Band structures of strained kagome lattices

Materials with kagome lattices have attracted significant research attention due to their nontrivial features in energy bands.We theoretically investigate the evolution of electronic band structures of kagome lattices in response to uniaxial strain using both a tight-binding model and an antidot model based on a periodic muffin-tin potential.It is found that the Dirac points move with applied strain.Furthermore,the flat band of unstrained kagome lattices is found to develop into a highly anisotropic shape under a stretching strain along y direction,forming a partially flat band with a region dispersionless along ky direction while dispersive along kx direction.Our results shed light on the possibility of engineering the electronic band structures of kagome materials by mechanical strain.

Meter-Scale Thin-Walled Structure with Lattice Infill for Fuel Tank Supporting Component of Satellite:Multiscale Design and Experimental Verification

Lightweight thin-walled structures with lattice infill are widely desired in satellite for their high stiffness-to-weight ratio and superior buckling strength resulting fromthe sandwich effect.Such structures can be fabricated bymetallic additive manufacturing technique,such as selective laser melting(SLM).However,the maximum dimensions of actual structures are usually in a sub-meter scale,which results in restrictions on their appliance in aerospace and other fields.In this work,a meter-scale thin-walled structure with lattice infill is designed for the fuel tank supporting component of the satellite by integrating a self-supporting lattice into the thickness optimization of the thin-wall.The designed structure is fabricated by SLM of AlSi10Mg and cold metal transfer welding technique.Quasi-static mechanical tests and vibration tests are both conducted to verify the mechanical strength of the designed large-scale lattice thin-walled structure.The experimental results indicate that themeter-scale thin-walled structure with lattice infill could meet the dimension and lightweight requirements of most spacecrafts.

Influence of manufacturing process-induced geometrical defects on the energy absorption capacity of polymer lattice structures

Modern additive manufacturing processes enable fabricating architected cellular materials of complex shape,which can be used for different purposes.Among them,lattice structures are increasingly used in applications requiring a compromise among lightness and suited mechanical properties,like improved energy absorption capacity and specific stiffness-to-weight and strength-to-weight ratios.A dedicated modeling strategy to assess the energy absorption capacity of lattice structures under uni-axial compression loading is presented in this work.The numerical model is developed in a non-linear framework accounting for the strain rate effect on the mechanical responses of the lattice structure.Four geometries,i.e.,cubic body centered cell,octet cell,rhombic-dodecahedron and truncated cuboctahedron 2+,are investigated.Specifically,the influence of the relative density of the representative volume element of each geometry,the strain-rate dependency of the bulk material and of the presence of the manufacturing process-induced geometrical imperfections on the energy absorption capacity of the lattice structure is investigated.The main outcome of this study points out the importance of correctly integrating geometrical imperfections into the modeling strategy when shock absorption applications are aimed for.

Ballistic performances of the hourglass lattice sandwich structures under high-velocity fragments

In this paper,the numerical simulation method is used to study the ballistic performances of hourglass lattice sandwich structures with the same mass under the vertical incidence of fragments.Attention is paid to elucidating the influences of rod cross-section dimensions,structure height,structure layer,and rod inclination angle on the deformation mode,ballistic performances,and ability to change the ballistic direction of fragments.The results show that the ballistic performances of hourglass lattice sandwich structures are mainly affected by their structural parameters.In this respect,structural parameters optimization of the hourglass lattice sandwich structures enable one to effectively improve their ballistic limit velocity and,consequently,ballistic performances.

Enhanced energy-absorbing and sound-absorbing capability of functionally graded and helicoidal lattice structures with triply periodic minimal surfaces

Lattice structures have drawn much attention in engineering applications due to their lightweight and multi-functional properties.In this work,a mathematical design approach for functionally graded(FG)and helicoidal lattice structures with triply periodic minimal surfaces is proposed.Four types of lattice structures including uniform,helicoidal,FG,and combined FG and helicoidal are fabricated by the additive manufacturing technology.The deformation behaviors,mechanical properties,energy absorption,and acoustic properties of lattice samples are thoroughly investigated.The load-bearing capability of helicoidal lattice samples is gradually improved in the plateau stage,leading to the plateau stress and total energy absorption improved by over 26.9%and 21.2%compared to the uniform sample,respectively.This phenomenon was attributed to the helicoidal design reduces the gap in unit cells and enhances fracture resistance.For acoustic properties,the design of helicoidal reduces the resonance frequency and improves the peak of absorption coefficient,while the FG design mainly influences the peak of absorption coefficient.Across broad range of frequency from 1000 to 6300 Hz,the maximum value of absorption coefficient is improved by18.6%-30%,and the number of points higher than 0.6 increased by 55.2%-61.7%by combining the FG and helicoidal designs.This study provides a novel strategy to simultaneously improve energy absorption and sound absorption properties by controlling the internal architecture of lattice structures.

