Three-dimensional Lattice Structure Research Articles

3D Chiral Energy-Absorbing Structures with a High Deformation Recovery Ratio Fabricated via Selective Laser Melting of the NiTi Alloy.

Excellent energy-absorbing structures have been highly sought after in engineering applications to improve devices and personal safety. The ideal energy absorption mechanism should exhibit characteristics such as lightweight, high energy absorption capacity, and efficient reusability. To address this demand, a novel three-dimensional (3D) chiral lattice structure with compression-twist coupling deformation is fabricated by combining the left and right chiral units. The proposed structure was fabricated in NiTi shape memory alloys (SMAs) by using laser powder bed fusion technology. The compression experiment result indicates that the shape recovery ratio is as high as 94% even when the compression strain is over 80%. Additionally, the platform strain reaches as high as 66%, offering high-level specific energy absorption, i.e., 213.02 J/g. The obtained results are of great significance for basic research and engineering applications of energy-absorbing structures with high deformation recovery ratios.

The role of flexible polymer composite materials properties in energy absorption of three-dimensional auxetic lattice structures

In this work, the ability of lattice structures with 3D periodic auxetic structure to absorb energy have been investigated. The lattice structures were printed using the FDM method from five types of filaments characterized by different strength, plasticity, and viscoelasticity ratios. The mechanical properties of the filaments were determined by tensile, hardness and impact tests. Quasi-static cyclic tests were used to investigate the viscoelastic behavior. The energy absorption ability of lattice structures was determined by compression tests. It has been established that TPU and nylon fibers are inferior to PLA filaments in terms of strength and hardness, but significantly surpass them in terms of the ability to withstand shock loads and damping properties. Significant differences in the mechanisms of strain energy absorption depending on the properties of the initial filaments have been demonstrated. PLA stuctures exhibit high energy values (0.06 – 0.12 J/cm3), but they are brittle and unable to recover their shape. TPU filaments provide the ability to restore shape, but absorb significantly less energy (0.011 J/cm3). Nylon fibers are less durable than PLA, but have a higher absorption energy (0.136 J/cm3) and are more prone to shape recovery. In further optimization of the structure and properties of 3D structures, it is advisable to use combined lattices consisting of materials with different plasticity and damping ability, which is proposed to be combined by mechanical behavior.

A novel auxetic 3D lattice structure for enhancing energy absorption

The auxetic lattice structures usually have excellent energy absorption characteristics since their failed part can resist crushing loads continuously. However, their platform stress is relatively lower and shorter than some conventional energy-absorbing lattice structures. A novel kind of auxetic three-dimensional (3D) lattice structure is proposed to overcome their shortcoming and improve energy absorption capacity. The proposed lattice structure is named as re-entrant-TPMS hexagonal (RTH), which consists of triply periodic minimal surface (TPMS) and 3D truss-based re-entrant hexagonal (RH) structures. The finite element (FE) method is employed to analyze the crashworthiness and Poisson’s ratio of RTH lattice structures, and the accuracy of the FE models is validated by comparing the existing experimental and theoretical results of the two sub-structures, respectively. The effect of various structural parameters on the energy absorption and negative Poisson’s ratio (NPR) effect of the RTH lattice structure is investigated to select the structure with better mechanical performance. The mechanism studies confirm that the platform stress is higher and longer compared to the 3D RH lattice structure. The NPR effect is also essentially consistent and accompanied by a stable shrinkage deformation due to the synergistic effect among the sub-structures. The proposed RTH lattice structure has potential applications in the crashworthiness design of carrier equipment for resisting more complex impact loads.

Synthesis of 2D type A molecular sieves by alkaline removal of natural kaolin

Type A molecular sieves have been extensively employed in various fields. It is noteworthy that the direct synthesis of type A molecular sieves from natural kaolin is a common practice among researchers. Traditional type A molecular sieves are characterized by a three-dimensional cubic lattice structure. In this study, our objective is to facilitate the transformation of type A molecular sieves into a two-dimensional layered configuration by employing a two-dimensional layered material as a templating agent. In this research, natural kaolin serves as the primary source material. To eliminate impurities including quartz, illite, and dolomite, an alkali-based solvent extraction method is employed, yielding amorphous silicon and aluminum compounds. Subsequently, a graphene-based templating agent is introduced, and a hydrothermal synthesis process is employed to fabricate two-dimensional type A molecular sieves. The method described herein yields two-dimensional layered type A molecular sieves with a crystallinity exceeding 90%, thereby resulting in a specific surface area that is approximately 11-fold greater compared to their three-dimensional type A counterparts. The applicability of this methodology can be extended to the valorization of low-grade natural mineral resources, optimizing their utility. Furthermore, the approach presented herein for the synthesis of two-dimensional molecular sieves is of a universal nature, offering valuable insights that can serve as a reference for the synthesis of various other categories of two-dimensional molecular sieves.

