Periodic Lattice Research Articles

Pneumatic elastostatics of multi-functional inflatable lattices: realization of extreme specific stiffness with active modulation and deployability.

As a consequence of intense investigation on possible topologies of periodic lattices, the limit of specific elastic moduli that can be achieved solely through unit cell-level geometries in artificially engineered lattice-based materials has reached a point of saturation. There exists a robust rationale to involve more elementary-level mechanics for pushing such boundaries further to develop extreme lightweight multi-functional materials with adequate stiffness. We propose a novel class of inflatable lattice materials where the global-level stiffness can be derived based on a fundamentally different mechanics compared with conventional lattices having beam-like solid members, leading to extreme specific stiffness due to the presence of air in most of the lattice volume. Furthermore, such inflatable lattices would add multi-functionality in terms of on-demand performances such as compact storing, portability and deployment along with active stiffness modulation as a function of air pressure. We have developed an efficient unit cell-based analytical approach therein to characterize the effective elastic properties including the effect of non-rigid joints. The proposed inflatable lattices would open new frontiers in engineered materials and structures that will find critical applications in a range of technologically demanding industries such as aircraft structures, defence, soft robotics, space technologies, biomedical and various other mechanical systems.

Lattice basis reduction techniques

Lattice basis reduction techniques

Bandgap formation and chaos in periodic lattices with graded bistable resonators

Bandgap formation and chaos in periodic lattices with graded bistable resonators

A novel triple periodic minimal surface-like plate lattice and its data-driven optimization method for superior mechanical properties

Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment, along with the advances in additive manufacturing (AM) technologies. In this work, a novel design of plate lattice structures described by a parametric model is proposed to enrich the design space of plate lattice structures with high connectivity suitable for AM processes. The parametric model takes the basic unit of the triple periodic minimal surface (TPMS) lattice as a skeleton and adopts a set of generation parameters to determine the plate lattice structure with different topologies, which takes the advantages of both plate lattices for superior specific mechanical properties and TPMS lattices for high connectivity, and therefore is referred to as a TPMS-like plate lattice (TLPL). Furthermore, a data-driven shape optimization method is proposed to optimize the TLPL structure for maximum mechanical properties with or without the isotropic constraints. In this method, the genetic algorithm for the optimization is utilized for global search capability, and an artificial neural network (ANN) model for individual fitness estimation is integrated for high efficiency. A set of optimized TLPLs at different relative densities are experimentally validated by the selective laser melting (SLM) fabricated samples. It is confirmed that the optimized TLPLs could achieve elastic isotropy and have superior stiffness over other isotropic lattice structures.

Sustainable 3D printing with recycled tire rubber-based filaments: an investigation of process parameters and mechanical behaviour

PurposeThis study evaluates the potential of using the material extrusion (MEX) process for recycling waste tire rubber (WTR). By investigating the process parameters, mechanical behaviour and morphological characterisation of a thermoplastic polyurethane-waste tire rubber composite filament (TPU-WTR), this study aims to establish a framework for end-of-life tire (ELT) recycling using the MEX technology.Design/methodology/approachThe research assesses the impact of various process parameters on the mechanical properties of the TPU-WTR filament. Hysteresis analysis and Poisson’s ratio estimation are conducted to investigate the material’s behaviour. In addition, the compressive performance of diverse TPU-WTR triply periodic minimal surface lattices is explored to test the filament suitability for printing intricate structures.FindingsResults demonstrate the potential of the TPU-WTR filament in developing sustainable structures. The MEX process can, therefore, contribute to the recycling of WTR. Mechanical testing has provided insights into the influence of process parameters on the material behaviour, while investigating various lattice structures has challenged the material’s capabilities in printing complex topologies.Social implicationsThis research holds significant social implications addressing the growing environmental sustainability and waste management concerns. Developing 3D-printed sustainable structures using recycled materials reduces resource consumption and promotes responsible production practices for a more environmentally conscious society.Originality/valueThis study contributes to the field by showcasing the use of MEX technology for ELT recycling, particularly focusing on the TPU-WTR filament, presenting a novel approach to sustainable consumption and production aligned with the United Nations Sustainable Development Goal 12.

Compact gap solitons and compact edge states of exciton–polariton condensates with spin–orbit coupling in a one-dimensional flatband lattice

We propose that the compact gap solitons and compact edge states can be excited in a flatband of the incoherently-pumped exciton–polariton condensate under a one-dimensional periodic potential lattice. The combined effects of spin–orbit coupling and periodic potential depth on the flatband structures are investigated. Then how the compact gap solitons and edge states are localized and extended inside only a fraction of a single lattice site will be studied with varying pump strengths, pump spot-sizes as well as energy detuning.

