Body-centered Cubic Lattice Structures Research Articles

Bending Response of Lattice Structure Filled Tubes under Transverse Loading

Thin-walled tubes are widely used as passive energy-absorbing structures in a variety of industries. These structures are typically filled with lightweight materials to improve their energy absorption capabilities. At this point, additive manufacturing technology offers a great chance researchers for the production of novel filler structures to increase the crashworthiness performance of thin-walled tubes. In the current work, additive manufacturable body-centered cubic (BCC) lattice structures are suggested as filling materials for thin-walled tubes, and the bending response of these structures is investigated under transverse loads via a finite element modeling approach. The aspect ratio and strut diameter are considered as design parameters, and three-point bending simulations are conducted to understand the transverse load bearing behaviors of the structures. Different loading offsets are also taken into account for three-point bending simulations. The numerical results revealed that the BCC lattice structures used as filler materials significantly increase the energy absorption performance of thin-walled tubes due to synergetic interactions. In particular, the simulation results revealed that the hybrid tubes can absorb up to 84% more energy than the empty tubes, while the crush force efficiency of these structures is up to 42% higher compared to the empty tubes. The present study also showed that the transverse crushing characteristics of tubes can be considerably improved by suitable selection of the design parameters. These primary outcomes reveal that the proposed lattice structures can be considered as a potential alternative to traditional filler materials for enhancing the bending response of thin-walled tubes under transverse loading.

Design, mechanical properties, and optimization of BCC lattice structures with taper struts

The fractures of lattice structures are mainly near the nodes during loading due to the stress concentration, resulting in low mechanical properties. In this study, a novel parametric approach was proposed for modelling Body-Centered Cubic (BCC) lattice structures with taper struts to reduce the stress concentration at nodes and improve the mechanical properties. The mechanical properties and deformation behavior of lattice structures with different taper struts were investigated through finite element analysis and uniaxial compression tests. The simulation results demonstrate that tapered struts significantly reduced the anisotropy of BCC lattice structures and increased the elastic modulus by up to 67%, while the shear modulus was only improved for a slight tapering by less than 2.92%. In addition, the fracture occurred due to the combination of high plastic strain and tensile stress, and the fracture site of BCC lattice structures changed from the node region to the center of strut due to the tapering of the strut cross-sections, which corresponded to the experimental results. Finally, an optimization strategy was developed to simultaneously optimize the distribution of volume fraction and strut geometry of BCC lattice structures, demonstrating the effectiveness of the proposed design and optimization method for lightweight applications.

A topologically gradient body centered lattice design with enhanced stiffness and energy absorption properties

Lattice structures have been widely used in biomedicine, transportation, infrastructure, and other engineering fields due to their high specific strength, strong energy absorption capacity, and tunable mechanical property. Existing researches mainly focus on the uniform lattice structure or gradient lattice structure with varying density, with the design potential of lattice structure not fully exploited. In this study, inspired by the functionally graded material, a novel topologically gradient lattice structure with varying cell topology is proposed to realize spacial adjustability of the mechanical properties. The new lattice structure evolves from the classical body-centered cubic (BCC) lattice, with the body center positions varying gradiently from cell to cell along the specified directions. The prototypes of the new lattice are additively manufactured by the Multi-Jet Fusion (MJF) technology and quasi-statically compressed by the universal testing machines. Experimental and numerical simulation results reveal that the proposed structure topology gradient can significantly improve both the stiffness and the energy absorption capacity compared with the classical BCC lattice structures. It is found that the mechanical properties of the topologically gradient lattice structures are sensitive to the gradient direction, the gradient magnitude and the loading direction. This study expands the design space of lattice structures by introducing the topology gradient of the composing cells across the space. In this way, further improvement in the mechanical properties of lightweight lattice structures can be achieved.

