Design Of Cellular Materials Research Articles

Fatigue behaviour of FDM-3D printed polymers, polymeric composites and architected cellular materials

Polymer-based materials are increasingly produced through fused deposition modelling (FDM) – an additive manufacturing process, due to its intrinsic advantages in manufacturing complex shapes and structures at low overhead costs. The versatility of this technology has attracted several industries to print complex geometrical structures. This underlines the importance of studying the mechanical strength of FDM printed polymeric materials, especially their fatigue behaviour in cyclic loading conditions. Conventionally manufactured polymeric materials (e.g. injection moulding) have superior fatigue performance than FDM printed materials. Unlike conventionally manufactured polymers, FDM-made polymers have layer by layer adhesion and the influence of printing parameters make fatigue analysis complex and critical. The influences of printing parameters and printing material characteristics have a significant impact on the fatigue behaviour of these materials. The underlying mechanism behind the fatigue of FDM printed polymers is crucial for the assessment of these materials in structural applications. However, the fatigue behaviour of FDM printed polymeric materials has not been reviewed in detail. Therefore, this article aims to evaluate 3D printed polymeric materials’ fatigue properties. The importance of fatigue in the FDM printed biomedical materials is also reviewed, and more importantly, the novel FDM printed architected cellular material fatigue properties are also introduced.

Bioinspired multilayered cellular composites with enhanced energy absorption and shape recovery

Inspired by the multiscale configuration of the microstructure of cork, the paper describes the design, 3D printing, and evaluation of a new type of multilayered cellular composite (MCC) structure composed of hard brittle and soft flexible phases. The mechanical behavior of 3D printed MCC structures have been investigated both experimentally and numerically. The experiments show that the MCC structure absorbs four times the amount of energy of a conventional cellular configuration under compressive strains up to 70 %. Finite element simulations and 2D digital image correlation (DIC) also show that the multilayered architecture provides a more uniform strain distribution and higher stress transfer efficiency, with a resulting progressive failure mode rather than a catastrophic one. Cyclic loading tests demonstrate that the MCC structure also possesses exceptional shape recoverability under compressive deformations up to 40 %. These remarkable performance characteristics result from synergies between the properties of the two constituent materials and the chosen multilayered cellular microstructure. The soft phase, in particular, plays a pivotal role in absorbing elastic energy during loading and then releasing the stored energy while unloading. The volume fraction of the soft phase is also essential to control energy absorption and the transition of failure modes. The deformation mechanisms demonstrated here are robust and applicable to other architected cellular materials across multiple length scales and suggest new ways to design lightweight and high-resilience structural materials.

Topology Optimization of Micro-Structured Materials Featured with the Specific Mechanical Properties

Micro-structured materials consisting of an array of microstructures are engineered to provide the specific material properties. This present work investigates the design of cellular materials under the framework of level set, so as to optimize the topologies and shapes of these porous material microstructures. Firstly, the energy-based homogenization method (EBHM) is applied to evaluate the material effective properties based on the topology of the material cell, where the effective elasticity property is evaluated by the average stress and strain theorems. Secondly, a parametric level set method (PLSM) is employed to optimize the microstructural topology until the specific mechanical properties can be achieved, including the maximum bulk modulus, the maximum shear modulus and their combinations, as well as the negative Poisson’s ratio (NPR). The complicated topological shape optimization of the material microstructure has been equivalent to evolve the sizes of the expansion coefficients in the interpolation of the level set function. Finally, several numerical examples are fully discussed to demonstrate the effectiveness of the developed method. A series of new and interesting material cells with the specific mechanical properties can be found.

