Mechanical Properties Of Cellular Materials Research Articles

The Effects of Manufacturing Techniques on the Mechanical Performance of an Auxetic Structure Manufactured by Fused Filament Fabrication and Multijet Fusion Processes

Additive manufacturing is increasingly becoming potential for short‐run part production. The aim of this work is to explore the mechanical properties of a hybrid auxetic structure fabricated by multijet fusion (MJF) and fused filament fabrication (FFF). The experimental measurements indicate that robust specimens with high‐dimensional accuracy are successfully achieved using MJF process. In the case of the FFF process, the walls–walls and walls–cylinders areas (connecting areas) suffer large pores, indicating poor printing quality. The 3D printed specimens via FFF process reveal smooth plateau stress, while plateau stress with high peaks is observed when the MJF specimens are compressed along the Y‐axis. Moreover, specimens manufactured by the MJF process reveal the highest specific energy absorption (SEA) per unit volume and per unit mass. The calculated values of SEA are 2.1 and 2.5 J g−1 (for specimens fabricated by MJF) in which they significantly outperform the SEA (0.495 and 0.480 J g−1) of those manufactured by the FFF process. Furthermore, the trend of auxetic features (negative Poisson's ratio) has not been affected by the manufacturing processes. This study sheds light on the influence of fabrication methods on the mechanical properties of cellular materials especially their ability to absorb energy.

Mechanical and failure characteristics of novel tailorable architected metamaterials against crash impact

The mechanical properties of cellular materials cannot be on-demand tuned after manufacture, and the crashworthiness of existing tailorable metamaterials is often limited. To combine desirable and tailorable crashworthiness with ease of manufacture, novel tailorable architected metamaterials that can be flexibly assembled using discrete modules are proposed in this study. The specimens are manufactured by 3D printing method, and matched finite element analysis is conducted using ABAQUS. The proposed metamaterials achieve specific energy absorption and the maximum efficiency respectively 76.1% and 39.9% larger than the existing self-locked systems. Moreover, the metamaterials exhibit critical failure characteristics such as omnidirectional self-locking capability and imperfection insensitivity. Furthermore, 3D expansion capability allows them to adapt to complex protective requirements. Finally, impact experiments have been conducted on a complex-shaped metamaterial specimen made of thermoplastic polyurethane (TPU) to showcase all the aforementioned advantages. This research paves new avenues for designing high-performance and multifunctional protective structures.

Relationship between topological structures and mechanical properties of artificially architected SiC cellular ceramics: Experimental and numerical study

Due to their topological superiority, the architected materials facilitate the improvement of the physical and mechanical properties of cellular materials. With the progress of additive manufacturing technologies, the fabrication of architected silicon carbide (SiC) cellular ceramics has become achievable. This study focuses on the indirect additive manufacturing method of SiC cellular ceramics consisting of 3D printing, replication, and reaction-bonded sintering. To study the impact of the topology on the mechanical performance, three strut-based unit cell structures and stochastic foam with robust solid struts were experimentally and numerically studied. Results showed that the hexahedron structure has the highest compression strength, the tetrakaidecahedron structure has the highest flexural strength, while the regular structures have higher mechanical performance than the stochastic foam. The deformation mechanisms of the topologies under the compression load indicated that the hexahedron, tetrakaidecahedron, and stochastic foam favor the bending-dominated deformation mode, while the octet favors the stretching-dominated deformation mode.

Auxetic and failure characteristics of composite stacked origami cellular materials under compression

The mechanical properties of cellular materials made by stacking layers of origami sheets could be designed over a wide range due to its rich suite of geometry parameters. However, due to the nature of high-volume fraction of air in the structure, these materials may show low stiffness and low strength. Fiber reinforced composites show both higher specific strength and specific stiffness compared with homogeneous materials such as metals and plastics. It could be expected that both the stiffness and strength of stacked origami structures can be improved by introducing fiber reinforced composites. In this investigation, hot molding process is used to produce composite fiber reinforced stacked origami structures. Composite stacked origami structures with different stacking angles and thickness of origami sheets are designed and fabricated. Finite element simulation and experimental compression tests are carried out to investigate their mechanical properties and auxetic characteristics. The effects of origami sheets thickness and stacking angles on the in-plane and out-of-plane auxetic characteristics of the structure are discussed. Finally, the failure modes of the structures during compression are analyzed, and their energy absorption capacity are compared with other honeycomb materials.