Planar triangular lattice of the LuMgGaO4: Clustered site-occupancy and the upconversion luminescence of the co-doped Er,Yb ions

The ordered and stable structure of inorganic lattice is the basis of constructing high-efficiency rare earth activated fluorescence, solid-state laser or other optical materials. The mixed sensitized and activated rare earth ions usually keeps a uniform space-occupying and the energy transfer depends much on the doping concentration, while the aggregation of rare earth dopants in order is rare. In this work, a series of LuMgGaO4 phosphors were synthesized and the detail lattice parameters are analyzed through Vietveld refinement and the new CIF file is provided. The site-occupancy of Er3+, Yb3+ shows clustered features and the Er–Yb sublattice structure with various Yb/Er ratios were constructed on the basis of planar triangular lattice. The long-distance excitation energy migration to lattice or defects can be effectively inhibited in case of the hexagonal circle Er-6Yb sublattice, in which the most intense green/red UCL was obtained. All the results demonstrate the novelty of regulating ordered site-occupancy of rare earth ions on a compact planar triangular lattice with higher efficiency of energy migration, which will pave a way for developing phosphor-converted materials or laser materials with better performance.

Shape transformers for crashworthiness of additively manufactured engineering resin lattice structures: Experimental and numerical investigations

Cellular materials have superior specific properties (e.g., specific strength, stiffness, and energy absorption) as compared to their monolithic material counterparts. With rapid advancements in additive manufacturing technology, the uniquely complex geometry of these materials – particularly periodic lattices – can be easily reproduced for additional experimental research, characterization, and potential industrial applications. This work utilizes the idea of shape transformers – previously employed to describe the structural efficiency of beams subjected to bending – to define new strut-based lattices, whose struts do not have the typical solid, circular cross-section shape. Both experimental and numerical model results have shown that this design parameter can be utilized to manipulate the crashworthiness efficiency of lattice materials. It is found that designing with a square or a rectangular cross-section could increase the plateau stress by up to 52% while increasing the mass normalized specific energy absorption by up to 32%.

Manipulating the Generation of Photonic Moiré Lattices Using Plasmonic Metasurfaces.

The generation of moiré lattices by superimposing two identical sublattices at a specific twist angle has garnered significant attention owing to its potential applications, ranging from two-dimensional materials to manipulating light propagation. While macroscale moiré lattices have been widely studied, further developments in manipulating moiré lattices at the subwavelength scale would be crucial for miniaturizing and integrating platforms. Here, we propose a plasmonic metasurface design consisting of rotated nanoslits arranged within N + N' round apertures for generating focused moiré lattices. By introducing a spin-dependent geometric phase through the rotated nanoslits, an overall lens and spiral phase can be achieved, allowing each individual set of round apertures to generate a periodic lattice in the focal plane. Superimposing two sets of N and N' apertures at specific twist angles and varying phase differences allows for the superposition of two sublattices with different periods, leading to the formation of diverse moiré patterns. Our simulations and theoretical results demonstrate the feasibility of our proposed metasurface design. Due to their compactness and tunability, the utilization of metasurfaces in creating nanoscale photonic moiré lattices is anticipated to find extensive applications in integrated and on-chip optical systems.

Designer artificial chiral kagome lattice with tunable flat bands and topological boundary states

The kagome lattice is a well-known model system for the investigation of strong correlation and topological electronic phenomena due to the intrinsic flat band, magnetic frustration, etc. Introducing chirality into the kagome lattice would bring about new physics due to the unique symmetry, which is still yet to be fully explored. Here we report the investigation on a two-dimensional chiral kagome lattice utilizing tight binding band calculation and topological index analysis. It is found that the periodic chiral kagome lattice would bring about a robust zero-energy flat band. Furthermore, in the Su–Schrieffer–Heeger type dimer-/trimerized breathing chiral kagome lattice with particular edge terminations, topological corner states or metallic edge states would appear, implying new candidates for the second-order topological insulator. We also proposed the construction strategy for such lattices employing the scanning tunneling microscope atom manipulation technique.

Ultralight, strong, and self-reprogrammable mechanical metamaterials.

