Three-dimensional Lattice Structure Research Articles

Design of vibrational filters based on 3D lattice material elongated structure

This study examines the potential of elongated periodic three-dimensional lattice structures for the design of vibration filters using so-called absolute band gaps. These filters are generally obtained by modifying the total stiffness of the structure, which decreases the propagation velocity of all wave polarisations. With a view to optimisation, we are implementing an original structure consisting of interconnected 3D beams with a sinusoidal accordion shape to control the speed of longitudinal waves. In addition, a central junction in the shape of a deformed cross controls the speed of transverse waves. To calculate the propagation of elastic waves in such structures, we use spectral element methods that take into account the longitudinal, torsional and bending motions of three-dimensional beams. The dispersion curves are obtained by applying the Floquet-Bloch periodicity conditions. They are analysed by a detailed study of the wave motion and polarisation. Finally, the geometrical parameters of the lattice cell are optimised using a genetic algorithm to generate the widest absolute band gap at the lowest frequency.

Bio-Inspired Curved-Elliptical Lattice Structures for Enhanced Mechanical Performance and Deformation Stability.

Lattice structures, characterized by their lightweight nature, high specific mechanical properties, and high design flexibility, have found widespread applications in fields such as aerospace and automotive engineering. However, the lightweight design of lattice structures often presents a trade-off between strength and stiffness. To tackle this issue, a bio-inspired curved-elliptical (BCE) lattice is proposed to enhance the mechanical performance and deformation stability of three-dimensional lattice structures. BCE lattice specimens with different parameters were fabricated using selective laser melting (SLM) technology, followed by quasi-static compression tests. Finite element (FE) numerical simulations were also carried out for validation. The results demonstrate that the proposed BCE lattice structures exhibit stronger mechanical performance and more stable deformation modes that can be adjusted through parameter tuning. Specifically, by adjusting the design parameters, the BCE lattice structure can exhibit a bending-dominated delocalized deformation mode, avoiding catastrophic collapse during deformation. The specific energy absorption (SEA) can reach 24.6 J/g at a relative density of only 8%, with enhancements of 48.5% and 297.6% compared with the traditional energy-absorbing lattices Octet and body-center cubic (BCC), respectively. Moreover, the crushing force efficiency (CFE) of the BCE lattice structure surpasses those of Octet and BCC by 34.9% and 15.8%, respectively. Through a parametric study of the influence of the number of peaks N and the curve amplitude A on the compression performance of the BCE lattice structure, the compression deformation mechanism is further analyzed. The results indicate that the curve amplitude A and the number of peaks N have significant impacts on the deformation mode of the BCE lattice. By adjusting the parameters N and A, a structure with a combination of high energy absorption, high stiffness, and strong fracture resistance can be obtained, integrating the advantages of tensile-dominated and bending-dominated lattice structures.

Designing three-dimensional lattice structures with anticipated properties through a deep learning method

Lattice structures have been a hot topic recently owing to their superior mechanical properties, which are significantly influenced by the unit cell structure. By leveraging the power of deep learning, inverse design can be conducted on the unit cell structure based on the mechanical properties of its lattice structure. Assisted by deep learning, this study introduces a novel data-driven approach to design three-dimensional (3D) unit cells for lattice structures with anticipated properties. The approach can be efficiently and accurately applied to various unit cell structures. An auto-encoder is trained to extract the geometric features from unit cell point clouds. The effective mechanical properties of the lattice structures are calculated by combining the homogenization method and the finite element method. Subsequently, a mapping relationship between mechanical properties and geometric features is established through the multi-layer perceptron neural network. The models are ultimately employed to design 3D unit cells given anticipated properties of lattice structures. The results show that the mechanical properties of the generated unit cells satisfy the anticipated values. The applications of proposed method are demonstrated in orthopedic implants, new hybrid unit cells, and functionally gradient structures. Furthermore, the method can be extended to unit cell design across diverse domains.