Compression behavior of 316L lattice structures produced by indirect additive manufacturing

As a new type of lightweight structure,metallic lattice structure has higher stiffness and strength to weight ratio.To freely obtain 316L lattice structures with designed cell structure and adjustable porosity,additive manufacturing combined with investment casting was conducted to fabricate the 316L lattice structures with Kelvin cell.The compression simulation of 316L lattice structures with different porosities was carried out by using the finite element method.The numerical simulation results were verified by compression experiment,and the simulated results were consistent with the compression tests.The compressive mechanical properties of 316L lattice structures are directly related to porosity and independent of strut diameters.The 316L lattice structures with Kelvin cell have a smooth stress-strain curve and obvious plastic platform,and the hump stress-strain curves are avoided.

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 threedimensional 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.

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.

Valley transport in Kekulé structures of graphene

Valleytronics is an emergent discipline in condensed matter physics and offers a new way to encode and manipulate information based on the valley degree of freedom in materials. Among the various materials being studied, Kekulé distorted graphene has emerged as a promising material for valleytronics applications. Graphene can be artificially distorted to form the Kekulé structures rendering the valley-related interaction. In this work, we review the recent progress of research on Kekulé structures of graphene and focus on the modified electronic bands due to different Kekulé distortions as well as their effects on the transport properties of electrons. We systematically discuss how the valley-related interaction in the Kekulé structures was used to control and affect the valley transport including the valley generation, manipulation, and detection. This article summarizes the current challenges and prospects for further research on Kekulé distorted graphene and its potential applications in valleytronics.

Seismic isolation analysis of FPS bearings in spatial lattice shell structures

A theoretical model of a friction pendulum system （FPS） is introduced to examine its application for the seismic isolation of spatial lattice shell structures. An equation of motion of the lattice shell with FPS bearings is developed. Then, seismic isolation studies are performed for both double-layer and single-layer lattice shell structures under different seismic input and design parameters of the FPS. The influence of frictional coefficients and radius of the FPS on seismic performance are discussed. Based on the study, some suggestions for seismic isolation design of lattice shells with FPS bearings are given and conclusions are made which could be helpful in the application of FPS.

Effect of lattice defects on the electronic structures and floatability of pyrites

The electronic structures of three types of lattice defects in pyrites （i.e., As-substituted, Co-substituted, and intercrystalline Au py-rites） were calculated using the density functional theory （DFT）. In addition, their band structures, density of states, and difference charge density were studied. The effect of the three types of lattice defects on the pyrite floatability was explored. The calculated results showed that the band-gaps of pyrites with Co-substitution and intercrystalline Au decreased significantly, which favors the oxidation of xanthate to dix-anthogen and the adsorption of dixanthogen during pyrite flotation. The stability of the pyrites increased in the following order： As-substituted 〈 perfect 〈 Co-substituted 〈 intercrystalline Au. Therefore, As-substituted pyrite is easier to be depressed by intensive oxidi-zation compared to perfect pyrite in a strongly alkaline medium. However, Co-substituted and intercrystalline Au pyrites are more difficult to be depressed compared to perfect pyrite. The analysis of the Mulliken bond population and the electron density difference indicates that the covalence characteristic of the S Fe bond is larger compared to the S S bond in perfect pyrite. In addition, the presence of the three types of lattice defects in the pyrite bulk results in an increase in the covalence level of the S Fe bond and a decrease in the covalence level of the S S bond, which affect the natural floatability of the pyrites.