Versatile programmable materials have long been envisioned that can reconfigure themselves to adapt to changing use cases in adaptive infrastructure, space exploration, disaster response, and more. We introduce a robotic structural system as an implementation of programmable matter, with mechanical performance and scale on par with conventional high-performance materials and truss systems. Fiber-reinforced composite truss-like building blocks form strong, stiff, and lightweight lattice structures as mechanical metamaterials. Two types of mobile robots operate over the exterior surface and through the interior of the system, performing transport, placement, and reversible fastening using the intrinsic lattice periodicity for indexing and metrology. Leveraging programmable matter algorithms to achieve scalability in size and complexity, this system design enables robust collective automated assembly and reconfiguration of large structures with simple robots. We describe the system design and experimental results from a 256-unit cell assembly demonstration and lattice mechanical testing, as well as a demonstration of disassembly and reconfiguration. The assembled structural lattice material exhibits ultralight mass density (0.0103 grams per cubic centimeter) with high strength and stiffness for its weight ( 11.38 kilopascals and 1.1129 megapascals, respectively), a material performance realm appropriate for applications like space structures. With simple robots and structure, high mass-specific structural performance, and competitive throughput, this system demonstrates the potential for self-reconfiguring autonomous metamaterials for diverse applications.

Synthesis and mechanistic approach to investigate crystallite size of NbSe2 nanoparticles

Niobium diselenide (NbSe2) belongs to the class of transition metal dichalcogenides (TMDCs) and exhibits peculiar features such as charge density waves, superconductivity, and periodic crystal lattice distortion. The main focus of the article is the synthesis and characterisation of NbSe2 NPs utilising the wet chemical precursor solution route at room temperature, followed by in-depth x-ray diffraction (XRD) characterisation and analysis using the aforementioned techniques. The EDS result demonstrated that the NbSe2 NPs are devoid of impurities and close to stoichiometry. The sample has a crystalline hexagonal structure with the lattice constants a = b = 3.443Å, c = 12.576 Å, and α = β = 90°, γ = 120°, according to the XRD results. The work emphasises the need of comprehending how lattice strain and crystallite size affect physical attributes. x-ray peak broadening was used to study the epitaxial crystallisation of NbSe2 NPs. Various methods for determining crystallite size, such as the Williamson–Hall (W-H) method, Debye–Scherrer plots, uniform deformation model (UDM), uniform stress deformation model (USDM), uniform deformation energy density model (UDEDM), size strain plot (SSP) method, and Halder-Wagner (H-W) method, are employed to comprehensively analyse the nanoparticle characteristics, and additionally, high-resolution transmission electron microscopy (HRTEM) is employed to visualise the morphology and particle size distribution of the synthesised NbSe2 NPs. Physical parameters, including lattice stress, strain, and energy density, are also evaluated more precisely from the XRD pattern reflection peaks. The outcomes shed light on the interplay between crystallite size, lattice strain, and their effects on the material’s properties and showed excellent intercorrelation of the average crystallite sizes as estimated by employing various methods.

Characterization of coincidence site lattices generated by the composition of simple reflections of cubic lattices

This work provides a comprehensive characterization of coincidence site lattices that arise from the compositions of the reflections of cubic lattices. For this purpose, we apply Cartan's theorem and use reflections as basic isometries, which allows the use of Clifford algebra as a powerful tool to handle reflections and products of reflections, leading to explicit expressions for coincidence indices and the basis of coincidence lattices. The three possible cases were studied: simple reflections, the product of two reflections (rotations), and the product of three reflections, where a factorization that produces improper rotations was provided. In the case of rotations, it is formally proven that Ranganathan's well‐known generating function of coincidence indices for cubic systems under rotations yields all possible coincidence lattices. Overall, this study provides valuable insights into the mathematical properties of coincidence site lattices and the use of Clifford algebras to describe orthogonal transformations.

A mechanical property prediction system for G-Lattices via machine learning

G-Lattices—a novel family of periodic lattice structures introduced by Arash Armanfar and Erkan Gunpinar—demonstrate diverse mechanical properties owing to their generatively designed shapes. To assess the properties of lattice structures effectively, experimental tests and finite element analysis (FEA) are commonly used. However, the complex nature of these structures poses challenges, leading to high computation time and costs. This study proposes a machine learning (ML) approach to predict the mechanical properties of G-Lattices quickly under defined loading conditions. G-Lattice training data is generated through a sampling technique, and voxelized data is employed as ML feature vectors for predicting properties determined by FEA. To address the uneven distribution of target values, samples are clustered and utilized to train a classification model. This two-step process involves the classification of G-Lattices, followed by the application of specific regression models trained for each cluster for precise predictions. According to experiments, the ML model obtained, which predicts stiffness-over-volume ratios for G-Lattices, achieved a mean absolute percentage error of 6.5% for 1600 G-Lattices in a few seconds. Furthermore, approximately 70% of the 40,000 G-Lattices exhibited errors within 5%. The ML model's rapid predictions and acceptable accuracy make it useful for quick decision-making and seamless integration into optimization processes.

