Octet-truss Lattice Research Articles

A fuzzy optimization method for octet-truss lattices

Purpose This paper aims to present a multiscale fuzzy optimization (FO) method to optimize both the density distribution and macrotopology of a uniform octet-truss lattice structure. Design/methodology/approach The design formulae for the strut radii are presented based on the effective mechanical properties obtained from the representative volume element. The proposed basic lattice material is applied in a normalization process to determine the material model with penalization. The solid isotropic material with penalization (SIMP) method is extended to solve the minimum compliance problem using the optimality criteria. The evolutionary deletion process is proposed to delete elements corresponding to thin-strut unit cells and to obtain the optimal macrotopology. Findings Both numerical cases indicate that the FO results significantly improved in structural performance compared with the results of the conventional SIMP. The deleting threshold controls the macrotopology of the graded-density lattice structures with negligible effects on the mechanical properties. Originality/value This paper presents one of the first multiscale optimization methods to optimize both the relative density and macrotopology of uniform octet-truss lattices. The material model and corresponding optimality criteria of octet-truss lattices are proposed and implemented in the optimization.

Uso de las nuevas tecnologías para estimar la calidad de vida en lactantes con enfermedades infecciosas prevenibles o potencialmente prevenibles mediante vacunación

A hierarchical structure featuring both nano- and macro- structure has emerged as prospective candidates for the application requiring high flow rates and specific surface area. A unique physical and mechanical behavior could be discovered by designing a special structure. A random orientated nanoporous copper thin film coated on a three-dimensional (3D) microporous periodical octet-truss lattice was utilized as a hierarchical structure to evaluate the mechanical and catalytic behaviors. Nanoporous copper films with ligament size ranging from 16 to 28 nm were synthesized using magnetron co-sputtering CuAl alloy films and subsequent dealloying process, while the octet-truss with a pore size of 120 μm was fabricated by digital light processing. The yield strengths of the octet-truss lattice with nanoporous Cu (L-NPC) films are 3 times higher than those of low-density bulk Cu or Cu films predicted by the Gibson-Ashby equation. The current densities and electrochemical surface area of the l-NPC films are also 10 times higher than those of octet-truss lattice with solid Cu films or NPC films coating on a two-dimensional substrate. In addition to the nano-scale pore size effect, the 3D polymer structure produced a high curly surface for NPC films to attach on the truss which could be the reason for the different mechanical and electrochemical behaviors.

Brittle fracture of three-dimensional lattice structure

This work aims to develop a greater understanding of fracture behaviour of a three-dimensional lattice structure. Octet-truss lattice was used in this study due to its high strength to density ratio and great potential in the advanced lightweight structure applications. The fracture toughness, KIC, was found to be almost isotropic while the modulus and strength were highly dependent on the model size and lattice orientation. The converged solution for the modulus and strength were obtained when model width is large compared to cell. The modulus can be varied by 20% and the strength can be doubled when lattice orientation was changed. The validity of linear elastic fracture mechanics (LEFM) was examined on different model geometries including single edge notch tension (SENT), compact tension (CT), single edge notch bending (SENB) and thumbnail crack model. It shows that the LEFM can be adequately used in the structures with linear crack fronts. In the thumbnail crack model, the curved crack front generates more complexity in the structure ahead of the crack tip which results in a significant discrepancy in measured toughness compared to the models with linear crack fronts. Moreover, great fracture performance was exhibited in the lattices, where an increase in fracture load was observed during the crack growth.