Efficacy of auxetic lattice structured shoe sole in advancing footwear comfort-From the perspective of plantar pressure and contact area.

Designing footwear for comfort is vital for preventing foot injuries and promoting foot health. This study explores the impact of auxetic structured shoe soles on plantar biomechanics and comfort, motivated by the integration of 3D printing in footwear production and the superior mechanical properties of auxetic designs. The shoe sole designs proposed in this study are based on a three-dimensional re-entrant auxetic lattice structure, orthogonally composed of re-entrant hexagonal honeycombs with internal angles less than 90 degrees. Materials fabricated using this lattice structure exhibit the characteristic of a negative Poisson's ratio, displaying lateral expansion under tension and densification under compression. The study conducted a comparative experiment among three different lattice structured (auxetic 60°, auxetic 75° and non-auxetic 90°) thermoplastic polyurethane (TPU) shoe soles and conventional polyurethane (PU) shoe sole through pedobarographic measurements and comfort rating under walking and running conditions. The study obtained peak plantar pressures (PPPs) and contact area across seven plantar regions of each shoe sole and analyzed the correlation between these biomechanical parameters and subjective comfort. Compared to non-auxetic shoe soles, auxetic structured shoe soles reduced PPPs across various foot regions and increased contact area. The Auxetic 60°, which had the highest comfort ratings, significantly lowered peak pressures and increased contact area compared to PU shoe sole. Correlation analysis showed that peak pressures in specific foot regions (hallux, second metatarsal head, and hindfoot when walking; second metatarsal head, third to fifth metatarsal head, midfoot, and hindfoot when running) were related to comfort. Furthermore, the contact area in all foot regions was significantly associated with comfort, regardless of the motion states. The pressure-relief performance and conformability of the auxetic lattice structure in the shoe sole contribute to enhancing footwear comfort. The insights provided guide designers in developing footwear focused on foot health and comfort using auxetic structures.

Strain to shine: stretching-induced three-dimensional symmetries in nanoparticle-assembled photonic crystals

Stretching elastic materials containing nanoparticle lattices is common in research and industrial settings, yet our knowledge of the deformation process remains limited. Understanding how such lattices reconfigure is critically important, as changes in microstructure lead to significant alterations in their performance. This understanding has been extremely difficult to achieve due to a lack of fundamental rules governing the rearrangements. Our study elucidates the physical processes and underlying mechanisms of three-dimensional lattice transformations in a polymeric photonic crystal from 0% to over 200% strain during uniaxial stretching. Corroborated by comprehensive experimental characterizations, we present analytical models that precisely predict both the three-dimensional lattice structures and the macroscale deformations throughout the stretching process. These models reveal how the nanoparticle lattice and matrix polymer jointly determine the resultant structures, which breaks the original structural symmetry and profoundly changes the dispersion of photonic bandgaps. Stretching induces shifting of the main pseudogap structure out from the 1st Brillouin zone and the merging of different symmetry points. Evolutions of multiple photonic bandgaps reveal potential optical singularities shifting with strain. This work sets a new benchmark for the reconfiguration of soft material structures and may lay the groundwork for the study of stretchable three-dimensional topological photonic crystals.

Multiscale topology optimization for the design of spatially-varying three-dimensional lattice structure

This paper introduces three dimensional (3D) topology optimization specifically tailored for designing spatially-varying primitive-cubic (CP) type lattice structures. The developed design process consists of three steps: pre-processing, main processing, and post-processing. In the pre-processing step, a surrogate model between lattice geometry variables and effective elasticity tensor is constructed using an artificial neural network. This surrogate model is essential because it enables the quick calculation of the effective elasticity tensor of lattice microstructure. In the subsequent main processing step, multiscale topology optimization is performed. During this step, lattice microstructure size and rotation design variables are optimized together with the macrostructure density design variables. Macrostructures are designed using a well-established three-field density scheme with a SIMP formulation. Formulations for spatially-varying 3D lattice microstructure are newly developed based on a unit quaternion rotation representation scheme. In the final post-processing step, a spatially-varying microstructure is restored using a de-homogenization scheme, newly developed particularly for the primitive-cubic (CP) type 3D lattice structures. The effectiveness and robustness of the proposed formulations are validated through three design examples for the compliance minimization problem. Moreover, a designed lattice structure is fabricated using an additive manufacturing machine.