Numerical simulation and experimental validation on fabrication of nickel-based superalloy Kagome lattice sandwich structures

Nickel-based superalloy lattice sandwich structures present higher stiffness,higher strength and higher temperature resistance in comparison with other metals.In this study,the Kagome unit was adopted to design the lattice sandwich structure and ProCAST software was used to simulate the filling and solidification processes of the nickel-based superalloy.Grain morphology and sizes of the nickel-based superalloy lattice sandwich structures were simulated by using of cellular automaton coupled with finite element model(CAFE),and indirect additive manufacture combining with investment casting were carried out to fabricate the nickel-based superalloy lattice sandwich structures.The calculated grain morphology and sizes are in good agreement with the experimental results.The grains are mainly equiaxed with an average size of about 500µm.The simulated results also show that the superheat of melting and the mold preheated temperature have significant influence on the grain size of the Kagome lattice sandwich structures,lower superheat of melting and mold preheated temperatures are encouraged to obtain the fine grains while assuring the integrity of the Kagome lattice sandwich structures for industrial application.

Compressive mechanical properties and shape memory effect of NiTi gradient lattice structures fabricated by laser powder bed fusion

Laser additive manufacturing (AM) of lattice structures with light weight, excellent impact resistance, and energy absorption performance is receiving considerable attention in aerospace, transportation, and mechanical equipment application fields. In this study, we designed four gradient lattice structures (GLSs) using the topology optimization method, including the unidirectional GLS, the bi-directional increasing GLS, the bi-directional decreasing GLS and the none-GLS. All GLSs were manufactureed by laser powder bed fusion (LPBF). The uniaxial compression tests and finite element analysis were conducted to investigate the influence of gradient distribution features on deformation modes and energy absorption performance of GLSs. The results showed that, compared with the 45° shear fracture characteristic of the none-GLS, the unidirectional GLS, the bi-directional increasing GLS and the bi-directional decreasing GLS had the characteristics of the layer-by-layer fracture, showing considerably improved energy absorption capacity. The bi-directional increasing GLS showed a unique combination of shear fracture and layer-by-layer fracture, having the optimal energy absorption performance with energy absorption and specific energy absorption of 235.6 J and 9.5 J g-1 at 0.5 strain, respectively. Combined with the shape memory effect of NiTi alloy, multiple compression-heat recovery experiments were carried out to verify the shape memory function of LPBF-processed NiTi GLSs. These findings have potential value for the future design of GLSs and the realization of shape memory function of NiTi components through laser AM.

Fabrication of silica-based ceramic cores with internal lattice structures by stereolithography

Ceramic cores are widely used in investment casting,and ideal properties of cores are essential for high-quality castings.Under the circumstances requiring thick cores,solid cores are likely to encounter deformation and cracking defects due to the accumulation of shrinkage.Therefore,with the superiority of ceramic stereolithography in producing complex ceramic parts,hollow cores with lattice structures were designed and fabricated.The dimensional accuracy and properties of the green and sintered bodies were evaluated.Results show the dimensional accuracy of sintered cores is controlled within±0.25 mm benefited from the precise green bodies.The mechanical properties are not obviously deteriorated.The bending strength reaches 11.94 MPa at room temperature and 12.87 MPa at 1,500℃ with a creep deformation of 0.345 mm.Furthermore,casting verifications prove that the hollow cores meet the requirements of investment casting.Smooth casting surfaces are obtained,at the same time,the core-removal efficiency is improved by over 3 times.

Phase field lattice Boltzmann model for non-dendritic structure formation in aluminum alloy from LSPSF machine

The formation of non-dendritic structures in the primary phase of an aluminum alloy solidified using low superheat pouring with a shearing field(LSPSF) machine was investigated by numerical simulation.The growth and motion of a dendrite during solidification was simulated by a combination of the lattice Boltzmann method and the phase field method.The simulation results indicated that enough shear flow helped homogenize the concentration fields,rotate crystals and altere microstructures from dendritic to non-dendritic.The interaction of grains was also discussed.A fragmentation criterion was established based on partial remelting of dendrite arms;fragmentation was enhanced by a strong shear flow and larger inclined angles.The simulation results were verified experimentally.