Frequency dependent effective modulus of square grid lattice using spectral element method

A spectral element method-based formulation is developed to obtain the frequency-dependent effective Young’s and shear modulus of a two-dimensional square grid lattice. The methodology presented in this work is a simplified approach to obtain effective parameters. The lattice is assumed to be constituted of Euler–Bernoulli beam elements which are arranged in a specific order to obtain the said geometry. Spectral element formulation of the beam element considering axial and flexural deformation is presented, which in due course is employed to obtain the global spectral element matrix of the unit cell. A detailed procedure to obtain the frequency-dependent stiffness matrix of the unit cell is presented on which proper boundary conditions are applied using specific transformation matrices for each case. The frequency-dependent properties are also calculated using the software package COMSOL Multiphysics to validate the results. Frequency responses of the unit cell are obtained using the proposed methodology as well as the software package, and the results are compared. It is observed that the proposed methodology predicts the peaks at nearly the same frequency range as obtained through the finite element solution obtained in COMSOL Multiphysics. Finally, the results are presented which show the frequency-dependent effective parameters for the unit cell. The methodology presented here opens up a new way to calculate the effective properties of two-dimensional lattice structures and with some modifications can also be extended to three-dimensional lattice structures.

Compressive properties of novel hybrid-dimensional gyroid lattice structure

This work proposed a novel hybrid method based on the three-dimensional gyroid lattice structure and two-dimensional honeycomb lattice structure. We choose a commercial stereolithography (SLA) printer to fabricate the lattice samples with 405 nm photosensitive resin material. Axial quasi-static compression is selected to test the mechanical properties. According to the experimental results, the multiple deformation behaviors and reinforcement of stress response at the post-plateau stage are observed in hybrid lattice samples. By the proportion of substructure, the compressive strength and energy absorption of the hybrid-dimensional lattice can be tailored, which is suitable to act as an effective energy absorber for various applications.

Three-Dimensional Lattice Structure to Reduce Parasitic Inductance for WBG Power Semiconductor-Based Converters

Wide bandgap (WBG) power semiconductors can achieve high efficiency and power density due to their low on-resistance and fast switching speeds. However, the fast-switching speed induces voltage to the parasitic inductance in the circuit, causing a significant overshoot in the drain-source voltage of the devices and the ringing of the drain current due to resonance with the parasitic capacitance. Thus, minimizing parasitic inductance is necessary for driving WBG power semiconductors in a stable manner. This paper proposes a three-dimensional lattice structure that reduces parasitic inductance through horizontal and vertical magnetic flux cancellations within a printed circuit board (PCB). The relationship between the magnetic flux cancellation and the parasitic inductance is analyzed, and the magnetic flux cancellation in the proposed structure is described. In addition, a practical PCB layout design procedure based on the proposed structure is provided. Simulation results demonstrate a 55.8% reduction in parasitic inductance, and experimental results show reduced overshoot and ringing at the switching transient, resulting in a 26% reduction in switching loss. As a result, the proposed method can improve the efficiency and stability of WBG device-based power converters.

A sinusoidal beam lattice structure with negative Poisson's ratio property

In this study, a three-dimensional (3D) beam lattice structure (BLS) with negative Poisson's ratio (NPR) effect is proposed by applying sinusoid-shaped beams. The finite element model of the BLS is established, and its sample is manufactured through selective laser sintering (SLS) technology. The axial compression experiment and simulation are performed to investigate the compression characteristics of BLS. BLS bends to one side in the later stages of compression. It can be concluded that the BLS possess strong NPR effect and excellent energy absorption performance. In addition, the effects of compression direction, amplitude and wavenumber on the compression characteristics of BLS are further analyzed. These BLSs exhibit significant anisotropic features, and they often show the deformation modes of S- and <-shaped. When the loading directions are z- and y-axes, these BLSs have more obvious NPR effect and better energy absorption characteristics compared with those of the x-axis. In addition, it is also found that the minimum values of PR (MPR) of these BLSs often appear in the initial stages of compression, and the maximum values of Poisson's ratio (PR) usually appear around the end of compression. In summary, the BLS has excellent mechanical properties and broad application prospects.