Experimental investigation of heat transfer and fluid flow in octet-truss lattice geometry

This paper undertakes an experimental measurement of effective thermal conductivity, permeability, inertial coefficient, friction factor and wall convective heat transfer from octet truss lattice (OTL) structures as air-cooled compressive load-bearing light-weight heat sinks. Three aluminium alloy (AlSi10Mg) OTL structures of porosities 70.6%, 86.9% and 91.3% were fabricated using an additive manufacturing technique. Experimentally measured effective thermal conductivity, permeability, inertial coefficient, friction factor and wall Nusselt number for OTL structures are reported. Owing to high solid-to-fluid thermal conductivity ratio (∼4250), heat flows through the metal ligament and air independently and establishes steady-state, i.e. peripheral conduction coupling between solid metal and air is negligible. This is conferred from various theoretical and semi-empirical models from the literature. Friction factor and wall Nusselt number are characterised using a single length scale as against different length-scales often used in the literature. Flows through OTL structures seem to follow Forchheimer's flow law with negligible viscous contribution even at low pressure gradients. Further, the results are compared with previous analytical and experimental results for stochastic open-cellular foams. Owing to periodic nature of OTL structures, friction factor is lower than stochastic foams as mechanical dispersion effects are negligible. In conclusion, OTL structures are an excellent candidate for multifunctional applications where heat sinks are expected to bear compressive loads as well as dissipate heat while being lightweight.

Characterisation of Reinforced Body Centered Cubic, Octahedral-Type and Octet Truss Lattice Structures

Developments in additive manufacturing have encouraged a dramatic increase in the production and integration of the space-filling unit cells known as lattice structures. As designers begin to leverage the useful benefits provided by lattice structures, and these structures are used more frequently in industrial designs of parts, there is a need to characterise the properties that different lattice structures possess to aid the design process. The functional requirements of a specimen will often change during the design stage and this means that a designer will always wish to select the most applicable lattice structure for the optimal result. To date, there is no repository of lattice structure design properties from which a designer can choose a structure that best suits the design requirements. This article aims to propose a methodology for testing the capabilities of lattice structures and building a database of unit cell type design properties through compression and 3-point bending tests. The samples were created with PA2200 manufactured through the selective laser sintering process on an EOS P396. The lattice structure specimens were parameterised in terms of overall specimen unit cell size and strut diameter. Through regression analysis, particular benefits of lattice structures were noted: Reinforced Body Centered Cubic (RBCC) performed best in bending, Octet Truss performed best in compression and Octahedral performed worst in both tests but resisted much greater deformation. Additionally, though increases in strut diameter or number of unit cells per sample increased both Young’s Modulus and Ultimate Compressive Strength, it was strut diameter increases that had a factor of 10 greater of an effect. To complete a repository, it is desirable to increase the number of stages per design parameter and test over a greater range of values - to fully model the shape of the output curve.Scientific Topics: Design Methodology, Design of Lattice Structures, Designing for Additive Manufacturing, Designing for Multifunctional Optimisation of Lattice Structures

Fluid flow and heat transfer characteristics of octet truss lattice geometry

Octet truss lattice structures are a potential candidate for developing multifunctional heat exchangers/sinks owing to their superior structural characteristics compared against stochastic open-cellular metal foams. Structural efficiency is achieved primarily due to increased nodal connectivity in octet-truss lattices. Designed octet trusses and periodic cellular materials, in general, lend themselves well to topology optimization and integration of multiple functions enabling a high degree of tailorability and superior performance benefits. Specific to heat transfer design, octet truss lattices can be tailored to achieve optimal strand cross-sectional area-to-length ratio for improved effective thermal conductivity while meeting surface-area per volume requirements for convective transport. In this work, we explore the heat and fluid flow characteristics using direct numerical simulations of a periodic unit-cell. Effective thermal conductivity, permeability, inertial coefficient, friction factor and Nusselt number for octet truss lattice structures are predicted and compared against stochastic foam experimental data. A range of porosities and pore densities are simulated and heat transfer and fluid flow characteristics are correlated using a single length scale in the form of Brinkman screening length, √K, as against existing literature where different geometric length scales are used. Further, octet truss lattice geometry is compared against existing stochastic metal foam heat and fluid flow empirical data. Normalized permeability of octet lattices were found to be 20–80% higher than stochastic foam for a given porosity. Similarly, for a fixed porosity, inertial coefficients of octet lattices were 50% of stochastic experimental measurements. For the range of Reynolds number considered, octet truss lattices show similar fluid and heat flow characteristics if not better performance than stochastic foams and thus making them ideally suited for tailored multifunctional heat sinks and exchangers.