Thermal transport in hollow metallic microlattices

While over the past decade architected cellular materials have been shown to possess unique mechanical properties, their thermal properties have received relatively little attention. Here, we investigate thermal transport in hollow nickel microlattices as a function of temperature and mechanical loading using infrared thermography. The effective thermal conductivity of hollow nickel microlattices with 99.9% porosity and 1 µm layer thickness is as low as 0.049 W m−1 K−1 at 320 K and increases to 0.075 W m−1 K−1 at 480 K, an increase we attribute to internal thermal radiation. By measuring the emissivity and using the Stephan-Boltzmann law, we estimate the contribution of thermal radiation in the effective thermal conductivity to range from 20% at 320 K to 49% at 480 K. The high porosity of microlattices strongly limits solid conduction and makes surface radiation very important in thermal transport. We further explore the impact of the strut surface condition by comparing hollow doped nickel microlattices with a smooth surface to those with a rough surface: the emissivity increases from 0.24 to 0.43, leading to increased thermal radiation contributions of 41% at 320 K to 58% at 480 K. Under mechanical loading, as the strain increases from 0% to 50%, decreasing the angle between the struts and the horizontal plane from 60° to 38°, the effective thermal conductivity decreases from 0.049 W m−1 K−1 to 0.016 W m−1 K−1. These findings indicate that architected cellular materials provide an excellent platform to control thermal properties independently on mechanical properties and to potentially develop thermal and thermomechanical metamaterials.

Mechanical properties of 3D double-U auxetic structures

Auxetic materials or structures, especially 3D cellular lattice architectures with negative Poisson's ratio (NPR) have attracted great attention due to their unprecedented mechanical behaviors and promising applications in recent years. Many 3D auxetic architected cellular materials have been manufactured and characterized with polymers and metals using additive manufacturing technology as well as some fibre reinforced polymers (FRP) composites via assembly method, however metal 3D printed auxetic structures with high-quality are rarely reported and FRP composites using assembly method contain a variety of defects which result in a knock-down effect on mechanical properties. Auxetic structures made from polymers are normally of low stiffness and strength and FRP composites are of low toughness and impact resistance, which causes limitations on their structural and functional applications. If rationally designed structures can be made from high-performance metal materials the specific stiffness and strength of which are much higher than polymers, their specific stiffness and strength can be significantly increased which will make them more suitable for various potential applications. This paper presents novel 3D double-U hierarchical structures (DUHs) based on double-V hierarchical structures (DVHs) with tunable Poisson's ratio and Young's modulus by tailoring the geometry parameters. Experimental, numerical and theoretical results show that DUHs have smooth geometry that can reduce manufacturing damage and stress concentration under elastic loading. Another advantage of DUHs is that the curved configurations have enhanced auxetic behavior and higher static collapse stress than DVHs under crushing. The advanced 3D printing technology and those excellent mechanical properties of 3D DUHs meet the requirements of structural and functional applications.

Multi-property cellular material design approach based on the mechanical behaviour analysis of the reinforced lattice structure

Lattice structures have advantages such as energy absorption and heat transfer; however, they can often suffer failure because of stress distribution and lack of stiffness. A spherical-node-body-centred-cubic (SNBCC) structure was developed to reduce the stress concentration and improve the stiffness. The relative density, surface area, and equivalent modulus of the SNBCC structure were studied, and a method to select suitable parameters was developed. The results showed that the prediction errors of the theoretical relative density and surface area were both <1.00% compared with that of the CAD model. The theoretical modulus's prediction error was approximately 10.00% compared with that of the finite element analysis. Compared with the BCC structure, the relative density of the SNBCC structure only increased from 1.00% to 7.00%, the stress concentration reduced from 10.00% to 30.00%, and the stiffness increased from 5.00% to 58.10%, when the ratio of the strut diameter to the unit cell length was within 0.02–0.10. The projection approach for the lattice structure's multi-property design was applied. If a solid material's modulus is 200.00 GPa, the design range of the relative density and the equivalent modulus can be within 0.0021–0.1197 and 0.10 MPa–1.00 GPa respectively.

Four Questions in Cellular Material Design.