Deformation mode and energy absorption of polycrystal-inspired square-cell lattice structures

Lattice structures are widely used in many engineering fields due to their excellent mechanical properties such as high specific strength and high specific energy absorption(SEA)capacity.In this paper,square-cell lattice structures with different lattice orientations are investigated in terms of the deformation modes and the energy absorption(EA)performance.Finite element(FE)simulations of in-plane compression are carried out,and the theoretical models from the energy balance principle are developed for calculating the EA of these lattice structures.Satisfactory agreement is achieved between the FE simulation results and the theoretical results.It indicates that the 30◦oriented lattice has the largest EA capacity.Furthermore,inspired by the polycrystal microstructure of metals,novel structures of bi-crystal lattices and quad-crystal lattices are developed through combining multiple singly oriented lattices together.The results of FE simulations of compression indicate that the EA performances of symmetric lattice bi-crystals and quad-crystals are better than those of the identical lattice polycrystal counterparts.This work confirms the feasibility of designing superior energy absorbers with architected meso-structures from the inspiration of metallurgical concepts and microstructures.

Short beam shear properties and failure modes of the wood-based X-type lattice sandwich structure

A wood-based X-type lattice sandwich structure was manufactured by insertion-glue method.The birch was used as core,and Oriented Strand Board was used as panel of the sandwich structure.The short beam shear properties and the failure modes of the wood-based X-type lattice sandwich structure with different core direction(vertical and parallel),unit specification(120 mm×60 mm and 60 mm×60 mm),core size(50 mm and 60 mm),and drilling depth(9 mm and 12 mm)were investigated by a short beam shear test and the establishment of a theoretical model to study the equivalent shear modulus and deflection response of the X-type lattice sandwich structure.Results from the short beam shear test and the theoretical model showed that the failure modes of the wood-based X-type lattice sandwich structure were mainly the wrinkling and crushing of the panels under three-point bending load.The experimental values of deflection response of various type specimens were higher than the theoretical values of them.For the core direction of parallel,the smaller the unit specification is,the shorter the core size is,and the deeper the drilling depth is,the greater the short beam shear properties of the wood-based X-type lattice sandwich structure is.

Multi-Material and Multiscale Topology Design Optimization of Thermoelastic Lattice Structures

This study establishes amultiscale andmulti-material topology optimization model for thermoelastic lattice structures(TLSs)consideringmechanical and thermal loading based on the ExtendedMultiscale Finite ElementMethod(EMsFEM).The corresponding multi-material and multiscale mathematical formulation have been established with minimizing strain energy and structural mass as the objective function and constraint,respectively.The Solid Isotropic Material with Penalization(SIMP)interpolation scheme has been adopted to realize micro-scale multi-material selection of truss microstructure.The modified volume preserving Heaviside function(VPHF)is utilized to obtain a clear 0/1 material of truss microstructure.Compared with the classic topology optimization of single-material TLSs,multi-material topology optimization can get a better structural design of the TLS.The effects of temperatures,size factor,and mass fraction on optimization results have been presented and discussed in the numerical examples.

A comparison study on the electronic structures, lattice dynamics and thermoelectric properties of bulk silicon and silicon nanotubes

In order to investigate the mechanism of the electron and phonon transport in a silicon nanotube （SiNT）, the elec- tronic structures, the lattice dynamics, and the thermoelectric properties of bulk silicon （bulk Si） and a SiNT have been calculated in this work using density functional theory and Boltzmann transport theory. Our results suggest that the thermal conductivity of a SiNT is reduced by a factor of 1, while its electrical conductivity is improved significantly, although the Seebeck coefficient is increased slightly as compared to those of the bulk Si. As a consequence, the figure of merit （ZT） of a SiNT at 1200 K is enhanced by 12 times from 0.08 for bulk Si to 1.10. The large enhancement in electrical conductivity originates from the largely increased density of states at the Fermi energy level and the obviously narrowed band gap. The significant reduction in thermal conductivity is ascribed to the remarkably suppressed phonon thermal conductivity caused by a weakened covalent bonding, a decreased phonon density of states, a reduced phonon vibration frequency, as well as a shortened mean free path of phonons. The other factors influencing the thermoelectric properties have also been studied from the perspective of electronic structures and lattice dynamics.

Energy band structure in optical of spin-1 condensates lattices

The energy band structure of spin-1 condensates with repulsive spimindependent and either ferromagnetic or antiferromagnetic spin-dependent interactions in one-dimensional （1D） periodic optical lattices is discussed. Within the two-mode approximation, Bloch bands of spin-1 condensates are presented. The results show that the Bloch bands exhibit a complex structure as the atom density of mF = 0 hyperfine state increases： bands splitting, reversion, intersection and loop structure are excited subsequently. The complex band structure should be related to the tunneling and spin-mixing dynamics.