Investigation of the effect of lattice structure on the fluid flow and heat transfer of supercritical CO2 in tubes

• Combined experimental and numerical methods to study supercritical heat transfer. • Effects of composite vortex on supercritical fluid and heat transfer were studied. • BCC lattice was used for supercritical CO 2 heat transfer experiment. • Experimental section was fabricated by SLM metal additive manufacturing. • The heat transfer deterioration was suppressed with an acceptable pressure drop. Under specific conditions of low mass flux and high heat flux, heat transfer deterioration (HTD) occurs in tubes, which is detrimental to the supercritical CO 2 heat exchanger. To suppress the HTD and promote the overall heat transfer capability of supercritical CO 2 in a vertical heated tube, the effect of the body-centered cubic (BCC) lattice structure on the fluid flow and heat transfer characteristics were studied. The BCC lattice structure was applied to a supercritical heat transfer experiment by exploiting selective laser melting (SLM) metal additive manufacturing. The results of the experimental and numerical studies indicate that the BCC lattice structure can effectively suppress the HTD by generating a composite vortex composed of a horseshoe vortex at the leading edge of the lattice ligaments, the streamwise vortex at the trailing edge of the ligaments, and the counter-rotating longitudinal vortex at the center of the ligaments. The vortex system strengthens the local turbulence intensity and enhances flow mixing, thus weakening the buoyancy effect and suppressing the HTD. Compared with the smooth tube, the average heat transfer coefficient of the tube with BCC lattice structure increased by up to 100%, whereas the pressure drop increased by 13.5%.

Study on the Shear Modulus Based Equivalent Homogenization Methods of Multi-Layer BCC Lattice Sandwich.

In this paper, the shear modulus based equivalent homogenization methods of multi-layer BCC (body-centered cubic) lattice sandwich structures have been studied using analytical, experimental, and finite element methods. In the analytical approach, the multiple strut-deformation patterns were introduced in the derivations of the shear modulus based on Euler–Bernoulli beam theory and Timoshenko beam theory according to different boundary conditions. The analytical shear modulus of three types of rectangle shaped sandwich BCC lattice structures was derived. Finite element models of the BCC lattice structures by ANSYS were conducted to estimate the analytical solutions. Butterfly style sandwich BCC lattice structures were printed by SLM technology using 304 stainless steel (06Cr19Ni10), and corresponding shear experiments using modified Arcan Rig experimental devices were conducted to validate the analytical and numerical calculations. Good agreements were observed among the analytical, numerical, and experimental results.

Experimental and numerical investigation of compressive behavior of lattice structures manufactured through projection micro stereolithography

The present work focuses on investigating the effect of lattice geometry on compression behavior, deformation mechanism and energy absorption capability of 3D printed polymeric micro-lattice structures. The mechanical characteristics of lattice cores comprising of periodic body centered cubic (BCC) architecture unit-cells, printed with projection micro-stereolithography (PμSL) based 3D printing technique were experimentally and numerically examined. For a fixed mass and corresponding relative density of lattice, five variants of BCC lattice structures were built by varying unit cell size, numbers and its strut diameter. The quasi-static compression tests were performed to determine the load-displacement history, stress-strain curves and deformation modes of lattice structures. The experimental results show that number of unit cells with in a certain volume of lattice block can have significant effect on compression properties of lattice structure. Within the same geometric envelop and mass properties, the lattice containing higher number of cells with reduced strut diameter tends absorb more energy as compared to a lattice with fewer number of cells with increased strut diameter. The elastic modulus, collapse and plateau stresses of lattice increase while densification strain decreases with the increase in number of unit cells. Moreover, there exists a certain number of cells in certain volume of lattice structure for which the energy absorption is higher, after that number the effect not significant. The deformation behavior of lattice was inspected and bending dominant deformation modes were observed in all lattice structures. The lattice with small cells shows progressive layer by layer collapse while for larger cell sized lattice show signs of buckling effect with central localized deformation modes. Lastly, the experimental outcomes were numerically implemented in finite element (FE) solver LS-DYNA to model the compression process, collapse behavior and deformation modes of lattice blocks. The compression characteristics and collapse modes predicted by FE model were in good agreement with experimental findings.

Stiffness design of a multilayer arbitrary BCC lattice structure with face sheets

In this paper, a theoretical stiffness design approach for a body-centered cubic (BCC) lattice structure is proposed. Although numerous studies have focused on lattice structures, particularly BCC lattice structure, there are still some issues that must be further investigated. Homogenization method is always followed that the mechanical properties of lattice structure can be achieved by directly solving the unit cell, since the structure is a periodically repeated sequence of a unit cell. However, the equivalent modulus varies a lot with different array configurations from our study, which indicates that the spatial array configuration also has an important influence on the equivalent mechanical properties. In this paper, “large unit cell” assumption is used to characterize the equivalent modulus of the lattice structure considering array configuration effect, and then validated using the finite element method (FEM) and experiment. The results demonstrate that the mechanical properties vary significantly for different array configurations, even those with the same unit cell topology. Furthermore, the proposed method is extended to an arbitrary BCC unit cell to broaden its application for stiffness design of engineering parts. This research provides a guidance for the stiffness design of lightweight lattice structures.

