Uniform Lattice Research Articles

Yield surface of multi-directional gradient lattices with octet architectures

In this paper, a theoretical method is developed to delineate the effective elastic properties and yield surface of the gradient cellular structure. Additionally, a technique is presented for the construction of multi-directional gradient lattices, and two novel tri-directional gradient lattices (TD-GLs) by assembling octet unit cells with side lengths following specified gradient topological parameters serve as an illustrative example. Their effective elastic properties and yield surfaces are systematically investigated with the aid of theoretical, experimental, and finite element methods. It is found that the effective elastic modulus of the proposed TD-GLs exceeds by 48.80% as compared to that of conventional uniform octet lattices. Moreover, the normalized yield surfaces are proposed to emphasize the predominant role of structural topological features by eliminating the influence of the relative density on the yield behavior of TD-GLs, and this method that also can be extrapolated to other tension-dominated lattices. Subsequently, a theoretical model is developed to establish closed-form yield functions for characterizing the yield behavior of TD-GLs. The predicted yield surfaces from the proposed theoretical model demonstrate good agreement with the simulated results. Finally, the proposed TD-GLs demonstrate outstanding yield performance in various directions deviating from their orthogonal principal axes or planes, compared to lattices with uni- or dual-directional gradient topological configurations. In summary, the proposed multi-directional gradient lattices in this study exhibit the exceptional stiffness and outstanding yield performance in various directions, offering valuable insights for the structural design and engineering applications of lattice structures.

Study on the fabrication and mechanical properties of SiCp/SiC gradient lattice structure based on selective laser sintering technology

ABSTRACT Conventional uniform lattice structures are subject to non-uniform loads or concentrated loads alternating back and forth during service, which can no longer meet the refinement requirements. In this paper, SiCp/SiC gradient lattice structures are prepared by selective laser sintering (SLS) technology and polymer impregnation pyrolysis (PIP) process, and compression standard specimens with different tilt angles are prepared according to the structural model by changing the printing direction, to analyze the influence of the anisotropic properties of the materials due to the SLS molding technology on the load-bearing behaviour of the core rod, and to further study the mechanical properties of the gradient lattice structures and the Failure behaviour. The results show that: with the increase of the angle of printing direction, the compression performance of the densification specimen decreases gradually; the compression strength of the gradient lattice structure is 13.95 MPa. During compression, the core rods with tilt angles of 60° and 75° mainly exhibit shear failure and crushing failure, respectively. The theoretical and simulated compression strengths were 16.08 and 16.32 MPa, respectively. This paper provides a new insight into the research and application of gradient lattice structures.

Mechanical and shape-memory properties of TPMS with hybrid configurations and materials

ABSTRACT Triply periodic minimal surface (TPMS) structures with excellent properties of stable energy absorption, light weight, and high specific strength could potentially spark immense interest for novel and programmable functions by combining smart materials, e.g. shape memory polymers (SMPs). This work proposes TPMS lattices with hybrid configurations and materials that are composed of viscoelastic and shape-memory materials with the aim to bring temperature-dependent mechanical properties and additional dissipation mechanisms. Different configurations and diverse materials of polylactic acid (PLA), fiber-reinforced PLA, and polydimethylsiloxane (PDMS) are induced, generating five types of TPMS lattices, including (Schoen’s I-WP) IWP uniform lattice, IWP lattice with density gradient, hybrid configurations, hybrid materials, and filled PDMS, which are fabricated by 3D printing. The fracture morphologies and the distribution of carbon fibers are demonstrated via scanning electron microscopy with a focus on the influence of carbon fiber on shape-memory and mechanical properties. Shape recovery tests are conducted, which proves good shape memory properties and reusable capability of TPMS lattice. The combined methods of experiments and numerical simulation are adopted to evaluate mechanical properties, which presents multi-stage energy absorption ability and tunable vibration isolation performances associated with temperature and hybridization designs. This work can promote extensive research and provide substantial opportunities for TPMS lattices in the development of functional applications.

Investigation of additively manufactured metamaterials for load-bearing structural applications

The study explores the potential application of Triply Periodic Minimal Surface (TPMS) metamaterials in structural engineering and architecture. It evaluates parametric design possibilities and analysis approaches while examining the mechanical properties of five TPMS structures (Gyroid, Schwarz, Diamond, Split, and Neovius). Comparisons are made between Additively Manufactured (AM) samples and numerical simulations. Gyroid and Diamond structures, which display advantageous properties, undergo further investigation with parametric design for uniform and non-uniform lattices. The study proposes simplified analytical formulations for metamaterial design, along with Homogenization analysis and detailed FEM analysis. Compression tests reveal distinct failure modes and stress-strain behaviors for each TPMS. The research suggests further investigation into the influence of the 3D printing process, void detection, and thermomechanical analysis. Finally, the study provides insights into tailored applications of these lattice metamaterials in structural engineering.