Lightweight Optimization Design of Structures with Multiple Cellular Materials

Cellular materials have been widely applied to a lightweight design of structures. The mechanical properties of those materials depend on their microstructures at the microlevel/mesolevel, and the optimizaiton design of lightweight structures using multiple cellular materials is still challenging. This paper develops a topology optimization algorithm for a lightweight design of structures constructed by multiple cellular materials with specified microstructures. The mechanical properties of cellular materials are homogenized according to their microstructures and then integrated into topology optimization. The topology optimization problem is defined by minimizing structural compliance subject to a specified mass constraint. In order to identify the distribution of multiple cellular materials within the design domain, the multiple design variables are introduced based on the volume fractions of multiple cellular materials within each element. Meanwhile, the homogenized mechanical properties are linearly interpolated, and multiple floating projection constraints are imposed on the relaxed design variables to push them toward 0 or 1. Numerical examples demonstrate the successful implementation of the proposed algorithm by the optimal distribution and selection of multiple cellular materials.

Effect of microstructure on dynamic compressive behavior of cellular materials

It is known that the microstructure of cellular materials has a significant impact on their compressive properties. To study these phenomena, a hierarchical Poisson disk sampling algorithm and Voronoi partitioning were used to create a 3D numerical analysis model of cellular materials. In this study, we prepared random, periodic, and ellipsoidal cell models to investigate the effects of cell shape randomness and oblateness. Numerical experiments were performed using the finite element method solver RADIOSS. In the numerical analysis, an object collided with the cellular materials at a velocity of 25 m/s. The results showed that the flow stress of the random cell model was higher than that of the periodic cell model. Further, it was found that the aspect ratio of the cell shape has a significant impact on the mechanical properties of cellular materials.

On hybrid cellular materials based on triply periodic minimal surfaces with extreme mechanical properties

The physical and mechanical properties of cellular materials not only depend on the constituent materials but also on the microstructures. Here we show that, when the cellular materials are constructed by self-repeated representative volume elements, their effective elastic tensor can be obtained by a fast Fourier transform-based homogenization method. Numerical examples confirm that the bulk modulus of cellular material with the topology of triply periodic minimal surfaces such as Diamond, Gyroid, Neovius, and Schwarz P surfaces can approach to the upper Hashin-Shtrikman bound. However, the high values of their Young's modulus are obtained at the cost of low shear modulus and vice versa. Such conflicting behavior suggests that these two individual moduli may complement each other in a hybrid structure via combining different surfaces in cellular material. It is envisaged that our approach will enable the creation of ideal isotropic materials with large Young's modulus, shear modulus, and bulk modulus.

Analysis of mechanical properties of cellular materials obtained by selective laser melting

Analysis of mechanical properties of cellular materials obtained by selective laser melting

Structurally Controlled Cellular Architectures for High-Performance Ultra-Lightweight Materials.

The design and synthesis of cellular structured materials are of both scientific and technological importance since they can impart remarkably improved material properties such as low density, high mechanical strength, and adjustable surface functionality compared to their bulk counterparts. Although reducing the density of porous structures would generally result in reductions in mechanical properties, this challenge can be addressed by introducing a structural hierarchy and using mechanically reinforced constituent materials. Thus, precise control over several design factors in structuring, including the type of constituent, symmetry of architectures, and dimension of the unit cells, is extremely important for maximizing the targeted performance. The feasibility of lightweight materials for advanced applications is broadly explored due to recent advances in synthetic approaches for different types of cellular architectures. Here, an overview of the development of lightweight cellular materials according to the structural interconnectivity and randomness of the internal pores is provided. Starting from a fundamental study on how material density is associated with mechanical performance, the resulting structural and mechanical properties of cellular materials are investigated for potential applications such as energy/mass absorption and electrical and thermal management. Finally, current challenges and perspectives on high-performance ultra-lightweight materials potentially implementable by well-controlled cellular architectures are discussed.

