Lattice Shape Research Articles

Flow Characterization in Triply Periodic Minimal Surface (TPMS)-Based Porous Geometries: Part 1—Hydrodynamics

The modeling of flow and heat transfer in porous media systems has always been a challenge, and the extended Darcy transport models are used for macro-level analysis. However, these models are subjected to the limitations depending upon the porous geometry such as pore size, pore type, effective porosity, tortuosity, permeability, and the flow characteristics. The forced convective flow of an incompressible viscous fluid through a channel filled with four different types of porous geometries constructed using the Triply Periodic Minimal Surface (or TPMS) model is presented in this study. Four TPMS lattice shapes, namely Diamond, I-WP, Primitive, and Gyroid, are created with same volume fraction of solid subdomain as 0.68 (or void fraction as 0.32). Using different configurations for the solid subdomain by treating it as (a) solid, (b) fluid, and (c) porous zone, three different classes of porous structures are further generated for each TPMS lattice. The present study is executed with the objective to investigate the effect of shape–morphology, tortuosity, microporosity, and effective porosity on permeability and inertial drag factor. A pore-scale direct numerical simulation approach is performed for the first two types of porous media by solving the Navier–Stokes equations. The specific microporosity is quantitatively induced in the solid subdomain where Darcy–Forchheimer equation is solved, whereas the Navier–Stokes equations are solved for the void subdomain in the third type of porous media. The results reveal that Darcy flow regime exists up to the mean velocity value of U < 0.0025 m/s (Re < 10) for all the cases discussed here, and it deviates at the higher mean velocity. The conductance to the flow shown by Darcy number has the maximum and minimum values for the Primitive Type 2 and I-WP Type 1 cases. The inertial drag coefficient is minimum in Diamond lattice and maximum in Primitive lattice at lower porosity (0.32), while Primitive lattice has minimum and I-WP lattice has maximum value of inertial drag coefficient for higher porosity (~ 1).

Functional aerogel coatings on tetrakaidecahedron lattice

This paper reports a new method of functional metamaterial structure fabrication based on ultra-porous aerogel skins introduced on the surfaces of solid tetrakaidecahedron lattices obtained via 3D-printing tools. The solid tetrakaidecahedron lattice shapes are first fabricated from acrylate resin systems using a stereolithography printer. The lattice is then coated with a skin of polyimide gel via sol–gel reaction process, post-curing, and solvent-aging. The aerogel skin is recovered from the gel using supercritical drying. The lattice is found uniformly coated with polyimide aerogel skin as confirmed from examination of surface morphology via scanning electron microscopy and X-ray tomography imaging. The concept is extended to coatings by silica and Kevlar aerogel systems. The mechanical and thermal properties of the resultant materials and a set of applications are discussed.

Continuum Soliton Chain Analog to Heisenberg Spin Chain System. Modulation Stability and Spectral Characteristics

The one-dimensional (1D) Heisenberg spin chain system (HSCS) allows to investigate anomalous features originating from strong quantum fluctuations, which become more significant than those in higher dimensions. A continuum model equation of the HSCS, based on the discrete model, was constructed in the literature. It is nonlinear Schrodinger equation (NLSE) with biquadratic dispersion and fifth degree nonlinearity. Rare research works were done in this area. Notably for deriving the exact solutions and investigate the physical phenomena produced. Our objective, here, is to obtain these solutions, which we think they are new. Further, an analog of the different geometric solutions structures to the known characteristics of HSCS is performed. The unified method is implemented to find the exact solutions of the continuum model equation. A variety of solutions are obtained where they are evaluated numerically and represented in graphs. In these graphs, it is remarked that the solutions exhibit soliton chain (or dense soliton chain).in an analog to spin chain. In the contour plots, they show different shapes of super lattices. Furthermore, complex chirped waves are observed. A significant result is that these solutions are bounded by − 1/4 and 1/4, which can be relevant to the spins− 1/2 and 1/2. The analysis of modulation stability is carried and it is found that there is a critical value for the dominant parameters, where below this value, modulation instability holds otherwise modulation stability occurs.For the spectral characteristics, it is shown that the wave number increases abruptly and decreases to an asymptotic state, while the frequency is monotonic increasing. The spectrum is periodic wave away from the origin, but near the origin it is soliton.