Electroplasticity mechanism of Ti2AlNb alloys under hot compression with the application of a lower electric current

In this study, a lower electric current (1.0–2.0 A/mm2) was applied during hot compression of Ti2AlNb alloys, and the mechanical response, microstructure evolution, and electroplasticity mechanism were investigated. The results showed that the maximum flow stress drop could reach 18.7 % after applying a lower electric current of 2.0 A/mm2, which confirms the existence of electroplasticity. The stress drop increased with increasing electric current density. However, the flow stresses of the samples in the isothermal compression test and those subjected to a 1.0 A/mm2 electric current compression test were similar, indicating that there is a threshold value for the electroplasticity effect on flow stress. The lower strain hardening rate caused by the electric current confirmed the electroplasticity effect, promoting the softening effect. Additionally, the lower average activation energy Q, affected by the electric current, implied the improvement of the deformability of the alloy due to the deformation mechanism of dynamic recovery (DRV), dynamic globularization, or dynamic recrystallization (DRX). The gradual reduction of dislocation density with increasing electric current density resulted in the stress drop, which can be ascribed to the directional drifting electrons colliding with dislocations, which promoted the movement of dislocations by arranging the dislocations in parallel. The local high temperature induced by the local Joule heating effect at the O lamella had a strong promoting effect on the globularization of the O lamella by producing uniform lattice distortion/local strain at the O/B2 interface. With increasing furnace temperature, the drifting electrons accelerated the transformation of LAGBs to HAGBs which promoted the appearance of dynamic recrystallization grains.

Mechanical characteristics of Si/SiC graded ceramic lattice structures with a triply periodic minimal surface fabricated by laser powder bed fusion

SiC graded ceramic lattice structures (GCLSs) have attracted rising attention owing to outperformed merits including ultra-lightweight and excellent specific strength compared with uniform ceramic lattice structures (UCLSs). In this study, Si/SiC Gyroid GCLSs with variable relative densities (35 % and 45 %) and different gradient directions were designed and fabricated via laser powder bed fusion combined with liquid silicon infiltration techniques. 35 % and 45 % UCLSs were also prepared as a reference. The manufacturing precision and mechanical responses of these CLSs were systematically investigated through compressive tests and micro-computed tomography analysis. The mechanical performances of 35 % GCLSs are lower than that of 35 % UCLSs. The weaker load-bearing capacity in the upper portion and the stress concentration in the inclined load-bearing surface lead to the knockdown of mechanical properties for 35 % GCLSs. The nonlinear superposition of mechanical properties in 45 % GCLSs is the main reason for the superior mechanical performance of 45 % GCLSs compared to 45 % UCLSs. Besides, various theoretical models and finite element simulations were implemented to evaluate the mechanical properties of SiC CLSs. The comparison of compressive strength with other ceramic porous structures emphasized the exceptional mechanical properties (16.07 MPa for 35 % UCLSs and 22.91 MPa for 45 % GCLSs) of Si/SiC CLSs.

Scale‐dependent mechanical performance variations in polylactic acid lattice structures fabricated via additive manufacturing

AbstractThe objective of this research is to explore the scale effect on the mechanical properties of sheet‐based triply periodic minimal surface (TPMS) uniform lattice structures fabricated with PLA (polylactic acid) under quasi‐static loading conditions. The scale dependency was evaluated by two additional breakdown categories, namely, wall thickness effect and unit cell size effect. Deformation mechanisms and failure modes as well as mechanical properties including stiffness, yield strength, first peak stress, and energy absorption based on the categories of wall thickness, unit cell size, and scale were evaluated experimentally. The assessment of the scale effect involved considering the combined influence of wall thickness and unit cell size. In addition, numerical analysis was also performed to investigate the stress distributions and compare with the experimental results for certain geometries. Ultimately, the relation between the normalized mechanical properties and relative density is evaluated and categorized, which can be used as an indication for future design practices.