Impact of the Lattice Angle on the Effective Properties of the Octet-Truss Lattice Structure

Cellular materials are found extensively in nature, such as wood, honeycomb, butterfly wings, and foam-like structures like trabecular bone and sponge. This class of materials proves to be structurally efficient by combining low weight with superior mechanical properties. Recent studies have shown that there are coupling relations between the mechanical properties of cellular materials and their relative density. Due to its favorable stretching‐dominated behavior, continuum models of the octet‐truss were developed to describe its effective mechanical properties. However, previous studies were only performed for the cubic symmetry case, where the lattice angle θ=45 deg. In this work, we study the impact of the lattice angle on the effective properties of the octet-truss: namely, the relative density, effective stiffness, and effective strength. The relative density formula is extended to account for different lattice angles up to a higher-order of approximation. Tensor transformations are utilized to obtain relations of the effective elastic and shear moduli, and Poisson's ratio at different lattice angles. Analytical formulas are developed to obtain the loading direction and value of the maximum and minimum specific elastic moduli at different lattice angles. In addition, tridimensional polar representations of the macroscopic strength of the octet‐truss are analyzed for different lattice angles. Finally, collapse surfaces for plastic yielding and elastic buckling are investigated for different loading combinations at different lattice angles. It has been found that lattice angles lower than 45 deg result in higher maximum values of specific effective elastic moduli, shear moduli, and strength.

Porous Materials with Tunable Structure and Mechanical Properties via Templated Layer-by-Layer Assembly.

The deposition of stiff and strong coatings onto porous templates offers a novel strategy for fabricating macroscale materials with controlled architectures at the micro- and nanoscale. Here, layer-by-layer assembly is utilized to fabricate nanocomposite-coated foams with highly customizable properties by depositing polymer-nanoclay coatings onto open-cell foam templates. The compressive mechanical behavior of these materials evolves in a predictable manner that is qualitatively captured by scaling laws for the mechanical properties of cellular materials. The observed and predicted properties span a remarkable range of density-stiffness space, extending from regions of very soft elastomer foams to very stiff, lightweight honeycomb and lattice materials.

Investigation of the Effect of Internal Pores Distribution on the Elastic Properties of Closed-Cell Aluminum Foam: A Comparison with Cancellous Bone

Closed-cell aluminum foams belong to the class of cellular solid materials, which have wide application in automotive and aerospace industries. Improving the mechanical properties and modifying the manufacturing process of such materials is always on demand. It has been shown that the mechanical properties of cellular materials are highly depending on geometrical arrangement, mechanical properties of solid constituents and the relative density of these materials. In this study, using a manufacturing process of foaming by expansion of a blowing agent, we prepared two types of closed-cell aluminum foams with isotropic distribution of cells along length and foams with gradient of pores along its length. We hypothesized that such variation of pores can induce microstructural directionality along the length of foam samples and improve their mechanical properties. For this aim, we studied the microstructural properties by micro-CT imaging and found their relation to macroscopic mechanical properties of foam samples by conducting monotonic compression tests. We compared these results with the one of the bovine femur trabecular bone as they show a dominant microstructural anisotropy due to alignment with the maximum strength direction in body. We also conducted numerical analyses and validated them for the elastic part based on our experimental work.Our results showed that gradient variation in porosity in closed-cell aluminum foams have a minor effect on their macroscopic mechanical properties. Although using such materials in sandwich panel structures, the strength of the material slightly increased. In addition, parameters of a power law model for the description of mechanical properties of foam sample and their relative density and properties of the solid compartment were characterized. The presented results are considered as a preliminary study for improvement of mechanical properties of closed-cell aluminum foams.