Shielding Factor due to the Arrangement of Different Lattice Shape Thicknesses in the Open Type Lattice Structure Magnetically Shielded Room

Shielding Factor due to the Arrangement of Different Lattice Shape Thicknesses in the Open Type Lattice Structure Magnetically Shielded Room

Spin wave stiffness and damping in a frustrated chiral helimagnet Co8Zn8Mn4 as measured by small-angle neutron scattering

Multiple intriguing low-temperature phenomena have recently been discovered in the family of chiral cubic Co-Zn-Mn compounds with a $\ensuremath{\beta}$-Mn-type structure. In particular, ${\mathrm{Co}}_{8}{\mathrm{Zn}}_{8}{\mathrm{Mn}}_{4}$ displays a reduction of the helical spiral pitch on cooling along with lattice shape transformations of metastable skyrmions and the manifestation of peculiar magnetic textures due to strong magnetocrystalline anisotropy. Here we report on temperature-dependent measurements of helimagnon excitations in the field polarized regime ${\mathrm{Co}}_{8}{\mathrm{Zn}}_{8}{\mathrm{Mn}}_{4}$ using the spin-wave (SW) small-angle neutron-scattering technique. By applying a new analytical expression to interpret the data, quantitative estimates for both SW stiffness and damping are extracted across a wide temperature range between 70 and 250 K. We speculate that their nontrivial temperature dependencies arise due to the effects of magnetic frustration arising from Mn magnetic moments, which is further reflected in continuous variations of both exchange and Dzyaloshinskii-Moriya interactions.

Planes in four-space and four associated CM points

To any two-dimensional rational plane in four-dimensional space one can naturally attach a point in the Grassmannian Gr(2,4) and four shapes of lattices of rank two. Here, the first two lattices originate from the plane and its orthogonal complement, and the second two essentially arise from the accidental local isomorphism between SO(4) and SO(3)×SO(3). As an application of a recent result of Einsiedler and Lindenstrauss on algebraicity of joinings, we prove simultaneous equidistribution of all of these objects under two splitting conditions.

Light‐Actuated Anisotropic Microactuators from CNT/Hydrogel Nanocomposites

AbstractOver the past decades, functional hydrogels that respond to a variety of mechanical and chemical stimuli with a volume change of more than 100% have been developed. Despite this impressive behavior, practical applications of conventional hydrogels are limited by the need to transform their isotropic swelling/contraction into useful deformations, as well as their slow response times. Here, these challenges are addressed by combining poly(N‐isopropylacrylamide) (PNIPAM), a widely used temperature‐responsive polymer, with carbon nanotubes (CNTs). To ensure strong PNIPAM−CNT cohesion, the hydrogel is synthesized directly on the CNT surfaces using in situ redox polymerization. The anisotropy of vertically‐aligned CNT forests is used to transform the isotropic (de)swelling of PNIPAM into anisotropic motion. This material combination is particularly attractive because the high optical absorption and heat conductivity of carbon nanotubes converts light irradiation into PNIPAM actuation. A wide variety of CNT‐skeleton microstructures are tested to reveal a range of actuation behaviors. The authors demonstrate fast reversible movement, active switching from low to high light absorption states, lattice shape changes, and good cycling stability.

Manipulation of photon states in photonic crystals based on silicon

Coupling between the active centers generated by localized states and the two-dimensional photonic crystals (2D-PCs) has been used to select model in the nano-laser and the optical interconnects on silicon chip. The photonic crystals have been investigated in the simulating calculation, and the physical model has been built in the manipulation of photon states. New quantum phenomena appear in the photonic crystals as well as in the atomic crystals. We have numerically studied on the band structure of 2D-PCs with different types of lattice and various shapes in the optical communication windows. The simulating calculation results show that the band gap of photon states can be effectively manipulated in 2D-PCs by using the competition between the quantum confinement effect and the lattice symmetry effect, in which the band gap width of the photon states will obviously increase by changing the lattice symmetry and by increasing the filling rate of the air hole to restrain photons in 2D-PCs on silicon. It is interesting to make a comparison between the transverse electric (TE) polarization and the transverse magnetic (TM) polarization, in which a wider band gap occurs in the TM mode. By adjusting the defect mode in 2D-PCs, the photon states can be localized into the second and third windows of optical communication for selecting modes and resonating on silicon chip.