The design of cellular materials has recently undergone a paradigm shift, enabled by developments in Additive Manufacturing and design software. No longer do cellular materials have to be limited to traditional shapes such as honeycomb panels or stochastic foams. With this increase in design freedom comes a significant increase in optionality, which can be overwhelming to the designer. This paper aims to provide a framework for thinking about the four key questions in cellular material design: how to select a unit cell, how to vary cell size spatially, what the optimal parameters are, and finally, how best to integrate a cellular material within the structure at large. These questions are posed with the intent of stimulating further research that can address them individually, as well as integrate them in a systematic methodology for cellular material design. Different state-of-the-art solution approaches are also presented in order to provoke further investigation by the reader.

Cluster-Based Optimization of Cellular Materials and Structures for Crashworthiness

The objective of this work is to establish a cluster-based optimization method for the optimal design of cellular materials and structures for crashworthiness, which involves the use of nonlinear, dynamic finite element models. The proposed method uses a cluster-based structural optimization approach consisting of four steps: conceptual design generation, clustering, metamodel-based global optimization, and cellular material design. The conceptual design is generated using structural optimization methods. K-means clustering is applied to the conceptual design to reduce the dimensional of the design space as well as define the internal architectures of the multimaterial structure. With reduced dimension space, global optimization aims to improve the crashworthiness of the structure can be performed efficiently. The cellular material design incorporates two homogenization methods, namely, energy-based homogenization for linear and nonlinear elastic material models and mean-field homogenization for (fully) nonlinear material models. The proposed methodology is demonstrated using three designs for crashworthiness that include linear, geometrically nonlinear, and nonlinear models.

In-plane and out-of-plane buckling of architected cellular plates: Numerical and experimental study

Abstract In this article, the nature of instability in architected cellular materials is explored through computational modelling and experimental testing. The in-plane and out-of-plane buckling as two major instability mechanisms in cellular materials are distinguished and the effects of their microarchitectural parameters on the buckling behavior are demonstrated. Different architected cellular materials in the form of cellular plates are analysed with a finite element method (FEM) by eigen buckling and nonlinear analyses, while a few samples of elastomeric architected cellular materials are prototyped and experimentally tested to corroborate our numerical predictions for the buckling load. We show that an appropriate gradient of cell architecture within the cellular plates could lead to an increase in both out-of-plane and in-plane buckling loads. The experimental tests conducted on the casted cellular plates with uniform and graded microarchitectures, made of a two-component silicone elastomer , confirm that different buckling mode shapes can be observed by tailoring the microarchitectures of cellular plates. This idea can pave the path for devising advanced reconfigurable materials, for shape matching and energy absorption applications, whose mode shapes and resistance to buckling can be programmed based on the desirable functionalities without compromising their total mass.

Analytical models of the geometric properties of solid and hollow architected lattice cellular materials

Abstract

Optimal microstructures of elastoplastic cellular materials under various macroscopic strains

Topology optimization has been applied widely in cellular material design by optimizing the microstructure of periodic base cell (PBC). So far, most works are focused on the design of microstructures with linear material properties using the inverse homogenization method. When accounting elastoplastic constitutive behaviors, there is in usual no overall closed-form constitutive expression for the cellular microstructure as the case of linear elasticity, the design is therefore dependent on the specific applied loading. Due to the importance of topology optimization concerning elastoplastic material, the microstructural topology optimization procedure of elastoplastic cellular material with the objective of maximizing their nonlinear responses in terms of the strain energy density is proposed by using the bi-directional evolutionary structural optimization (BESO) method in this paper. Analytical sensitivity analysis is derived in a clear and rigorous manner using the adjoint method and incorporated into the BESO algorithm. The effectiveness of the proposed approach is validated through a series of numerical examples for various macroscopic strain loadings.

Harnessing Instabilities to Design Tunable Architected Cellular Materials

Mechanical instabilities are traditionally regarded as a route toward failure. However, they can also be exploited to design architected cellular materials with tunable functionality. In this review, we focus on three examples and show that mechanical instabilities in architected cellular materials can be harnessed (a) to design auxetic materials, (b) to control the propagation of elastic waves, and (c) to realize reusable energy-absorbing materials. Together, these examples highlight a new strategy to design tunable systems across a wide range of length scales.

