Uniform Lattice Research Articles

Localized magnetic moments variation for strengthening and tuning thermal expansion behavior of Mg alloys

We proposed the localized magnetic moments (LMMs) variation-induced strengthening for Mg alloys. Due to the strong interplay of magnetic and elastic, the introduction of merely 7 wt.% Mn3Ga0.7Ge0.3N in WE43 Mg alloy could not only reduce the coefficient of thermal expansion (CTE) but also enable an enhancement of ∼70% on compressive yield strength and less decrease of ∼2.1% on the elongation. We observed localized uniform lattice deformations and magnetic phase transitions for stress response and verified that the strain involves LMMs variation in the frustrated antiperovskite system, realizing simultaneously reinforcing and toughening in the compressive deformation process. Meanwhile, these magnetic transitions are accompanied by volume shrinkage and thus reduce the CTE of the WE43 Mg alloy. These results demonstrate that the introduction of the secondary phase with the variation of LMMs for stress response is an effective design strategy for alloys to achieve tunable thermal expansion behavior combined with high strength and moderate compressive deformability.

Characterization of mechanical equivalent properties for node enhanced graded lattice structure

Abstract Considering the stress concentration at the rod connection of traditional body-centered cubic (BCC) lattice structure, a node enhanced BCC (NBCC) lattice structure was proposed. In recent years, graded lattice structure has gradually attracted attention due to their unique mechanical properties. In this paper, two different graded NBCC lattice structures were designed and their static mechanical properties were evaluated through quasi-static compression experiments and simulations. Moreover, homogenization theory was applied to calculate the equivalent modulus of lattice structure. This method was extended from uniform lattice structure to graded lattice structure by improving the application of periodic boundary conditions. The obtained results were in good agreement with the experimental and simulation data. The quasi-static compression tests demonstrated that NBCC can effectively reduce the stress concentration and improve the load-bearing capacity about 25% compared to BCC. The graded lattice structures exhibit varying mechanical properties depending on their design and present better mechanical performance in the anisotropic direction. Finally, the relative relationship between the equivalent elastic modulus and the equivalent shear modulus in the lattice structure was studied. The prediction formula for equivalent shear modulus was extended based on the Gibson-Ashby formula.

A study of multi-stage energy absorption characteristics of hybrid sheet TPMS lattices

Triply periodic minimal surface (TPMS) has many excellent properties, such as stable energy absorption, a high specific strength, a large surface area, etc. The functional multi-stage design and research of TPMS lattices were carried out to improve the mechanical performance. The deformation modes and curves of three uniform TPMS lattices (Primitive, Gyroid, and Diamond) and their hybrid lattices were analyzed by quasi-static compression experiments and numerical simulations. Based on the uniform TPMS lattice, hybrid sheet TPMS lattices were designed to realize the multi-stage energy absorption (multi-stage platform) and multi-stage protection integrated porous structure. The two-stage energy absorption characteristics of hybrid sheet TPMS lattices were systematically studied, and the effects of hybrid TPMS composition, width of the transition layer, relative weight, and hybridization method on the multi-stage energy absorption were obtained. The results indicated that the Gyroid–Diamond hybrid lattice performed the best, with the specific energy absorption (SEA) increasing by 30.48% and 0.51%, and the yield stress decreasing by 14.01% and 30.07%, respectively, as compared to the single TPMS lattice. Width of the transition layer has little effect on the two-stage energy absorption. The relative weight will shorten or widen the length of the two-stage platform stress. The hybridization method shows that the sequence hybridization along the loading direction based on the TPMS lattice yield strength is the best arrangement to achieve the effect of multi-stage energy absorption. Finally, the three-stage energy absorption characteristics of hybrid Primitive–Gyroid–Diamond lattices are further studied. The results show that with the increase of layers of TPMS lattices, the fluctuation of the multi-stage curve and the yield stress will increase.

Adaptive enhancement design of triply periodic minimal surface lattice structure based on non-uniform stress distribution

The Schwarz primitive triply periodic minimal surface (P-type TPMS) lattice structures are widely used. However, these lattice structures have weak load-bearing capacity compared with other cellular structures. In this paper, an adaptive enhancement design method based on the non-uniform stress distribution in structures with uniform thickness is proposed to design the P-type TPMS lattice structures with higher mechanical properties. Two types of structures are designed by adjusting the adaptive thickness distribution in the TPMS. One keeps the same relative density, and the other keeps the same of non-enhanced region thickness. Compared with the uniform lattice structure, the elastic modulus for the structure with the same relative density increases by more than 17%, and the yield strength increases by more than 10.2%. Three kinds of TPMS lattice structures are fabricated by laser powder bed fusion (L-PBF) with 316L stainless steel to verify the proposed enhanced design. The manufacture-induced geometric deviation between the as-design and as-printed models is measured by micro X-ray computed tomography (µ-CT) scans. The quasi-static compression experimental results of P-type TPMS lattice structures show that the reinforced structures have stronger elastic moduli, ultimate strengths, and energy absorption capabilities than the homogeneous P-TPMS lattice structure.