Effect of scanning tracks on the contour morphology and dimensional accuracy of the fine structure manufactured by laser powder bed fusion

Surface quality and dimension accuracy are severe challenges encountered by fine structures like three-dimensional lattice structures manufactured by laser powder bed fusion, which seriously affect the mechanical and functional performance. Previous research paid close attention to the surface roughness but neglected the contour morphology. For the fine features with curved surfaces, scanning tracks significantly influence the contour morphology and distort the profile. Therefore, to demonstrate the influence of scanning parameters, such as hatch spacing, orthometric remelting scanning, and laser power on the contour morphology, the cross sections of vertical cylindrical struts were examined based on the image analysis technique. The effect mechanism of scanning parameters was explored experimentally and numerically. AlSi10Mg as feedstock was used in this work. The results show that scanning tracks have an important effect on the profile of the cross-section and dimension accuracy. Affected by the deflection and resolution of tracks, the geometry morphology of part will distort. When the hatch spacing increases from 100 μm to 150 μm, the surface quality will deteriorate, and the circularity and aspect ratio of the contour will further deviate from the designed model. Keeping the hatch spacing of 150 μm unchanged, orthometric remelting scanning can improve the contour tolerance slightly. Among all those schemes, increasing laser power from 200W to 320 W is proved to be the most effective method to improve the contour morphology, and this scheme also contributes to the stability of print quality. However, increasing laser power will cause serious deviation of size due to bigger molten pool size, so it is recommended that larger laser power should be matched with reasonable settings of border offset.

Tailoring 3D Star-Shaped Auxetic Structures for Enhanced Mechanical Performance

Auxetic lattice structures are three-dimensionally designed intricately repeating units with multifunctionality in three-dimensional space, especially with the emergence of additive manufacturing (AM) technologies. In aerospace applications, these structures have potential for use in high-performance lightweight components, contributing to enhanced efficiency. This paper investigates the design, numerical simulation, manufacturing, and testing of three-dimensional (3D) star-shaped lattice structures with tailored mechanical properties. Finite element analysis (FEA) was employed to examine the effect of a lattice unit’s vertex angle and strut diameter on the lattice structure’s Poisson’s ratio and effective elastic modulus. The strut diameter was altered from 0.2 to 1 mm, while the star-shaped vertex angle was adjusted from 15 to 90 degrees. Laser powder bed fusion (LPBF), an AM technique, was employed to experimentally fabricate 3D star-shaped honeycomb structures made of Ti6Al4V alloy, which were then subjected to compression testing to verify the modelling results. The effective elastic modulus was shown to decrease when increasing the vertex angle or decreasing the strut diameter, while the Poisson’s ratio had a complex behaviour depending on the geometrical characteristics of the structure. By tailoring the unit vertex angle and strut diameter, the printed structures exhibited negative, zero, and positive Poisson’s ratios, making them applicable across a wide range of aerospace components such as impact absorption systems, aircraft wings, fuselage sections, landing gear, and engine mounts. This optimization will support the growing demand for lightweight structures across the aerospace sector.