Structure genome based machine learning method for woven lattice structures

As a type of lightweight composite material, three-dimensional (3D) woven lattice structure (WLS) has been extensively applied in various fields. It is extremely significant to investigate its mechanical properties. Complex structure parameters make property prediction a great challenge. In this research, structure genome (SG) of 3D WLSs was defined with four SG characteristics, including the panel thickness, the meridional and zonal angles of fiber pillars and the mass fraction of the resin. A SG-based deep neural network method was conducted to predict the fundamental mechanical properties, including the flatwise compression strength and the out-of-plane elastic modulus. The effectiveness of the proposed method was verified by comparing the experimental data with the predictions. The results show that the prediction accuracy is more than 90% for most parts of the testing set. Through sensitivity analysis, the panel thickness and the mass fraction of the resin were identified as the most dominant parameter characteristics, which determine the overall performance. The method provides guidance for structure design of 3D WLSs.

Photonic features of blue phase liquid crystals under curved confinement.

Blue phase (BP) liquid crystals represent a fascinating state of soft matter that showcases unique optical and electro-optical properties. Existing between chiral nematic and isotropic phases, BPs are characterized by a three-dimensional cubic lattice structure resulting in selective Bragg reflections of light and consequent vivid structural colors. However, the practical realization of these material systems is hampered by their narrow thermal stability and multi-domain crystalline nature. This feature article provides an overview of the efforts devoted to stabilizing these phases and creating monodomain structures. In particular, it delves into the complex relationship between geometrical confinement, induced curvature, and the structural stability and photonic features of BPs. Understanding the interaction of curved confinement and structural stability of BPs proves crucially important for the integration of these materials into flexible and miniaturized devices. By shedding light on these critical aspects, this feature review aims to highlight the significance of understanding the coupling effects of physical and mechanical forces on the structural stability of these systems, which can pave the way for the development of efficient and practical devices based on BP liquid crystals.

Skeleton-Based Volumetric Parameterizations for Lattice Structures

Lattice structures with excellent physical properties have attracted great research interest. In this paper, a novel volume parametric modeling method based on the skeleton model is proposed for the construction of three-dimensional lattice structures. The skeleton model is divided into three types of nodes. And the corresponding algorithms are utilized to construct diverse types of volume parametric nodes. The unit-cell is assembled with distinct nodes according to the geometric features. The final lattice structure is created by the periodic arrangement of unit-cells. Several different types of volume parametric lattice structures are constructed to prove the stability and applicability of the proposed method. The quality is assessed in terms of the value of the Jacobian matrix. Moreover, the volume parametric lattice structures are tested with the isogeometric analysis to verify the feasibility of integration of modeling and simulation.

Development and Implementation of Element Deletion Algorithm into an Open-Source Software Based on the Fracture Locus of Materials

An accurate fracture simulation is often associated with how reliably the material model is represented. Hence, many models dealing with the calibration of ductile damage of materials have already been developed to predict failure initiation. Nevertheless, the challenge remains in obtaining an accurate representation of the fracture growth. Herein, an element deletion algorithm is developed and implemented into finite element open-source software. The deleted elements are replaced by new cells made of a virtual low-stiffness material. To better visualize the failure progression, the final model excludes these virtual cells from the representation. The functionality of the algorithm is tested through a series of two-dimensional simulations on three different geometries with a well-known behavior under uniaxial tension. Moreover, the failure response of a three-dimensional lattice structure is numerically investigated and compared against experimental data. The results of the two-dimensional simulations showed the capability of the algorithm to predict the onset of failure, crack nucleation, and fracture growth. Similarly, the onset and the initial fracture region were accurately captured in the three-dimensional case, with some convergence issues that prevent the visualization of the fracture growth. Overall, the results are encouraging, and the algorithm can be improved to introduce other computational functionalities.