Flexible design of cellular Al2TiO5 and Al2TiO5-Al2O3 composite monoliths by reactive firing

Cellular Al2TiO5 and Al2TiO5 – Al2O3 composite ceramics were obtained by emulsification of liquid paraffin in aqueous suspensions of mixed TiO2+Al2O3 powders, with subsequent burnout of the organic phase and 2-step reactive firing at high temperatures. The reactants ratio and paraffin to suspension volume ratio were used as primary parameters to control the phase composition and relevant microstructural features, while firing conditions were also adjusted for greater flexibility in designing Al2TiO5-based cellular materials. Taguchi experimental planning was used to assess the relevant impacts of 2-step firing parameters on phase composition and porosity, characterized by detailed XRD/SEM/EDS studies. The results emphasized the positive effects of Al2O3 excess in Al2TiO5 – Al2O3 composite ceramics on stabilization of the Al2TiO5 phase and also for flexible design of cellular materials with controlled porosity and phase distributions. Analysis of correlation matrixes identified the 2-step firing parameters with greatest impact on the porosity and phase composition, and these trends were confirmed by multivariate linear regression. The observed trends indicated significant differences in reactivity and densification mechanisms between compositions with nominal Al2TiO5 stoichiometry and composite materials. These differences were most obvious for samples with significant residual fractions of unreacted titania.

Dynamic material parameters of closed-cell foams under high-velocity impact

Cellular materials under high-velocity impact have highly localized deformation with the cells layer-wise collapse, which is usually characterized by the propagation of shock wave. Researches have shown that the shock wave speed is strongly dependent on the impact velocity, but the effect of the meso-structural and base-material parameters is unclear. In this study, the dynamic material parameters of closed-cell foams are investigated with cell-based finite element models. The one-dimensional velocity distribution along the loading direction is used to capture the propagation of shock front. The shock wave speed is thus determined and it exhibits a linear relationship with impact velocity when the impact velocity is high enough. The difference between the shock wave speed and the impact velocity is a dynamic material parameter of cellular material and the effect of meso-structural and base-material parameters on this dynamic material parameter is investigated with dimensional analysis. An expression of the dynamic material parameter with respect to the relative density and the base-material parameters is obtained. It shows that the dynamic material parameter intensively relies on the relative density and increases linearly with the relative density. The investigation of dynamic stresses with the aid of a shock model shows that the initial crushing stress increases in a power-law tendency with the increase of relative density. As a result, a stress–strain relation involving the relative density of material cellular and the yield stress and density of base material is obtained for the closed-cell foams considered. The effects of hardening behaviors of cell-wall material and gas trapped within cells are also considered. It is found that the dynamic material parameter exhibits nearly linear increase with the increase of hardening parameters of base material and initial gas pressure, while the dynamic initial crushing stress is independent of the strain-hardening parameter and the entrapped gas pressure but increases with the strain-rate hardening parameter linearly. These findings may be helpful for guiding the crashworthiness design of cellular materials and structures.

New paradigms in cellular material design and fabrication

This paper presents an effective method for designing three dimensional (3D) cellular materials containing complex internal cellular microstructures. The volumetric distance field (VDF) strategy is developed to eliminate voxelization and interpolation processes required in the conventional voxel based DF method. By introducing a hybrid method based on the VDF and triply periodic minimal surface (TPMS) cellular topology, we can design a variety of 3D cellular materials with intricate internal microstructures and arbitrarily-shaped external surfaces with unprecedented efficiency and accuracy. Experimental results show that the proposed design method has the capability to combine the perfectly interconnected channel networks based on the TPMS microstructures and the given object geometries in a consistent framework irrespective of the complexity of objects. In addition, in order to show the generality and versatility of the proposed method, a set of valuable applications are also illustrated through the innovative heat sink, heat exchanger, and enhanced lightweight cellular structure designs. Our findings suggest that the proposed design principles offered by TPMS-based cellular topology and VDF can be applied to create a wide range of advanced 3D cellular materials.