Understanding the foamability and mechanical properties of foamed polypropylene blends by using extensional rheology

ABSTRACTIn this article, the influence of the rheological behavior of miscible blends of a linear and a high melt strength, branched, polypropylene (HMS PP), on the cellular structure and mechanical properties of cellular materials, with a fixed relative density, has been investigated. The rheological properties of the PP melts were investigated in steady and oscillatory shear flow and in uniaxial elongation in order to calculate the strain hardening coefficient. While the linear PP does not exhibit strain hardening, the blends of the linear and the HMS PP show pronounced strain hardening, increasing with the concentration of HMS PP. Related to the cellular structure, in general, the amount of open cells, the cell size, and the width of the cell size distribution increase with the amount of linear PP in the blends. Also mechanical properties are conditioned by the extensional rheological behavior of PP blends. Cellular materials with the best mechanical properties are those that have been fabricated using large amounts of HMS PP. The results demonstrate the importance of the extensional rheological behavior of the base polymers for a better understanding and steering of the cellular structure and properties of the cellular materials. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 42430.

Superelastic cellular NiTi tube-based materials: Fabrication, experiments and modeling

The aim of this paper is to present an experimental and modeling study as the first step towards designing and optimizing architectured materials constituted of NiTi tubes. The idea is to combine the intrinsic and novel properties of nickel–titanium shape memory alloys with purposely engineered topologies. By joining thin-wall superelastic tubes via electrical resistance welding, we create regular cellular material demonstrators. The superelastic behavior of two simple architectured materials based on identical tubes, but with two topologies, are experimentally characterized and modeled using finite element approaches. The predicted behaviors are compared by simulating complex loading, exploring the influence of the constitutive material behavior on the effective mechanical properties of cellular materials. The parameters of the constitutive equations are identified on tensile tests performed on small dog-bone shaped specimens, machined from the tubes by spark cutting. The modeling results are finally compared with compression tests performed on these simple architectured NiTi materials. As a further validation of the proposed study, two large cell structures (square and hexagonal stacking) were modeled to gain greater insight into the role of different architectures.

Mechanical behaviour of hollow-tube stackings: Experimental characterization and modelling of the role of their constitutive material behaviour

Architectured cellular materials are very promising as lightweight aeronautical frames thanks to their superior specific mechanical properties such as structural or impact resistance. However, because of the processing routes and heat treatments used in the production process, the material within the cell walls may behave differently from the bulk, and therefore the in situ mechanical properties are often unknown. The present work aims at exploring the influence of the constitutive material behaviour on effective mechanical properties of cellular materials. To address this issue, small brazed sandwich structures with hollow-tube stacking cores have been considered as “model” materials. Compression tests have been performed on these structures, coupled with a detailed analysis of microstructures resulting from brazing heat treatments. Also, tensile tests on isolated tubes and microindentation tests have been conducted in order to have access to in situ constitutive mechanical properties. Experimental data have then been introduced in a finite-element modelling of those sandwich structures. Based on the modelling, different mechanical behaviours have been assumed for the constitutive material. Various degrees of modelling extension have been considered, introducing progressively a specific behaviour for brazes and accounting for the damage and cracks observed experimentally around braze extremities. Their influence on the effective behaviour of the stackings is discussed in detail.

Elastic behavior of multi-scale, open-cell foams

The mechanical properties of cellular materials are still subject to numerous theoretical and experimental investigations. In particular, the impact of cell size on the foam’s elastic response has not been studied systematically mainly due to the lack of experimental techniques with which the cell size and relative density of materials can be varied independently. This paper presents the results of a study of the elastic behavior of open-cell foams as a function of relative density and the size of the interconnected, spherical pores. First, the chemical procedure allowed us to produce polystyrene open-cell foams in which the relative density and the average cell diameters were varied independently. The results of compression tests performed on these foams showed an unexpected influence of the cell diameter (at constant relative density) on the elastic response. The analysis of the microstructure of the foam revealed the presence of a complex nanostructure in the edge of the cells that appeared during the synthesis procedure. An analytical model (an extension of the Gibson–Ashby model) is presented, which takes into account the complex multi-scale structure of the foam and accurately describes the observed dependence of the measured Young’s moduli on cell size. This approach was confirmed further by a finite element numerical simulation. We concluded that the observed dependence of elastic modulus on cell size was due to the heterogeneous nature of the material that constitutes the walls of the cells.