High hardness and its strong layer-thickness dependence induced by martensitic transforming constituent in NiTi/Nb nanolayered thin films

Bulk composites made of transforming matrix and nanoinclusions possess exeptional mechanical properties owing to excellent interfacical strain matching as implemented by uniform lattice shear of martensitic constituents. Such an effect remains however largely unexploited in thin films. In this study, NiTi/Nb multilayered thin films with various individual layer thickness (h) were prepared by magnetron sputtering. Strong h-dependence in indentation hardness (23 GPa/nm−1/2) is discovered in NiTi/Nb multilayers, as compared to those (4–18 GPa/nm−1/2) in conventional bimetallic X/Nb multilayers where X = Cu, Ti, Ag, Al etc. Indentation hardness of NiTi/Nb multilayers saturates at 12 GPa, as compared to 2.6–8.5 GPa of X/Nb multilayers. In situ grazing incidence synchrotron X-ray diffraction reveals that the lattice strain of Nb in NiTi/Nb is 60–240 % greater than that in X/Nb. We suggest that such discrepancies may arise from the interfacial strain concentration relief facilitated by the transforming NiTi layers.

Antiferromagnetic phase transition in a 3D fermionic Hubbard model.

The fermionic Hubbard model (FHM)1 describes a wide range of physical phenomena resulting from strong electron-electron correlations, including conjectured mechanisms for unconventional superconductivity. Resolving its low-temperature physics is, however, challenging theoretically or numerically. Ultracold fermions in optical lattices2,3 provide a clean and well-controlled platform offering a path to simulate the FHM. Doping the antiferromagnetic ground state of a FHM simulator at half-filling is expected to yield various exotic phases, including stripe order4, pseudogap5, and d-wave superfluid6, offering valuable insights into high-temperature superconductivity7-9. Although the observation of antiferromagnetic correlations over short10 and extended distances11 has been obtained, the antiferromagnetic phase has yet to be realized as it requires sufficiently low temperatures in a large and uniform quantum simulator. Here we report the observation of the antiferromagnetic phase transition in a three-dimensional fermionic Hubbard system comprising lithium-6 atoms in a uniform optical lattice with approximately 800,000 sites. When the interaction strength, temperature and doping concentration are finely tuned to approach their respective critical values, a sharp increase in the spin structure factor is observed. These observations can be well described by a power-law divergence, with a critical exponent of 1.396 from the Heisenberg universality class12. At half-filling and with optimal interaction strength, the measured spin structure factor reaches 123(8), signifying the establishment of an antiferromagnetic phase. Our results provide opportunities for exploring the low-temperature phase diagram of the FHM.

Model geometries dominated by locally finite graphs

We study model geometries of finitely generated groups. We show that a finitely generated group possesses a model geometry not dominated by a locally finite graph if and only if it contains either a commensurated finite rank free abelian subgroup, or a uniformly commensurated subgroup that is a uniform lattice in a semisimple Lie group. This characterises finitely generated groups that embed as uniform lattices in locally compact groups that are not compact-by-(totally disconnected). We also prove the only such groups of cohomological two are surface groups and generalised Baumslag–Solitar groups.

Fatigue properties of SiC graded ceramic lattice structures with a triply periodic minimal surface manufactured by laser powder bed fusion

SiC graded ceramic lattice structure (GCLS) offers superior mechanical strength and its impact on fatigue warrants investigation. In this work, SiC triply periodic minimal surface (TPMS) GCLSs were prepared via laser powder bed fusion technology and liquid silicon infiltration process, alongside SiC TPMS uniform ceramic lattice structure (UCLS) as a reference. Fatigue properties, fatigue failure, and strengthening mechanisms were systematically investigated through compression fatigue tests, finite element (FE) simulations, and theoretical analysis. Fatigue failures of SiC UCLSs and GCLSs are influenced by cyclic ratcheting and fatigue damage, with cyclic ratcheting dominance. The fatigue strength ratios of UCLS and GCLS are 0.7 and 0.74, indicating that GCLSs exhibit stronger deformation resistance and superior fatigue performance. FE results show that surface tensile stress level in GCLS is lower than in UCLS, resulting in slower fatigue crack initiation. Stress redistribution and higher crack thresholds contribute to enhanced fatigue resistance in SiC TPMS GCLSs.