Determination of the Elasticity Modulus of 3D-Printed Octet-Truss Structures for Use in Porous Prosthesis Implants.

In tissue engineering, scaffolds can be obtained by means of 3D printing. Different structures are used in order to reduce the stiffness of the solid material. The present article analyzes the mechanical behavior of octet-truss microstructures. Three different octet structures with strut radii of 0.4, 0.5, and 0.6 mm were studied. The theoretical relative densities corresponding to these structures were 34.7%, 48.3%, and 61.8%, respectively. Two different values for the ratio of height (H) to width (W) were considered, H/W = 2 and H/W = 4. Several specimens of each structure were printed, which had the shape of a square base prism. Compression tests were performed and the elasticity modulus (E) of the octet-truss lattice-structured material was determined, both, experimentally and by means of Finite Element Methods (FEM). The greater the strut radius, the higher the modulus of elasticity and the compressive strength. Better agreement was found between the experimental and the simulated modulus of elasticity results for H/W = 4 than for H/W = 2. The octet-truss lattice can be considered to be a promising structure for printing in the field of tissue engineering.

Mechanical behaviour of additively-manufactured polymeric octet-truss lattice structures under quasi-static and dynamic compressive loading

Two different polymer resins were used to create three different octet-truss lattice structures of different densities. The mechanical behaviour of these structures has been examined under both quasi-static and dynamic compressive loading. The structures were printed using stereolithography (SLA) additive manufacturing. The basic building octet unit has a fixed strut length of L=10mm, with the designed strut radius varying from R=0.7mm to 1.3mm to provide structures of different densities. It has been found that the mechanical behaviour of the printed octet structures depends on both the relative density and the intrinsic material properties. Higher density structures show larger effective yield and compressive strengths, while the basic printing material fundamentally determines its macroscopic properties: one material provides a brittle mechanical response under compression while the other provides a tough response. The former lattice structures behaved in a brittle manner at all relative densities, fracturing at small strains. For the latter resin lattice structures, on the other hand, under quasi-static compression, the stress-strain curves changed from a slightly stress oscillating mode at low relative density (i.e. ρ¯=0.13) to a stable stress plateau mode at high relative density (i.e. ρ¯=0.41). The Specific Energy Absorption (SEA) of both lattice structures had a monotonically increasing relationship with relative density, the SEA of the brittle resin specimen is higher than that of the tough resin specimen, while the tough resin specimen exhibits its excellent energy absorption under a wide displacement range. For the dynamic compressive tests, the tougher resin structures displayed strain-rate effects, while the more brittle ones did not. The numerically predicted response of both lattice structures agreed closely with the experimental results.

Design and strengthening mechanisms in hierarchical architected materials processed using additive manufacturing

Natural structural materials which feature hierarchical architectures, like bone and glass sponge skeletons, often display remarkable mechanical properties. Employing the principle of hierarchy can create self-similar architected metamaterials across multiple length-scales, but the strengthening mechanisms remain to be fully understood. In the present study, self-similar hierarchical octet-truss lattice materials were fabricated via additive manufacturing and deformed in uniaxial compression. Experimental results indicated that the mechanical properties of such hierarchical lattice materials were not determined by relative density, unlike those of non-hierarchical ones, but varied with strut slenderness ratios in the two hierarchical levels. In terms of specific strength and stiffness, hierarchical architected structures do not necessarily outperform non-hierarchical structures. To explain the underlying mechanisms of these phenomena, analytical models considering effects of complex nodal microstructure were established. The upper and lower bounds of strength for the hierarchical lattice materials were deduced and compared with that for the non-hierarchical materials; these comparisons suggested that the hierarchical construction could be used to access unique mechanical properties that are unachievable in traditional materials. Additional levels of hierarchy beyond the second order could be similarly analyzed. This study discerns how hierarchical architecture can be used to access the unique properties of lattice materials, provides insight into the role of design in regulating the mechanical properties of such mechanical metamaterials.