Manipulation of Mixed Ligands to Form Single-Layer and Double-Layer Lanthanide Clusters and Their Magnetic Properties

There have been many examples of synthesizing multinuclear lanthanide clusters of special shapes, such as spherical, cage-shaped, tubular, and so on. However, synthesizing multinuclear lanthanide clusters with distinct layered structures possess a challenge. We use the ligands 2,3-dihydroxybenzaldehyde, benzohydrazide and pyridin-2-ylmethanamine to obtain a single layer of six-core lanthanide clusters [Dy6(μ3-O)(μ3-OH)4(L2)3(L3)3(L4)3(H2O)3]Cl6·CH3OH (1) and [Gd6(μ3-O)(μ3-OH)4(L2)3(L3)3(L4)3(H2O)2(CH3OH)]Cl6·CH3OH·3CH3CN (2). The central metal ion of cluster 1 presents a triangular lattice shape. We changed the ligands to 2-hydroxy-3-methoxybenzaldehyde and 2-aminobenzoic acid and obtained the double-layer eight-core lanthanide clusters [Dy8(μ3-OH)6(L5)2(L6)8] (3) and [Gd8(μ3-OH)6(L5)2(L6)8]·4CH3OH·CH3CN (4). The upper and lower layers of cluster 3 have four metal ions, respectively, forming a huge cavity inside the structure. This is the first time that a multinuclear lanthanide cluster with a layered structure has been constructed by the in situ reaction of mixed ligands. AC susceptibility test shows that the imaginary part signals of cluster 1 do not show frequency dependence and the imaginary part signals of cluster 3 show frequency dependence at low temperatures. By fitting the Arrhenius equation, we obtain Ueff = 2.87 K and τ0 = 2.76 × 10–4 s.

Temperature dependent magnetic studies of Ba0.5Sr0.5Co0.2Fe11.8O19 prepared by solid state reaction method

Ba0.5Sr0.5Co0.2Fe11.8O19 was synthesized using solid state reaction method. Lattice parameters ‘a’ and ‘c’ were found to be 5.886 Å and 23.110 Å respectively. Scanning electron microscopy studies showed platelet type structures in the sample and the elemental mapping showed the uniform distribution of cations throughout the sample. The spontaneous magnetization (Ms) of 62 emu/g with coercivity (Hc) of 1.22 kOe was observed at 300K. The Ms value increased whereas the Hc decreased with the decreasing measurement temperature. The highest Ms value of 88 emu/g was observed at 60K. Curie temperature of 819 K was observed for the sample. The anisotropy constant (K1) and anisotropy field (Ha) were found to be increased with the decrease in measurement temperature. The observed magnetic behaviour can be explained on the basis of distribution of cations in the lattice sites and shape anisotropy of the prepared sample.

Electrical and Structural Properties of CuBa2LaCa2Cu4O11+δ Superconducting System

In this work, the superconducting CuBa2LaCa2Cu4O11+δ compound was prepared by citrate precursor method and the electrical and structural properties were studied. The electrical resistivity has been measured using four probe test to find the critical temperature Tc(offset) and Tc(onset). It was found that Tc (offset) at zero resistivity has 101 K and Tc (onset) has 116 K. The X-ray diffraction (XRD) analysis exhibited that a prepared compound has a tetragonal structure. The crystal size and microscopic strain due to lattice deformation of CuBa2LaCa2Cu4O11+δ were estimated by four methods, namely Scherer(S), Halder-Wagner(H-W), size-strain plot (SSP) and Williamson-Hall, (W-H) methods. Results of crystal sizes obtained by these methods were compared with each other. In all these methods, the values of βhkl (full-width half-maximum (FWHM) for diffraction peaks) and miler indices (hkl) are determined from the results obtained from Fullprof, Mach, Origin and VESTA software. The lattice parameters a, b and c, lattice shape, d and degree of crystallization were calculated. It was found that the crystal size which are calculating by S, W-H, SSP and H-W were (174.8472, 171.1776, 173.1009 and 175.4386) A0 respectively while the lattice strain values were (none, 0.0025, 0.004 and 0.003464), respectively.