Disorder scattering in classical flat channel transport of particles between twisted magnetic square patterns

We measure the trajectories of macroscopic magnetic particles pulled against gravity between twisted alternating magnetic square patterns in a superposed homogeneous magnetic field normal to both patterns. The two patterns are built from a set of magentic cubes having a distribution of magnetization. The magnetic potential between the patterns is a sum of three contributions: two being periodic on two lattices with different magnitude and orientation, and the third random contribution arising from the distribution of magnetization of the cubes. As one varies the twist angle between the two patterns each time the twist angle coincides with a magic twist angle one of the two periodic lattices becomes a sublattice of the other lattice. Simulations of particles moving through patterns with a precise cube magnetization produce pronounced mobility peaks near magic twist angles that are associated with flat channels. Weak random fluctuations of the cube magnetization in the experiment and the simulations cause enhanced random disorder of the potential and reduce the mobility by scattering particles into the interior of the twisted Wigner Seitz cells. The mobility undergoes an Anderson transition from magic to generic behavior as the magnetization disorder increases beyond half of a percent of the cube magnetization.

Acoustic Bessel-like beam generation using phononic crystals

Diffraction-free beams with large depth-of-field have a lot of potential in the field of acoustics, such as imaging, sensing, and particle manipulation. In this study, an acoustic Bessel-like beam is produced using an axicon-sonic crystal lens. The sonic crystal is created using cylindrical glass rods arranged in a triangular shape with a centered square lattice configuration. The numerical simulation between 4 and 8 kHz indicates that the axicon-sonic crystal converts the plane acoustic wave into a Bessel-like beam. The analysis of the beam indicates that the depth of field of this beam depends on the size and periodicity (lattice parameter) of the sonic crystal. The axicon lens also displays variable focal lengths at different frequencies. A graded index layer was implemented to mitigate the reflection caused by the significant impedance mismatch. Experimental validation of acoustic Bessel-like beam formation is also reported for the working frequencies. At 8 kHz, the measured range to the 50% on-axis intensity was 34λ, while the focus width at the same frequency was measured to be 2λ. The integration of three distinct design strategies—axicon shape, sonic crystal, and graded index—expands the possibilities for sound focusing applications.

Hopfion based magnonic crystal

We conduct a numerical analysis to explore the magnonic band structure of spin waves (SWs) within a unique magnonic crystal. The latter is composed of a waveguide hosting a linear array of hopfions, evenly spaced along its center, generated through micromagnetic simulations. The computed dispersion relationship of spin waves (SWs) in the envisioned hopfions magnonic crystal, illustrating the frequency versus wave vector, demonstrates a periodic attribute, a hallmark of conventional magnonic crystal band structures. Likewise, the computed magnonic spectra reveal both permitted frequency bands and restricted frequency bandgaps. These results may inspire additional exploration into the diverse functionalities offered by magnonic crystals built on periodic Hopfion lattices.

Enhanced transmission capacity through a specialty multi-channel topological optical fiber

We propose a multi-channel specialty topological fiber based on 1D periodic geometry which supports three coexisting and non-interacting topologically-protected robust light states in the mid-infrared wavelength range. Each channel comprises two topologically-distinct 1D periodic lattices that are characterized by the topological invariant, Zak phase. The interface between the trivial and the nontrivial lattices is made unconventional to provide a strong transverse confinement of the light state. Moreover, the observed multiple interface states exhibit robust simultaneous transmission of light through all the channels keeping in contact with each other with an inter-channel cross-talk of ∼−27 dB. Such highly stable, scatter-free, and robust interface states have the potential to increase the transmission capacity of the existing optical communication channels, and can eventually be utilized as an alternative platform via the space-division multiplexing schemes.

High-performance plasmonic metasurface sensor by triangular nano-structures

The increasing need to sense different materials has caused sensors and efforts to improve their performance to receive a lot of attention in the optics field. In this report, we present a high-performance plasmonic metasurface sensor by the DGTD method that includes a two-dimensional periodic lattice of nano-triangles on a glass film and a TiN mirror. The TiN prevents light transmission from the resonators, causing a deeper reflection dip. Two resonances are observed, which offer a maximum sensitivity of about 417 nm/RIU and 735 nm/RIU, correspondingly. In this structure, augmenting the nano-triangles enhances hot spots, improving spectral response and sensitivity. Moreover, the structure maintains an almost unchanged spectral response for small angles. Overall, this sensor can be suitable for various applications such as biosensing.

Homogenization mapping method for equivalent properties of generalized periodic lattice structures

Homogenization mapping method for equivalent properties of generalized periodic lattice structures