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.

CAD TOOLS AND FILE FORMAT PERFORMANCE EVALUATION IN DESIGNING LATTICE STRUCTURES FOR ADDITIVE MANUFACTURING

Additive manufacturing has opened the door to the creation of lightweight lattice structures. However, present Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) software are unsuitable for these types of structures. The objective of this research is to examine the performances of current CAD and CAE software to design lattice structures and to demonstrate their limitations and propose requirements for future developments. A performance evaluation of a case study for lattice structure designs was conducted. The criteria used for the evaluation were CAD human-machine-interface, RAM consumption, data exchange between CAD, CAE and CAM tools and finite element analysis (FEA) duration and file sizes. The CAD tool was incapable of executing a repetition function for octet-truss lattice structures of 150 x 150 x 150 mm dimensions or larger and the software stopped working. For 70 × 70 × 70 mm octet-truss lattice structure, the FEA computation file size reached 36.6 GB. The CAD file size of a 200 x 200 x 200 mm octet-truss lattice structure reached nearly 290 MB. In conclusion, this study exposes the performance inadequacy of current CAD and CAE tools and CAD file formats to design lattice structures for additive manufacturing parts.

Drop-weight impact characteristics of additively manufactured sandwich structures with different cellular designs

In the design of sandwich panels with cellular cores for energy absorption, the geometrical effect of the cellular core design has not been investigated in details previously. In this work three cellular core designs, including re-entrant auxetic, octet-truss, and BCC lattice, were experimentally investigated for their performance under low-energy impact as sandwich structures. Samples with different cellular core designs were fabricated by laser sintering additive manufacturing process using Nylon 12 as material, and evaluated by drop weight testing under multiple strikes and at two levels of elevated temperatures (93°C and 121°C). It was found that beside relative densities, the geometrical design of the cellular cores could also significantly influence the impact energy absorption performance of the sandwich structures. It was also found that the impact energy absorption of the cellular structures investigated in this study does not have a significant correlation with either the quasi-static mechanical properties or the temperature. In addition, the auxetic cellular structure exhibits optimal overall energy absorption performance compared to both the octet-truss and the BCC lattice.

Elastically-isotropic truss lattice materials of reduced plastic anisotropy

The elastically-anisotropic octet truss lattice exhibits high specific stiffness due to its stretching-dominated mechanical behavior. Here, elastically-isotropic truss lattices are designed in a way that the constituent beams respond in a stretching-dominated manner instead of bending. Topology constraints ensuring an isotropic elastic response at the macroscopic level are derived from a detailed theoretical analysis of generic periodic truss structures. Specific elastically-isotropic structures are designed by combining elementary cubic truss lattices including the Simple Cubic (SC), Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattices. It is shown through periodic homogenization that these isotropic truss lattice compositions exhibit less initial yield anisotropy than the octet truss lattice. For example, the ratio of maximum to minimum yield stress of an SC-BCC-FCC truss lattice composition is 1.4 as compared to 2 for the octet truss lattice. Computational unit cell analysis is carried out to confirm the analytical Young's modulus and yield stress estimates. Selected isotropic structures of 20% relative density are built from a photopolymer using stereolithography. The Young's modulus and Poison's ratio measurements on specimens with different lattice orientations confirm the validity of the design constraints. In addition, the trends regarding the plastic anisotropy are confirmed by the experimental results.