Numerical Simulation of Mechanical Properties of Cellular Materials Using Computed Tomography Analysis

The IUPAC study ‘‘Structure and Properties of Linear and Cross-Linked Structural Polyvinylchloride Foams’’ (IUPAC no. 2003-038-4-400) of the IUPAC Subcommittee ‘‘Structure and Properties of Commercial Polymers’’ elucidates the mechanical properties of Polyvinylchloride foams. In order to predict the mechanical properties of polymer foams several simplified models were developed which take into account the density and stiffness of the bulk material, but do not apply any morphological information. Previous results on Polyvinylchloride foams indicate that the cubic model of Gibson and Ashby is not suitable to predict their compressive modulus. In this article, we discuss several alternatives for the prediction of the mechanical properties. In particular, a novel approach is presented in order to transfer cell morphological data obtained by computer tomography to realistic finite element meshes for numerical simulations. This approach allows to take into account the statistical character of the foam morphology and can be applied to predict the mechanical properties of foams. First, a computer tomography analysis was performed to determine the size distribution of the polymer foams using a nondestructive technique. The computer tomography information was applied to build finite element meshes using a tessellation of modified Kelvin cell units or truncated octahedra of various cell sizes. Then finite element simulations were performed using these meshes in order to predict the compressive behavior of polymer foams. The results of the numerical simulations were in a good agreement with those of experimental data. In conclusion, the mechanical properties of cellular polymers can be adequately predicted by taking into account the inhomogeneous foam structure, in particular the cell size distribution.

Effect of defects on elastic–plastic behavior of cellular materials

Cellular solids such as foams are widely used in engineering applications. In these applications, it is important to know their mechanical properties and the variation of these properties with the presence of defects. Several models have been proposed to obtain the mechanical properties of cellular materials. However, these models are usually based on idealized unit cell structures, and are not suitable for finding the mechanical properties of cellular materials with defects. The objective of this work is to understand the effect of missing walls and filled cells on elastic–plastic behavior of both regular hexagonal and non-periodic Voronoi structures using finite element analysis. The results show that the missing walls have a significant effect on overall elastic properties of the cellular structure. For both regular hexagonal and Voronoi materials, the yield strength of the cellular structure decreases by more than 60% by introducing 10% missing walls. In contrast, the results indicate that filled cells have much less effect on the mechanical properties of both regular hexagonal and Voronoi materials. The effects of material strain hardening on the yield strength of cellular materials are also investigated.

Size effects in the mechanical behavior of cellular materials

Effective mechanical properties of cellular materials depend strongly on the specimen size to the cell size ratio. Experimental studies performed on aluminium foams show that under uniaxial compression, the stiffness of these materials falls below the corresponding bulk value, when the ratio of the specimen size to the cell size is small. Conversely, in the case of simple shear and indentation, the overall stiffness rises above the bulk value. Classical continuum theory, lacking a length scale, cannot explain this size dependent mechanical behaviour. One way to account for these size effects is to explicitly model the discrete cellular morphology. We performed shear, compression and bending tests using discrete models, for hexagonal (regular and irregular) microstructures. Even though discrete models give a very good agreement with the experiments, they are computationally expensive for complex microstructures, especially in three dimensions. To overcome this, one can use a generalized continuum theory, such as Cosserat continuum theory, which incorporates a material length scale. We fit the Cosserat elastic constants of the models by comparing the discrete calculations with the analytical Cosserat continuum solutions in terms of macroscopic properties. We critically address the limitations of the Cosserat continuum theory.

Variability in mechanical properties of a metal foam

Mechanical properties of cellular materials depend on their relative densities. In this paper, variability in elastic modulus, plastic strength, and energy absorption of a closed-cell Al foam, ALPORAS, and their connection with the variability in the density was examined. It was found that the tangent modulus in initial loading is considerably lower and has higher variability vis-à-vis the unloading modulus, a result of the higher sensitivity of the former to morphological defects in the cellular structure. The variability in the plastic strength and energy absorption are found to be similar, because of their interdependence. Within the range of the specimen volumes examined, no size-scaling of properties was observed. The variance in modulus and plastic strength are correlated with that in the density with the aid of the scaling relationships and error propagation techniques. Furthermore, the variability in plastic strength is related to the variance in the cell-size by considering the micromechanism of deformation in closed-cell foams, which is the collective collapse of 5–6 cells. Implications of these results in the context of manufacturing and testing strategies are discussed.