Analysis of universal joint using virtual simulation method

The guiding framework and directing section are the standouts amongst the most significant gadgets of a car. It is an extremely critical part to accomplish the steadiness and relentless development of the vehicle. Just like an insect in this part, a cross joint is formed made up of poles having some type of burdens on each pole. The poles due to the force which are applied to them tend to experience shear as well as torsion force. Movement transmission arrangement of vehicles comprises a few parts which some of the time experience disastrous disappointments. Forces combine to form a turning part and this tends to experience weakness due to variable torque. In this research paper, we have limited our investigation of just segment to understand its pressure and dislodging effect with regards to the last item. For virtual construction of the object framework, a solid works tool was utilized and for analysis purposes, ANSYS programming was utilized. Hereby using FEA methodologies we can understand as well as distinguish between different types of stresses. This can be further studied by assessing the impact on the heap, limit conditions, the geometry of the mass, and the nature of the yoke. The directing framework and guiding section are the standouts amongst the most significant gadgets of a vehicle. it is an exceptionally essential part to accomplish security and unfaltering development of the vehicle. Just like insects, it has poles which were due to cross formed at the middle of the road part having burdens on both of its pole which were joined at the middle like a cross joint which was used in cross joints. Due to forces applied on the cross joint poles, it experiences both shear as well as torsion force. Movement transmission arrangement of vehicles comprises a few segments which at times experience heartbreaking disappointments. We have optimized and analyzed the universal joint according to lattice and free size and shape methodology.

Finite element analysis of knee joint implant for varying bio material using ANSYS

In this research we want to carry out the finite element analysis of knee implant for a patient at static state and then compare it with materials used in commercially available knee implant and then comprehend its stress analysis results. In this research, we have used the STP file of the knee joint and this design was proposed taking general data of a human being. The 3D CAD model was designed by utilizing the CAD tool Catia which is one of the best in surface CAD modelling after that the model was meshed in ANSYS and finally a finite element analysis is performed for different materials of knee implant for the constant load of 500 N. The obtained results are compared with each other and the material with the least stress is suggested for usage in the knee joint. Well as torsion force. Movement transmission arrangement of vehicles comprises a few segments which at times experience heartbreaking disappointments. We have optimized and analyzed the universal joint according to lattice and free size and shape methodology.

Infill topology and shape optimization of lattice‐skin structures

AbstractLattice‐skin structures composed of a thin‐shell skin and a lattice infill are widespread in nature and large‐scale engineering due to their efficiency and exceptional mechanical properties. Recent advances in additive manufacturing, or 3D printing, make it possible to create lattice‐skin structures of almost any size with arbitrary shape and geometric complexity. We propose a novel gradient‐based approach to optimizing both the shape and infill of lattice‐skin structures to improve their efficiency further. The respective gradients are computed by fully considering the lattice‐skin coupling while the lattice topology and shape optimization problems are solved in a sequential manner. The shell is modeled as a Kirchhoff–Love shell and analyzed using isogeometric subdivision surfaces, whereas the lattice is modeled as a pin‐jointed truss. The lattice consists of many cells, possibly of different sizes, with each containing a small number of struts. We propose a penalization approach akin to the SIMP (solid isotropic material with penalization) method for topology optimization of the lattice. Furthermore, a corresponding sensitivity filter and a lattice extraction technique are introduced to ensure the stability of the optimization process and to eliminate scattered struts of small cross‐sectional areas. The developed topology optimization technique is suitable for nonperiodic, nonuniform lattices. For shape optimization of both the shell and the lattice, the geometry of the lattice‐skin structure is parameterized using the free‐form deformation technique. The topology and shape optimization problems are solved in an iterative, sequential manner. The effectiveness of the proposed approach and the influence of different algorithmic parameters are demonstrated with several numerical examples.

Existence of corner modes in elastic twisted kagome lattices

This Letter investigates the emergence of corner modes in elastic twisted Kagome lattices at a critical twist angle, known as self-dual point. We show that a special type of corner modes exist and they are localized at a very specific type of corners independent of the overall shape of the finite lattice. Moreover, these modes appear even in the perturbed lattice at the corners with mirror planes. By exploring its counterpart in electronic system, we attribute such corner modes to charge accumulation at the boundary, which is confirmed by the plot of charge distribution in a finite lattice.