Ultra-strong architected Cu meso-lattices

3-dimensional solid Cu octet meso-lattices with characteristic features on the micron-scale were fabricated and mechanically tested under uniaxial compression. These architected cellular materials were fabricated by a three-step process: (1) direct laser writing of the lattice pattern into a polymer template, (2) electroplating of Cu into the template, and (3) removal of the polymer matrix. The microstructure of the electroplated Cu mainly consists of polycrystalline grains with average diameters of 2μm such that cross-sections of lattice beams mostly consist of a single grain. We discovered that the compressive yield strengths of the open-cell Cu meso-lattices can exceed the yield strength of monolithic bulk Cu as measured from a Cu thin film made with identical conditions. Meso-lattices with relative density of 0.8 had a strength of 332 MPa, which surpassed the bulk yield strength by 80%. This is diametrically opposite to predictions from structural mechanics theory, which states that strength scales linearly with relative density for the octet structure. We attribute the ability of solid Cu meso-lattices to attain such high strengths to the “smaller is stronger” size effect present in single crystalline metals with sub-micron dimensions. This work demonstrates the use and proliferation of the size-dependent strengthening unique to nanostructures in an architected structural material.

Topology Optimization for Cellular Material Design

ABSTRACTTopology optimization is a systematic, computational approach to the design of structure, defined as the layout of materials (and pores) across a domain. Typically employed at the component-level scale, topology optimization is increasingly being used to design the architecture of high performance materials. The resulting design problem is posed as an optimization problem with governing unit cell and upscaling mechanics embedded in the formulation, and solved with formal mathematical programming. This paper will describe recent advances in topology optimization, including incorporation of manufacturing processes and objectives governed by nonlinear mechanics and multiple physics, and demonstrate their application to the design of cellular materials. Optimized material architectures are shown to (computationally) approach theoretical bounds when available, and can be used to generate estimations of bounds when such bounds are unknown.

Topology optimization of microstructures of cellular materials and composites for macrostructures

This paper introduces a topology optimization algorithm for the optimal design of cellular materials and composites with periodic microstructures so that the resulting macrostructure has the maximum stiffness (or minimum mean compliance). The effective properties of the heterogeneous material are obtained through the homogenization theory, and these properties are integrated into the analysis of the macrostructure. The sensitivity analysis for the material unit cell is established for such a two-scale optimization problem. Then, a bi-directional evolutionary structural optimization (BESO) approach is developed to achieve a clear and optimized topology for the material microstructure. Several numerical examples are presented to validate the proposed optimization algorithm and a variety of anisotropic microstructures of cellular materials and composites are obtained. The various effects on the topological design of the material microstructure are discussed.

Elastic Modulus of Rhombus Dodecahedron Closed-Cell Cellular Materials

Based on the pore formation principle, geometrical model to describe cellular materials was constructed. The model is closed-cell rhombus dodecahedron with thick edges. The dependence of relative density on microstructure parameters and the unitary relation have been obtained. By finite elements method, the relative elastic modulus was simulated, the influence of microstructure and relative density on elastic modulus was analyzed. The results show that the wall-face connective curvature radius is the primary affecting factor of relative density increment and the wall-thickness is less significant; the solid materials added at the intersecting part of the wall-faces produce same effect on elastic modulus. The conclusion can be applied in optimization design of cellular materials.

Dynamic Crushing of Hexagonal Honeycombs under In-Plane Loading

The in-plane dynamic crushing of hexagonal honeycombs was numerically studied by means of explicit dynamic finite element method using ANSYS/LS-DYNA. Under the assumption that the edge length and thickness were the same, the metal honeycomb models filled with convex and concave cells were established. And then the effects of expanding angle and impact velocity on the plateau stress and the energy absorption capacities of hexagonal honeycombs were discussed in detail. Numerical results show that the energy absorption capacities of convex hexagonal honeycombs are stronger than the concave ones. These results will provide some useful guides for the dynamic energy absorption design of cellular materials.