Experimental investigation and numerical modeling of laser powder bed fusion process-induced angle-dependent defects in strut-based lattice structure

The emergence of additive manufacturing technology has enabled the fabrication of advanced structures with intricate geometric topologies. However, additive manufacturing induces geometric defects in as-printed structures which may result in deviation from the parent material’s properties. The defects and impaired material properties greatly influence the performance of the fabricated structure. In this paper, the effect of build angle is investigated. The angle-dependency for the geometric defect distribution characteristics is verified through X-ray tomography. The mathematical relationship between the parent material’s properties and the build angle is established. A numerical model is developed for predicting the mechanical performance of laser powder bed fusion fabricated lattice structures proposed by using the experimental results. The positioning geometric defects are introduced into this model to achieve higher predicting accuracy. This work proposes a reliable and low-cost numerical analysis method based on the angle dependence and helps in predicting the mechanical performance of additive-manufactured complex three-dimensional lattice structures.

Influence of microstructure on stainless steel 316L lattice structures fabricated by electron beam and laser powder bed fusion

In this work, three-dimensional stainless steel 316L re-entrant lattice structures were fabricated by two mainstream powder bed fusion (PBF) techniques, namely electron beam PBF (EB-PBF) and laser PBF (L-PBF). Different grain morphology and crystallographic textures were found in the EB-PBF and L-PBF samples, which significantly influenced their mechanical properties through microscopic deformation. The EB-PBF and L-PBF samples achieved energy absorption capacities of 627.4 mJ/mm3 and 834.8 mJ/mm3, respectively, at a lattice relative density of ∼24%. The EB-PBF sample exhibited equiaxed and elongated grains, while elongated grains were primarily observed in the L-PBF sample. The dominant deformation mechanism of the EB-PBF sample was obtained through dislocation. In contrast, the dislocations trapped inside the solidification cellular walls and deformation-induced twinning were the dominant deformation mechanisms for the L-PBF sample, which contributed to its superior compressive strength and energy absorption capacities. This work provides insights into the enhancement of the mechanical properties of the additively manufactured metallic lattice structures through microstructural control.

Elastic Instability of Cubic Blue Phase Nano Crystals in Curved Shells.

Many crystallization processes, including biomineralization and ice-freezing, occur in small and curved volumes, where surface curvature can strain the crystal, leading to unusual configurations and defect formation. The role of curvature on crystallization, however, remains poorly understood. Here, we study the crystallization of blue phase (BP) liquid crystals under curved confinement, which provides insights into the mechanism by which BPs reconfigure their three-dimensional lattice structure to adapt to curvature. BPs are a three-dimensional assembly of high-chirality liquid crystal molecules arranged into body-centered (BPI) or simple cubic (BPII) symmetries. BPs with submicrometer cubic-crystalline lattices exhibit tunable Bragg reflection and submillisecond response time to external stimuli such as an electric field, making them attractive for advanced photonic materials. In this work, we have systematically studied BPs confined in spherical shells with well-defined curvature and boundary conditions. The optical behavior of shells has also been examined at room temperature, where the cholesteric structure forms. In the cholesteric phase, perpendicular anchoring generates focal conic domains on the shell's surface, which transition into stripe patterns as the degree of curvature increases. Our results demonstrate that both higher degrees of curvature and strong spatial confinement destabilize BPI and reconfigure that phase to adopt the structure and optical features of BPII. We also show that the coupling of curvature and confinement nucleates skyrmions at greater thicknesses than those observed for a flat geometry. These findings are particularly important for integrating BPs into miniaturized and curved/flexible devices, including flexible displays, wearable sensors, and smart fabrics.

Multifunctional 3D lattice metamaterials for vibration mitigation and energy absorption

Complex engineering applications have created an increasing demand for engineering structures or materials with multiple desired properties. In this context, metamaterials endowed with multifunctionalities through their structural configuration show unique advantages over traditional materials. Here, we present a novel three-dimensional lattice structure with simultaneous vibration mitigation and energy absorption capabilities. The results of numerical simulations and experimental tests demonstrate that the proposed metastructure is capable of attenuating low-frequency elastic waves through local resonance and absorbing impact energy through buckling deformation. Importantly, the local resonance is achieved by introducing the lightweight struts rather than additional heavy masses. Moreover, a functionally graded strategy is implemented to further enhance the vibration mitigation and energy absorption performance of the lattice metamaterial. The findings obtained in this study suggest a promising pathway for the development of multifunctional metamaterials for various specific applications.