A case study of depolymerization in silicates: Melting of quartz and zircon crystallization at high pressure

The experimental study of depolymerization reaction SiO2 + ZrO2 → ZrSiO4 reveals that melting of quartz and crystallization of zircon in the presence of water increases at high pressure. The melting rate of quartz is identified as the rate-determining step of the reaction. In highly polymerized silicates, Si-O-Si bond angles are subject to alteration under the influence of pressure. This phenomenon is particularly noticeable within the three-dimensional lattice structure of quartz, where each corner of the tetrahedra is shared. Theoretical analysis of the Si-O-Si bond angle bending demonstrates a change in oxygen hybridization from sp to sp2, favoring larger Si-O distances. The sp2 hybridization in bridging oxygen promotes acid attack by hydrogen ions of water, resulting in SiO bond heterolysis in quartz. The depolymerization from tectosilicates to nesosilicates leads to an increase in oxygen “size” and polarizability, as well of closer packing of oxygen atoms. This change in behavior and packing of oxygens is further illustrated by the high-pressure-driven transition from tridymite to stishovite. Additionally, the impact of network-modifying elements on the structure of polymerized silicates is investigated; particularly those acting as electron donors, which lengthen Si-O distances in quartz. The findings are discussed in relation to key topics in Earth Sciences, including the crystal chemical basis of the Bowen's reaction series, the “metallization” in rocky planets and the structural controls of hydrous and dry melting in silicates.

Extended multiscale FEM-based concurrent optimization of three-dimensional graded lattice structures with multiple microstructure configurations

In this work, a novel concurrent design method for three-dimensional graded lattice structures considering multiple microstructure configurations is proposed. Firstly, the Multiple Variable Cutting (M-VCUT) level set method is employed to represent the geometry of lattice microstructures and define the optimization parameters. Then, the extended multiscale finite element method (EMsFEM) is implemented for calculating the equivalent stiffness matrices of microstructures in offline form. Compared with the traditional homogenization-based multiscale approaches, the proposed method eliminates the scale separation assumptions and takes into account the coupling effects in different directions of materials. In addition, a data-driven method and a parallel computing approach are integrated together so that computational efficiency can be greatly improved. After the iteration process, the optimized full-scale graded structures are reconstructed using interpolation technology to generate well-connected microstructures in neighboring cells. Finally, several 3D numerical examples are utilized to validate the effectiveness of the proposed method, where multiple lattice microstructure configurations are considered, including truss-lattices and plate-lattices.

A Review of Functional Composite Materials using PSZ-based Siliconnitride Preceramic Polymer

Abstract: The silicon-nitride ceramics gain a lot of interest for applications under severe conditions due to their thermal stability, thermal shock resistance and chemical stability arising from the threedimensional lattice structure. The silicon-nitride ceramics can be synthesized from silicon-nitride preceramic polymers based on polysilazane (PSZ), as the ability to fabricate ceramic components of specific geometries is difficult to obtain otherwise. This review systematically summarized the applications of PSZ-based silicon-nitride preceramic polymers in the processing of functional materials. A particular focus is made on the relation between the chemical structure of polymer and the properties of the polymer-derived ceramic. The tailored properties as well as characteristics of ceramic are highlighted and the trend of nowadays research for the future evolution of silicon-nitride preceramic polymer was proposed.

Experimental, analytical, and numerical studies of the energy absorption capacity of bi-material lattice structures based on quadrilateral bipyramid unit cell

The present study investigates the mechanical performance and energy absorption capacity of bi-material 3D lattice structures via experimental, analytical, and numerical approaches. The analytical model has been developed to obtain the effective parameters in energy absorption, such as equivalent elastic modulus and yield stress. Analytical relations based on hyperbolic shear deformation beam theory were extended to calculate the mechanical properties of an extracted unit cell from the lattice structure subjected to applied loads and appropriate boundary conditions. Then, experimental and nonlinear numerical studies have been conducted to analyze the energy absorption properties of the bi-material lattice structure. Quasi-static compression tests were conducted to analyze this lattice structure's mechanical properties and energy absorption capacity. As the numerical study, the elastic-plastic damage behavior was implemented in finite element analyses to examine the nonlinear response of considered structures. The obtained results reveal that the numerical models exhibit an acceptable prediction. According to the results, not only does the use of hybrid structures provide more energy absorption and improve mechanical properties, but also, in comparison to the usual lattice structures fabricated with a single material, the rational combination of two materials makes the bi-material three-dimensional lattice structure to inherit the optimum energy absorption and stiffness.