Ab initio prediction of coexistence of two magnetic states in Mn[formula omitted]Sn ([formula omitted]Sc, Ti, and V) Heusler alloys under applied pressure

The structural, magnetic and electronic properties of Mn2YSn (Y=Sc, Ti, and V) Heusler alloys under applied hydrostatic pressure are studied by the first-principle calculations and Monte Carlo simulations. We find that two magnetic reference states with low and high magnetic moment at the low and high crystal lattice volume, respectively, can coexist together due to the almost equal energy under applied pressure of 3.4, −2.9 and −3.25 GPa for Mn2ScSn, Mn2TiSn, and Mn2VSn, correspondingly. The positive/negative pressure correspond to the uniform lattice contraction/expansion. We show that for all compounds, the low magnetic state (LMS) is characterized by the almost half-metallic behavior and it is maintained against hydrostatic pressure. However, the electronic structure of the high magnetic state (HMS) takes on a metallic character. For HMS, the magnetic exchange parameters and Curie temperatures are found to be sufficiently larger values as compared to those of LMS. To identify stable phases at given pressures, the phase diagrams are constructed. The pressure-induced switching mechanism between almost half-metallic and metallic states with different magnetization is proposed.

Mechanical Response and Energy Absorption of 316L Stainless Steel Body‐Centered‐Cubic Functionally Graded Lattice Structures under Quasistatic Compressive Test

Five different density gradient variation strategies are proposed for body‐centered‐cubic (BCC) lattice structures in parallel to the loading direction prepared by selective laser melting with 316 L stainless steel as the building material, and the mechanical properties, deformation behavior, and energy absorption capacity of lattice structures with different density gradient variations and uniform lattice structure under compressive loading are investigated and compared. The results show that the elastic modulus and compressive strength of the uniform lattice structure are better than those of the lattice structure with density gradient parallel to the loading direction, provided that the relative densities are similar. However, through a reasonable design of density gradient, the lattice structure with density gradient parallel to the loading direction can obtain higher plateau stress than the uniform lattice structure and increase the onset densification strain to a certain extent, which obviously improves the energy absorption capacity of the lattice structure. The results obtained by finite‐element calculations are in good agreement with the experimental results and can better restore the deformation behavior of the lattice structure under compressive loading. This work provides inspiration for the design of the density gradient of the lattice structure.

Interaction of electrons and positrons with two-dimensional artificially generated proton lattice and with carbon lattice

A many-body classical trajectory Monte Carlo (CTMC) method is applied in the study of scattering probabilities of electrons and positrons after interacting with a two-dimensional (2D) artificially generated, uniform lattice, composed of fixed protons. We used different lattice parameters between the protons for different simulations, where the projectiles have kinetic energies of 500 and 1000 eV. We found a very strong focusing of electrons and a very strong defocusing of the positrons at lower lattice parameters. Furthermore, we found, these effects get weaker with increasing lattice parameters. Interesting changes took place at lattice parameters 2 and 3 au. which are close to the lattice parameter between carbon atoms in graphene of value 2.68 au. We also performed a simulation of a defective lattice by removing some protons and noticed distinguishable changes in the spectra compared to the spectra of an ideal lattice. This comparison may open a way for the detection of lattice defects in real samples.

Magnetic phase diagram in the three-dimensional triangular-lattice antiferromagnet Sr3CoTa2O9 with small easy-axis anisotropy

We report the results of low-temperature magnetization and specific heat measurements of ${\mathrm{Sr}}_{3}{\mathrm{CoTa}}_{2}{\mathrm{O}}_{9}$ powder, in which ${\mathrm{Co}}^{2+}$ ions with effective spin-1/2 form a uniform triangular lattice in the $ab$ plane. It was found that ${\mathrm{Sr}}_{3}{\mathrm{CoTa}}_{2}{\mathrm{O}}_{9}$ undergoes successive antiferromagnetic transitions at ${T}_{\mathrm{N}1}=0.97\phantom{\rule{4pt}{0ex}}\mathrm{K}$ and ${T}_{\mathrm{N}2}=0.79\phantom{\rule{4pt}{0ex}}\mathrm{K}$ at zero magnetic field. As the magnetic field increases, both ${T}_{\mathrm{N}1}$ and ${T}_{\mathrm{N}2}$ decrease monotonically. The obtained magnetic field vs temperature phase diagram together with a sharp magnetization anomaly at a saturation field of ${\ensuremath{\mu}}_{0}{H}_{\mathrm{s}}=2.3$ T indicates that ${\mathrm{Sr}}_{3}{\mathrm{CoTa}}_{2}{\mathrm{O}}_{9}$ is described as a spin-1/2 three-dimensional triangular-lattice antiferromagnet with a weak easy-axis anisotropy. We discuss the characteristics of the magnetic phase diagram, which approximates the phase diagram for the magnetic field perpendicular to the $c$ axis.