Energy absorption performance of woven metallic lattices with orthogonal spiral wires under quasi-static compression

Woven metallic lattice (WML) structures are gaining attention for their beneficial mechanical properties, such as low weight and special energy absorption capability. They hold potential for diverse applications, including energy absorption components in aerospace. Drawing inspiration from the traditional double-arrow lattice, this study proposes a novel WML design featuring multi-plateau stresses. The deformation behavior of this structure under compression was investigated using finite element analysis and experimental methods. Three gradient structures defined by the different layer arrangements along load direction associated with specific structure variables, namely positive gradient (PG), negative gradient (NG), and hybrid gradient (HG), were introduced, along with an examination of their mechanical properties. The study explored the influence of key parameters of the cell structure on compression characteristics. Findings suggest that enhancing cell vertex angle and wire diameter can improve energy absorption, while the opposite holds true for cell base angle. Among the gradient structures analyzed, the PG WML structure demonstrates optimal energy absorption due to its dual-plateau stress characteristics. The NG WML structure is noteworthy for its uniform lattice deformation during initial compression stages, which is crucial for precision engineering with subtle deformation control strategies. Lastly, the deformation pattern of the HG WML structure during compression progresses from low to high strength.

Embracing disorder in quantum materials design

Many of the most exciting materials discoveries in fundamental condensed matter physics are made in systems hosting some degree of intrinsic disorder. While disorder has historically been regarded as something to be avoided in materials design, it is often of central importance to correlated and quantum materials. This is largely driven by the conceptual and theoretical ease to handle, predict, and understand highly uniform systems that exhibit complex interactions, symmetries, and band structures. In this Perspective, we highlight how flipping this paradigm has enabled exciting possibilities in the emerging field of high entropy materials, focusing primarily on high entropy oxide and chalcogenide quantum materials. These materials host high levels of cation or anion compositional disorder while maintaining unexpectedly uniform single crystal lattices. The diversity of atomic scale interactions of spin, charge, orbital, and lattice degrees of freedom are found to emerge into coherent properties on much larger length scales. Thus, altering the variance and magnitudes of the atomic scale properties through elemental selection can open new routes to tune global correlated phases, such as magnetism, metal–insulator transitions, ferroelectricity, and even emergent topological responses. The strategy of embracing disorder in this way provides a much broader pallet from which functional states can be designed for next-generation microelectronic and quantum information systems.

Photovoltaic spatial gap solitons in biased photorefractive optical lattices

We investigate the existence and characteristics of spatially confined optical gap solitons within an optical lattice embedded in a biased bulk photovoltaic photorefractive crystal. The Floquet-Bloch theory is used to analyze the uniform lattice and derive the optical lattice band structure. In the photonic band gaps, which are typically opaque to light transmission, the photorefractive nonlinearity permits the formation of solitons. The paraxial Helmholtz equation is set up and solved thereby discovering single hump and double hump soliton states in both band gaps. Interestingly, we have not found any multi peak solitons to exist in this particular case. We examine the characteristics of these gap solitons, finding that the soliton width (an indicator of nonlinearity) and intensity depend on their location within the band gap. We find that the magnitude of the external electric field profoundly affects the gap soliton characteristics. Additionally, the Vakhitov-Kolokolov (VK) criterion, perturbation analysis and numerical techniques are used to analyze the stability of the various types of the spatial gap solitons in both the band gaps.

Evaluation of highly conductive cermet cathodes synthesized with organic chelating agents and sintered at low temperatures for IT-SOFCs

A novel semi-organic combustion approach using orange and lemon juice as chelating agents is employed to synthesize the perovskite Sr0.8X0.2Co0.2Fe0.8O3-δ (x = La, Ce) cathode for IT-SOFCs. This approach has been found to exhibit lower toxicity compared to chemical routes and lower impurities compared to green routes. The structural analysis validated the successful synthesis of perovskite Sr0.8X0.2Co0.2Fe0.8O3-δ (La, Ce) cathode materials with no prominent secondary phase of impurities while surface morphology revealed a porous and well-connected network of particles. EDS confirmed the composition and thermo-gravimetric analysis showed weight losses related to the creation of vacancies. The functional groups were investigated through FTIR and the conductivity measurements revealed higher electrical conductivity for Sr0.8X0.2Co0.2Fe0.8O3-δ (x = La, Ce) synthesized with orange juice as a chelating agent with Sr0.8La0.2Co0.2Fe0.8O3-δ exhibiting slightly higher value compared to Sr0.8Ce0.2Co0.2Fe0.8O3-δ. The electrochemical performance showed the highest power density of 354 and 313 mW·cm−2 at 700 °C obtained for cells having Sr0.8X0.2Co0.2Fe0.8O3-δ (x = La, Ce) cathodes synthesized with orange juice which was attributed to better crystallinity and uniform lattice. This work shows that a novel semi-organic route is successfully employed to synthesize the perovskite cathode materials for IT-SOFCs.