A multifunctional three-dimensional lattice material integrating auxeticity, negative compressibility and negative thermal expansion

This manuscript presents a pioneering three-dimensional lattice structure that can simultaneously exhibit negative Poisson's ratio (NPR), negative compressibility (NC), and negative thermal expansion (NTE). The coexistence of the three negative indexes, whether in natural materials or in artificial structures, is extremely rare. The lattice unit cell integrates an auxetic egg-rack structure with a non-auxetic cage-like structure. Analytical expressions for the elastic constants of the unit cell are derived by using Euler-Bernoulli beam theory and subsequently validated through finite element simulations. The analytical results show that the lattice exhibits not only NPR, but also NC in a direction or specific areas as well as NTE in a direction, certain areas, or even throughout the entire volume when appropriately tailored geometries and constituent materials are employed. Furthermore, parametric analysis revealed that these properties can be adjusted within a broader range, encompassing negative and positive values, enabling diverse combinations. Metamaterials that possess multiple and adjustable negative properties enable the development of multifunctional devices capable of adapting to mechanical loads, hydrostatic pressures, and temperature fluctuations.

Investigation of Anticancer Therapy Using pH-Sensitive Carbon Dots-Functionalized Doxorubicin in Cubosomes.

Cancer remains a highly lethal disease due to its elusive early detection, rapid spread, and significant side effects. Nanomedicine has emerged as a promising platform for drug delivery, diagnosis, and treatment monitoring. In particular, carbon dots (CDs), a type of fluorescent nanomaterial, offer excellent fluorescence properties and the ability to carry multiple drugs simultaneously through covalent bonding. In this work, CDs with carbonyl groups on the surface were prepared by aldol condensation and reacted with amine groups in the structure of doxorubicin (DOX) through Schiff base reaction to generate pH-responsive CDs-DOX. On the other hand, cubosomes with three-dimensional lattice structures formed by lipid bilayers have advantageous capabilities of encapsulating various hydrophilic, amphiphilic, and hydrophobic substances. The pH-responsive CDs-DOX are subsequently loaded into cubosomes to form an anticancer therapeutic nanosystem, CDs-DOX@cubosome. Leveraging the unique properties of CDs-DOX and cubosomes, our CDs-DOX@cubosome can enter tumor tissue through the enhanced permeation and retention effect first and conduct membrane fusion with tumor cells to intracellularly release CDs-DOX. Then, the imine bond in CDs-DOX breaks under acidic conditions within human cancer cell lines (HeLa and HepG-2 cells), releasing DOX and achieving enhanced treatment of tumors. Additionally, fluorescent CDs can synchronously achieve real-time in situ diagnosis of tumor tissue. We demonstrate that our CDs-DOX@cubosome works as an excellent drug delivery system with therapeutic efficiency enhancement to the tumor and reduced side effects.

Synergetic Adsorption of Dyes in Water by Three-Dimensional Graphene and Manganese Dioxide (PU@RGO@MnO2) Structures for Efficient Wastewater Purification