Large deformation response of additively-manufactured FCC metamaterials: From octet truss lattices towards continuous shell mesostructures

Starting with the statically-determinate solid octet truss lattice, the large strain compression response of different metamaterial architectures is analyzed through finite element analysis and compression experiments on additively-manufactured stainless steel specimens. Simulation results clearly demonstrate that for a relative density of 20% the conventional solid octet-truss lattice has a lower specific energy absorption capability than some simple periodic shell structures. The analysis of the closed-packed hollow sphere assembly subject to hydrostatic compression reveals that the constituent hollow spheres initially transform into rhombic dodecahedra, which results in significant strengthening at the macroscopic level. Unlike the octet-truss with solid struts, hollow octet truss structures remain stable for hydrostatic, confined and uniaxial compression at the lowest relative density considered. Its strength, in particular at small plastic strains, is substantially improved when substituting the geometric hollow truss joints for hollow spheres. The continuous shell mesostructures defined by the Hybrid (hollow) Truss-Sphere (HTS) and the hollow octet truss assembly exhibited the highest strength and energy absorption potential at 20% relative density for the high and low strain-hardening materials considered, respectively. Moreover, it is found that the HTS metamaterial exhibits the highest relative Young's and bulk moduli among all four architectures considered. It is also shown computationally that hollow rhombic dodecahedral mesostructures could provide nearly twice the strength and energy absorption of the conventional octet truss.

Stress-Strain Behavior of an Octahedral and Octet-Truss Lattice Structure Fabricated Using the CLIP Technology

In the rapidly growing field of additive manufacturing (AM), the focus in recent years has shifted from prototyping to manufacturing fully functional, ultralight, ultrastiff end-use parts. This research investigates the stress-strain behavior of an octahedral-and octet-truss lattice structured polyacrylate fabricated using Continuous Liquid Interface Production (CLIP) technology based on 3D printing and additive manufacturing processes. Continuous Liquid Interface Production (CLIP) is a breakthrough technology that grows parts instead of printing them layer by layer. Lattice structures such as the octahedral-and octet-truss lattice have recently attracted a lot of attention since they are often structurally more efficient than foams of a similar density made from the same material, and the ease with which these structures can now be produced using 3D printing and additive manufacturing. This research investigates the stress-strain behavior under compression of an octahedral-and octet-truss lattice structured polyacrylate fabricated using CLIP technology

Mechanical properties of copper octet-truss nanolattices

We investigate the mechanical properties of copper (Cu) octet-truss nanolattices through a combination of classical molecular dynamics (MD) simulations and theoretical analysis. The MD simulations show that Cu nanolattices with high relative density are stronger than bulk Cu, while also achieving higher strength at a lower relative density as compared to Cu meso-lattices. We demonstrate that modifying the classical octet-truss lattice model by accounting for nodal volume and bending effects through the free body diagram method is critical to obtaining good agreement between the theoretical model and the MD simulations. In particular, we find that as the relative density increases, nodal volume is the key factor governing the stiffness scaling of the nanolattices, while bending dominates the strength scaling. Most surprisingly, our analytic modeling shows that surface effects have little influence on the stiffness and strength scaling of the nanolattices, even though the cross sectional sizes of the nanowires that act as the lattice struts are on the order of 6nm or smaller. This is because, unlike for individual nanowires, the mechanical response of the nanowire struts that form the nanolattice structure is also a function of bending and nodal volume effects, all of which depend nonlinearly on the nanolattice relative density. Overall, these results imply that nanoscale architected materials can access a new regime of architected material performance by simultaneously achieving ultrahigh strength and low density.

Mechanical Response of Octahedral and Octet-Truss Lattice Structures Fabricated Using the CLIP Technology