Stress-driven generative design and numerical assessment of customized additive manufactured lattice structures

The rise of additive manufacturing (AM) has positioned lattice infilling as a pivotal strategy for creating lightweight, customized engineering components. This study presents a generative method that enables the conformal design and stiffness prediction of complex gradient strut-node lattice structures. A stress-driven Multi-Agent System (MAS) is introduced for the parametric optimization of lattice material distribution, incorporating geometric limitations, stress factors, and AM constraints. A beam element model simplifies the numerical analysis of the structure linear stiffness. By applying the Response Surface Method (RSM), a numerical model is established, not only conducting a quantitative analysis on the sensitivity of MAS design variables but predicting mechanical performance. This method is validated by designing a supporting component, demonstrating that the optimized lattice design can achieve a linear stiffness 1.4 times greater than that of conventional uniform lattice infills for the same mass. This research provides a comprehensive framework for the efficient design and analysis of irregular lattice structures at a macroscopic scale.

Discrete modeling of elastic heterogeneous media

Discrete models provide advantages in simulating fracture in quasi-brittle materials due, in part, to their simplicity in representing cracking and other forms of displacement discontinuity. However, the stress analyses that form the basis for fracture simulation are complicated by difficulties in modeling the Poisson effect and other aspects of elastic behavior. The capabilities of Voronoi-cell lattice models, which are a form of particle-based lattice model, for elastic stress analysis are evaluated. It is found that the conventional means for representing the Poisson effect in particle-based lattice models result in spatially correlated stress oscillations that, at first glance, mimic the effects of material heterogeneity. The correlation length is dependent on discretization size. Alternatively, material heterogeneity can be introduced into elastically uniform lattice models via random assignments of material properties, independent of mesh size and geometry.

Towards high-performance polarimeters with large-area uniform chiral shells: a comparative study on the polarization detection precision enabled by the Mueller matrix and deep learning algorithm

Polarization detection and imaging technologies have attracted significant attention for their extensive applications in remote sensing, biological diagnosis, and beyond. However, previously reported polarimeters heavily relied on polarization-sensitive materials and pre- established mapping relationships between the Stokes parameters and detected light intensities. This dependence, along with fabrication and detection errors, severely constrain the working waveband and detection precision. In this work, we demonstrated a highly precise, stable, and broadband full-Stokes polarimeter based on large-area uniform chiral shells and a post-established mapping relationship. By precisely controlling the geometry through the deposition of Ag on a large-area microsphere monolayer with a uniform lattice, the optical chirality and anisotropy of chiral shells can reach about 0.15 (circular dichroism, CD) and 1.7, respectively. The post-established mapping relationship between the Stokes parameters and detected light intensities is established through training a deep learning algorithm (DLA) or fitting the derived mapping-relationship formula based on the Mueller matrix theory with a large dataset collected from our home-built polarization system. For the detection precision with DLA, the mean squared errors (MSEs) at 710 nm can reach 0.10% (S1), 0.41% (S2), and 0.24% (S3), while for the Mueller matrix theory, the corresponding values are 0.14% (S1), 0.46% (S2), and 0.48% (S3). The in-depth comparative studies indicate that the DLA outperforms the Mueller matrix theory in terms of detection precision and robustness, especially for weak illumination, small optical anisotropy and chirality. The averaged MSEs over a broad waveband ranging from 500 nm to 750 nm are 0.16% (S1), 0.46% (S2), and 0.61% (S3), which are significantly smaller than those derived from the Mueller matrix theory (0.45% (S1), 1% (S2), and 39.8% (S3)). The optical properties of chiral shells, the theory and DLA enabled mapping-relationships, the combination modes of chiral shells, and the MSE spectra have been systematically investigated.

Embedding lattice structures into ship hulls for structural optimization and additive manufacturing

Additive manufacturing (AM) has been making inroads into the shipbuilding industry. The maritime sector has recognized the potential benefits of AM in terms of cost savings, design flexibility, and rapid prototyping. Lattice structures, known for their vast applications in AM and associated benefits like lightweight design, energy efficiency, and improved material usage, serve as a focal point in this shifting landscape.This paper presents a pioneering approach to integrating lattice structures into shipbuilding via AM, specifically for supporting ship volumes. The method introduces algorithms to create both conformal and uniform lattice structures for structural optimization. According to the case studies in this work, ship models with lattice structures have superior structural properties compared to conventional support elements.

Incommensurable lattices in Baumslag–Solitar complexes

AbstractThis paper concerns locally finite 2‐complexes that are combinatorial models for the Baumslag–Solitar groups . We show that, in many cases, the locally compact group contains incommensurable uniform lattices. The lattices we construct also admit isomorphic Cayley graphs and are finitely presented, torsion‐free, and coherent.