Effect of strut length and orientation on elastic mechanical response of modified body-centered cubic lattice structures

Lattice structures (LSs) have been exploited for wide range of applications including mechanical, thermal, and biomedical structures because of their unique attributes combining the light weight and high strength. The main goal of this research is to investigate the effect of strut length and orientation on the mechanical characteristics of modified body-centered cubic (BCC) LS subjected to a quasi-static axial compressive loading within linear elastic limit using finite element analysis. In this study, two sets of LS were built and analyzed in commercial finite element software, ABAQUS/CAE/EXPLICIT 6.16, using a “smart procedure,” which was developed for this research to reduce the computational time and increase the accuracy of results by creating hexahedral mesh elements. The first set comprises 13 models having fixed strut length with strut angle variation from 40° to 100° with a step of 5°. The second set also includes 13 models; however, having variant strut length, kept constant for a single unit cell and through the entire model but varied from one model to another, with the same strut angle variation as the first set. In addition, the BCC LS with a strut angle of 70.53° was replicated in both sets because it was considered as a reference model to compare the results with it. Furthermore, specimens of the reference model were fabricated by a fused deposition modeling- (FDM) based 3D printer using acrylonitrile butadiene styrene (ABS) material and tested experimentally under compression. Experimental results are observed to be in good agreement with those of the finite element simulation, hence the same loading and boundary conditions were adopted for all other models. It was observed that the fixed strut length BCC LS with a strut angle of 100° offers the highest modulus. However, the highest specific strain energy absorption and specific stiffness as well as the least value of weight were dictated by a variant strut length BCC LS with a strut angle of 40°.

Determination of the strength of a multilayer BCC lattice structure with face sheets

The body-centered cubic (BCC) lattice, as a type of cellular lattice structure, has been widely researched with the representative volume element (RVE) homogenization method. This ideal theoretical approach requires infinite unit cells in a structure, which is unrealistic and unfeasible with the current manufacturing technology. In this paper, a new theoretical approach considering the effect of array configuration is developed to predict the strength of a multilayer BCC lattice structure. First, the compression behavior of the multilayer BCC lattice structure is analyzed by finite element method (FEM) simulation. Then, an analytical model inspired by the combination of the derived stress-strain curve and the specific contour is built. Predictions of the compression strength are compared with the FEM results for multilayer structures with various spatial array configurations to validate the applicability of the proposed model. And, they are in very good agreement within acceptable errors.

Improved Mechanical Properties and Energy Absorption of BCC Lattice Structures with Triply Periodic Minimal Surfaces Fabricated by SLM

The triply periodic minimal surface (TPMS) method is a novel approach for lattice design in a range of fields, such as impact protection and structural lightweighting. In this paper, we used the TPMS formula to rapidly and accurately generate the most common lattice structure, named the body centered cubic (BCC) structure, with certain volume fractions. TPMS-based and computer aided design (CAD) based BCC lattice structures with volume fractions in the range of 10–30% were fabricated by selective laser melting (SLM) technology with Ti–6Al–4V and subjected to compressive tests. The results demonstrated that local geometric features changed the volume and stress distributions, revealing that the TPMS-based samples were superior to the CAD-based ones, with elastic modulus, yield strength and compression strength increasing in the ranges of 18.9–42.2%, 19.2–29.5%, and 2–36.6%, respectively. The failure mechanism of the TPMS-based samples with a high volume fraction changed to brittle failure observed by scanning electron microscope (SEM), as their struts were more affected by the axial force and fractured on struts. It was also found that the TPMS-based samples have a favorable capacity to absorb energy, particularly with a 30% volume fraction, the energy absorbed up to 50% strain was approximately three times higher than that of the CAD-based sample with an equal volume fraction. Furthermore, the theoretic Gibson–Ashby mode was established in order to predict and design the mechanical properties of the lattice structures. In summary, these results can be used to rapidly create BCC lattice structures with superior compressive properties for engineering applications.