In the rapidly growing field of additive manufacturing (AM), the focus in recent years has shifted from prototyping to manufacturing fully functional, ultralight, ultrastiff end-use parts. This research investigates the mechanical behavior of octahedral- and octet-truss lattice structured polyacrylate fabricated using Continuous Liquid Interface Production (CLIP) technology based on 3D printing and additive manufacturing processes. Continuous Liquid Interface Production (CLIP) is a breakthrough technology that grows parts instead of printing them layer by layer. CLIP is a chemical process that carefully balances UV light and oxygen to eliminate additional mechanical steps for part delamination and resin refill. UV light triggers photopolymerization and oxygen inhibits it. By carefully balancing the interaction of light and oxygen, CLIP grows objects from a pool of resin. Lattice structures such as the octahedral- and octet-truss lattice have recently attracted a lot of attention since they are often structurally more efficient than foams of a similar density made from the same material, and the ease with which these structures can now be produced using 3D printing and additive manufacturing. This research investigates the mechanical response under compression of octahedral- and octet-truss lattice structured polyacrylate fabricated using CLIP technology. It was found that the elastic modulus and strength of the octahedral-truss structured materials are proportional to each other over a relative density range of 0.07 to 0.35. Finally, even though the octet-truss lattice structure is a stretch-dominated unit cell structure, it was found to have a lower stiffness and strength as compared to an octahedral-truss structure of the same relative density. This can be attributed to the smaller diameter and therefore larger l/d of individual struts.

The fracture toughness of octet-truss lattices

The only engineering materials with both high strength and toughness, and with densities less than 1000kgm−3, are natural materials (woods) and some plastics. Cellular structures such as the octet lattice, when made from periodic arrangements of strong, low-density metallic trusses, are known to have high specific strengths and elastic moduli. However, much less is known of their resistance to fracture. Here we investigate the fracture toughness of a Ti-6Al-4V alloy octet-lattice truss structure manufactured using a ‘snap-fit’ method. The samples had densities between 360 and 855kgm−3 (relative densities of 8–19%) and free truss lengths between 4 and 15mm. Their fracture resistance was determined using the J-integral compliance method applied to single-edge notched bend specimens. The toughness is shown to increase linearly with the relative density and with the square root of the cell size, while the strength was confirmed to scale only with relative density and the strength of the solid. A moderate increase in resistance with crack length (an R-curve effect) was seen for the higher relative density and larger cell size samples. With a fracture toughness between 2 and 14MPam1/2 and a compressive strength between 20 and 70MPa, these structures offer a new lightweight engineering material solution for use at temperatures up to 450°C.

Geometrical control of lattice structures produced by EBM through chemical etching: Investigations at the scale of individual struts

A major drawback of metal additive manufacturing is the surface roughness of the manufactured components. This is even more critical when complex lattice structures are considered. An octet-truss lattice structure was fabricated by Electron Beam Melting. A chemical post-treatment was applied in order to improve the surface quality. The morphology of individual struts was characterized experimentally by high resolution X-ray tomography after different chemical etching times. The chemical etching treatment was found to be beneficial as it decreases significantly the occurrence of surface defects. The evolution of the elastic mechanical properties with the etching time was determined by FFT computations directly applied to the 3D volume of the struts. A cellular automaton based model was also developed in order to predict the morphological evolution of the as-built strut during etching. The model enables to predict the kinetics of dissolution as well as the evolution of the surface defects and the elastic mechanical properties of the samples. It also enables to determine the required etching time to firstly remove powder particles stuck to the surface and secondly to reduce the plate-pile like defect occurrence.

Shear response of carbon fiber composite octet-truss lattice structures

Ultralight three dimensional space filling octet-truss lattice structures have been fabricated from carbon fiber reinforced polymer (CFRP) laminates using a mechanical snap-fitting and adhesive bonding technique. The lattice structures moduli and strengths have been measured during (001) in-plane shear as a function of the lattice relative density (ρ¯). Their strength was determined by the activation of two strut failure modes: elastic buckling of the struts governed the response when ρ¯<5%, while delamination failure controlled the strength for 16%>ρ¯>5%. The measured shear strengths are shown to be well predicted by micromechanics models based on the elastic buckling and delamination failure of the struts. Snap-fit CFRP octet-truss lattice structures with densities of 24–230kgm−3 are found to have mechanical properties superior to polymer and metal foams, and are competitive with Balsa wood and recently reported Ti–6Al–4V octet-truss lattices. They provide new opportunities for ultra-lightweight multi-axially loaded structures.