogenization technique and with data for rubber honeycombs over a wide range of relative densities and cell geometries. The comparisons show that both the new analytical equations and numerical solutions give a remarkably good description of the data. The results provide new insights into understanding the mechanics of honeycombs and designing new cellular materials in the future.

An evaluation of the interface behaviour of rail subballast stabilised with geogrids and geomembranes

In a rail track, the compacted granular medium (subballast) placed underneath the ballast influences track resiliency, and controls the load propagation to the softer subgrade (e.g. clay). A series of large-scale direct shear tests were carried out to investigate the interface shear strength of subballast stabilised with geogrids and geomembranes, respectively. In this study, the beneficial effects of these two different types of geosynthetics on the stress-strain behaviour of unreinforced and reinforced subballast were examined. The influences of normal stress (σn), relative density (DR), and the shearing displacement rate (SR) were studied. The results showed that the shear strength of the subballast–geogrid interface was significantly higher than that of the subballast–geomembrane interface. These results also showed that the reinforced subballast with a higher density provided enhanced performance over a wide range of relative densities. The results also indicated that the shear strength was significantly affected by the shearing rate.