Optimally variable density lattice to reduce warping thermal distortion of laser powder bed fusion

Reduction of the thermal distortion caused by the fabrication process of metal additive manufacturing is an important issue. Considering the problem of forming an object having lattices inside it to reduce the thermal distortion, we perform a lattice density distribution optimization and its experimental verification. In the optimization, assuming a cube with a sphere void as the base lattice shape, the lattice’s distribution optimization is constructed based on the recurrent formula inherent strain method and a gradient method. The lattices are approximately handled as solid materials having effective stiffness calculated by the homogenization method. In the experiment, the laser powder bed fusion is introduced to fabricate test pieces. The test pieces are partially cut from the baseplate by a wire electric discharge machine, and the edge clearance caused by warping deformation is measured. The thermo-mechanical analysis is also introduced for the mechanical interpretation of the results. The reduction rate of the clearance caused by warping deformation in the experiment was 10.4%–24.8% in the quasi 2D example (comparison with 61.0%–91.4% volume fraction uniform lattices and a solid test piece) and 6.0% in the 3D example (comparison with the same volume fraction uniform lattice with the optimal lattice).

Optical Probing of Crystal Lattice Configurations in Single CsPbBr3 Nanoplatelets.

Quantum-confined nanostructures of CsPbBr3 with luminescence quantum efficiencies approaching unity have shown tremendous potential for lighting and quantum light applications. In contrast to CsPbBr3 quantum dots, where the fine structure of the emissive exciton state has been intensely discussed, the relationship among lattice orientation, shape anisotropy, and exciton fine structure in lead halide nanoplatelets has not yet been established. In this work, we investigate the fine structure of the bright triplet exciton of individual CsPbBr3 nanoplatelets by polarization-resolved micro- and magnetophotoluminescence spectroscopy at liquid helium temperature and find a large zero-field splitting of up to 2.5 meV. A unique relation between the crystal structure and the photoluminescence emission confirms the existence of two distinct crystal configurations in such nanoplatelets with different alignments of the crystal axes with respect to the nanoplatelet facets. Polarization-resolved experiments eventually allow us to determine the absolute orientation of an individual nanoplatelet on the substrate purely by optical means.

Engineering of inorganic nanostructures with hierarchy of chiral geometries at multiple scales

Engineering of inorganic nanostructures with hierarchy of chiral geometries at multiple scales

Low-velocity impact response of sandwich plates with GRC face sheets and FG auxetic 3D lattice cores

This paper presents multi-scale modeling and nonlinear low-velocity impact analysis of sandwich plates with graphene reinforced composite (GRC) face sheets and functionally graded (FG) auxetic 3D lattice cores. The temperature-dependent material properties of GRC face sheets are determined through a micromechanical model of extended Halpin-Tsai type. The 3D lattice cores are designed to have negative effective Poisson's ratios (EPRs) and possess two FG configurations through the plate thickness direction. Considering the localized deformation and accompanying shape and effective properties changes of 3D lattices, a full-scale FE simulation was then conducted. Numerical results demonstrated that, when compared with their non-auxetic compactors, the auxetic 3D lattice cores can bring about significantly enhanced impact resistance. Moreover, distinct effects of FG configurations are found on both the back face sheet displacements and contact forces of sandwich plates subjected to a rigid spherical impactor. Numerical results show the superiority of FG auxetic lattices. The present model is expected to be instructive for potential engineering applications and beneficial for further research.

A Review on Mechanical Performance of Hybrid Natural Fiber Polymer Composites for Structural Applications.

In the field of hybrid natural fiber polymer composites, there has been a recent surge in research and innovation for structural applications. To expand the strengths and applications of this category of materials, significant effort was put into improving their mechanical properties. Hybridization is a designed technique for fiber-reinforced composite materials that involves combining two or more fibers of different groups within a single matrix to manipulate the desired properties. They may be made from a mix of natural and synthetic fibers, synthetic and synthetic fibers, or natural fiber and carbonaceous materials. Owing to their diverse properties, hybrid natural fiber composite materials are manufactured from a variety of materials, including rubber, elastomer, metal, ceramics, glasses, and plants, which come in composite, sandwich laminate, lattice, and segmented shapes. Hybrid composites have a wide range of uses, including in aerospace interiors, naval, civil building, industrial, and sporting goods. This study intends to provide a summary of the factors that contribute to natural fiber-reinforced polymer composites’ mechanical and structural failure as well as overview the details and developments that have been achieved with the composites.