On impact behaviors of 3D concave structures with negative Poisson’s ratio

Lattice structures with high mechanical properties and lightweight performance attracted increasing attention to the application of automotive, railway vehicle, and aerospace industries. This work developed a novel three-dimensional concave lattice structure using a hyper-elastic soft photopolymer via the digital light processing technique. The axial low-velocity impact behaviors of the proposed structures were investigated by a drop hammer machine and numerical simulation. The results showed that the novel 3D concave structures could present continuous auxetic behaviors with large negative Poisson’s ratios. The structural design parameters such as concave angle and thickness had significant effects on Poisson’s ratio and energy absorption. Specifically, the structures with concave angles from 10° to 20° and with thicknesses from 0.5 mm to 1.0 mm presented the higher negative Poisson’s ratio. The highest negative Poisson’s ratio of −0.86 was obtained. This work offered a new insight into designing novel meta-lattice structures with improved impact resistance.

Multi-scale collaborative optimization of lattice structures using laser additive manufacturing

In the present work, an effective and efficient design approach is proposed to obtain a three-dimensional multi-scale graded lattice structure by virtue of multiple control parameters via density-based topology optimization. To balance the computational accuracy and cost, a Parameterized Interpolation of Lattice Structure (PILS) model was established, and the math formula combined two novel designing parameters: relative density at macro-scale and aspect ratio at micro-scale. A multinomial function was employed to describe the explicit association between control parameters and equivalent elastic constants with regard to relative density and aspect ratio, which avoided tedious homogenization computation burden in the structural optimization process. Consequently, the multi-scale collaborative design approach could optimize the macro material density distribution and the micro cell topology in an integrated manner. Numerical examples with respect to compliance optimization were offered to validate the benefits of the proposed approach. Finally, the quasi-static and dynamic compression tests were respectively implemented by universal testing machine and Split Hopkinson Pressure Bar (SHPB) system on lattice structures manufactured by laser powder bed fusion (LPBF). The outcomes reveal that graded lattice structures exhibit remarkably improved load-bearing performance than the uniform lattice structures.

Regenerative Topology Optimization of Fine Lattice Structures.

We present a generative approach for creating three-dimensional lattice structures optimized for mass and deflection composed of thousands of one-dimensional strut primitives. Our approach draws inspiration from topology optimization principles. The proposed method iteratively determines unnecessary lattice struts through stress analysis, erodes those struts, and then randomly generates new struts across the entire structure. The objects resulting from this distributed optimization technique demonstrate high strength-to-weight ratios that are at par with state-of-the-art topology optimization approaches, but are qualitatively very different. We use a dynamics simulator that allows optimization of structures subject to dynamic load cases, such as vibrating structures and robotic components. Because optimization is performed simultaneously with simulation, the process scales efficiently on massively parallel graphics processing units. The intricate nature of the output lattices contributes to a new class of objects intended specifically for additive manufacturing. Our work contributes a highly parallel simulation method and simultaneous algorithm for analyzing and optimizing lattices with thousands of struts. In this study, we validate multiple versions of our algorithm across sample load cases, to show its potential for creating high-resolution objects with implicit optimized microstructural patterns.

Effect of Architected Structural Members on the Viscoelastic Response of 3D Printed Simple Cubic Lattice Structures.

Three-dimensional printed polymeric lattice structures have recently gained interests in several engineering applications owing to their excellent properties such as low-density, energy absorption, strength-to-weight ratio, and damping performance. Three-dimensional (3D) lattice structure properties are governed by the topology of the microstructure and the base material that can be tailored to meet the application requirement. In this study, the effect of architected structural member geometry and base material on the viscoelastic response of 3D printed lattice structure has been investigated. The simple cubic lattice structures based on plate-, truss-, and shell-type structural members were used to describe the topology of the cellular solid. The proposed lattice structures were fabricated with two materials, i.e., PLA and ABS using the material extrusion (MEX) process. The quasi-static compression response of lattice structures was investigated, and mechanical properties were obtained. Then, the creep, relaxation and cyclic viscoelastic response of the lattice structure were characterized. Both material and topologies were observed to affect the mechanical properties and time-dependent behavior of lattice structure. Plate-based lattices were found to possess highest stiffness, while the highest viscoelastic behavior belongs to shell-based lattices. Among the studied lattice structures, we found that the plate-lattice is the best candidate to use as a creep-resistant LS and shell-based lattice is ideal for damping applications under quasi-static loading conditions. The proposed analysis approach is a step forward toward understanding the viscoelastic tolerance design of lattice structures.