The improper discharge of industrial wastewater causes severe environmental pollution and the textile industry’s dye usage contributes significantly to industrial wastewater pollution. Hence, an effective method for removing the harmful substance methylene blue (MB) from dye wastewater is proposed. This method adopts a three-dimensional graphene composite material based on manganese dioxide (MnO2), named polyurethane@ reduced graphene oxide@ MnO2 (PU@RGO@MnO2). First, graphene is prepared with hydrazine hydrate as a reducing agent and polyurethane as a framework. MnO2 nanoparticles are synthesized by the reaction of potassium permanganate (KMnO4) with carbon. These nanoparticles are then loaded onto the three-dimensional framework to create the composite material. Finally, adsorption and removal experiments for MB are conducted to compare the performance of the composite material. The results indicate that the graphene based on the polyurethane framework exhibits favorable mechanical properties. The unique three-dimensional lattice structure provides abundant active sites for loading MnO2 nanoparticles, significantly increasing the contact area between the adsorbent and MB solution and thus improving the adsorbent utilization rate (reaching 94%). The nanoparticles synthesized through the reaction of KMnO4 with carbon effectively suppress the agglomeration phenomenon. Additionally, the introduction of dynamic adsorption and dynamic removal modes, aided by a water pump, substantially enhances the adsorption and removal rates, showcasing excellent performance. The research on a multi-porous three-dimensional structure holds significant practical value in water treatment, offering a new research direction for dye wastewater treatment.

Research of Superplastic Forming, Mechanical Properties, and Thermal Insulation Performance of Titanium Alloy 3D Lattice Structure

A physically constitutive model based on microstructure evolution was constructed to describe the coupling relationship between various macro and micro variations of TA32 titanium alloy in superplastic deformation. Then, a finite element analysis model was established to simulate and analyse the superplastic forming process of titanium alloy based on the physically constitutive model. The deformation characteristics, mechanical properties and thermal insulation performance of the three dimensional lattice structure were analysed and tested. The results show that the three-dimensional lattice structure of titanium alloy has good formability, excellent mechanical properties, and good thermal insulation performance, indicating that it is a promising load-bearing functional integrated structure.

Curve beam for strengthening the negative Poisson's ratio effect of rotating auxetic metamaterial: Experiments and simulations

This article described a three-dimensional lattice design method for customizing the negative Poisson’s ratio effect in a rotating rigid structure. By using bent beams as the basic building blocks of the lattice, a new class of curved beam rotating auxetic (CBRA) lattice was proposed. Through a combination of numerical simulations and experimental tests, the mechanical responses of representative three-dimensional auxetic lattice structures under compressive load were systematically studied, including Poisson’s ratio, energy absorption, and a multi-stage deformation mode that facilitated the tuning of mechanical properties. Additionally, the influence of structural geometric parameters on the elastic performance was discussed in detail. Unlike most rotating auxetic materials that could only achieve the negative Poisson’s ratio effect within a small strain range, the results demonstrated that the uniform Poisson’s ratio of the proposed three-dimensional lattice structure could achieve positive and negative adjustment within a strain range of 0–0.5. The design flexibility would contribute to making it a promising candidate for industrial and biomedical applications, such as scaffolds and skin grafts. The acceleration of the application of new three-dimensional expandable lattice structures in engineering applications made this system more versatile than similar non-graded systems.

Study on buckling behavior of multilayer pyramid lattice structures

Three-dimensional lattice structures with high specific strength, specific stiffness and low apparent density, are widely employed across multiple engineering fields. Under uniaxial compressive loading, the lattice structure may experience local buckling or global buckling. This paper conducted a systematic parametric study of the various factors affecting the buckling behavior of multilayer pyramid lattice structures to investigate the mechanism of the two main instability modes, local and global buckling. It was found that the critical buckling load increases with the increase in the size of the unit cell and decreases with the increase in the total height of the structure for the same relative density. As the relative density increases, the buckling resistance of the lattice structure increases. It is possible to examine various buckling modes by varying the geometrical properties of the pyramid unit cell (slenderness ratio, rod inclination angle, cross-sectional size of strut connection parts). Finally, numerical simulations were performed to calculate the yield strength and buckling strength of the lattice structure under uniaxial compression load, in order to estimate the threshold relative density for structural buckling and yield failure. The results demonstrated that buckling failure should be considered for aluminum alloy pyramid lattice when the relative density is below 4.07%. This study provides design criteria for lattice structures dominated by buckling and offers ideas for improving the buckling capacity of truss-type lattice structures.

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.