Toughening Ceramic-Based Composites by Homogenizing the Lattice Strain at Phase Boundaries.

Ceramic-based composites generally have low fracture toughness, and toughening these materials without sacrificing their hardness has been a big challenge. This study presents an approach for toughening ceramic-based composites by modulating the strain partition and stress distribution in phase-boundary regions. A new concept of homogenizing the lattice strain to achieve high fracture toughness in ceramic-based composites is proposed based on the collective lattice shear of martensitic phase transformation. The strategy was demonstrated by ZrO2-containing WC-Co ceramic-metal composites as a prototype. The crystal planes along the WC/ZrO2 martensitic transforming phase boundaries exhibited significantly larger and uniform lattice strains compared with conventional dislocation pile-up phase boundaries with highly localized lattice strains. The homogeneous strain and stress distributions across interfaces enabled the composite to have simultaneously high fracture toughness and hardness. The "homogenizing the lattice strain" strategy proposed in this work is applicable to a broad range of ceramic-based composites to achieve superior comprehensive mechanical properties.

Evaluation of mechanical properties of Ti–6Al–4V BCC lattice structure with different density gradient variations prepared by L-PBF

Based on the optimized pore size distribution and relative density, the functionally graded lattice structure is capable of achieving better mechanical properties than a uniform lattice structure with similar porosity. In this study, in order to investigate the effect of the strategy of density gradient variation on the lattice structure with similar porosity, three different density gradients were designed for the BCC-based lattice structure in parallel and perpendicular to the loading direction based on Ti–6Al–4V alloy powder and laser beam powder bed fusion technology, respectively. The results showed that the elastic modulus, yield strength and compressive strength of the lattice structure with a density varying as a logarithmic function perpendicular to the loading direction were 39.91%, 51.85% and 51.72% higher than the uniform lattice structure respectively. Moreover, the layer-by-layer collapse phenomenon was the primary aspect impacting the energy absorption in the lattice structures with density gradient parallel to the loading direction. By observing the fracture morphology of the lattice structures, it was found that all specimens exhibited dimple and smooth plane morphological features for a mixed failure mechanism of cleavage and dimple rupture, indicating that the failure mode of the lattice structures are a combination of brittle and ductile deformation. Therefore, a reasonable density gradient design can significantly improve the mechanical properties of the lattice structure with similar porosity. This work provides valuable inspiration for the design of lattice structures in engineering applications.

Quasi-static and dynamic compression of additively manufactured functionally graded lattices: Experiments and simulations

In this paper, quasi-static and dynamic compressive behaviors of functionally graded (FG) lattices made of stainless steel (SS 316L) by electron beam melting (EBM) were experimentally investigated. The FG lattice structures were body-centered cubic (BCC) lattices with uni-directional density grading and bi-directional density grading. Their performance was compared with that of uniform lattices of the same relative density. The experimental results showed that, as compared with the uniform and uni-directional density graded lattices, the novel bi-directional density graded lattices witnessed the highest plateau stress and energy absorption capacity at the considered loading conditions. The deformation pattern and the stress distribution of the structures during the crush were further studied using finite element modelling (FEM). The finite element modelling showed that the enhanced strength and energy absorption were related to the periodic collapse of graded structures corresponding to the density gradient strategy. Two parametric studies were conducted using the experimentally validated FEM models to examine the influence of density gradient on the dynamic response of FG lattices.

Mechanically robust 3D printed elastomeric lattices inspired by strong and tough hierarchical structures

Lattice structures have been proven capable of a wide range of engineering applications due to their complex design arrangements, such as periodicity, topology, and morphologies. Yet, developing a hybrid design is challenging due to limitations of node boundaries, material, and fabrication constraints for improving mechanical performance. To overcome these challenges, hybrid designs were developed here using the vat photopolymerization technique by grading the bend- and stretch-dominant strut morphology in parallel and perpendicular directions. Firstly, numerical simulations predicted the unit cell performances, and then the structural behavior of periodically arranged 3D-printed elastomeric lattices was also investigated. As a result, hybrid design provided a better performance strategy under high load conditions, including a significant amount of mechanical performance (7 times) than the uniform lattice topology. In addition, a vat photopolymerization-based 3D printing technique was investigated by introducing a high-loaded silica filler in the polymer, as a filler reinforcement exhibiting the advantages of enhanced stiffness (12 times) and reduced buckling to the lattices. Finally, the performance of hybrid-graded design was examined via filler-coated surfaces, which could provide insight into their ability to adapt to lightweight devices and engineering applications.

Impact Performance of 3D Printed Spatially Varying Elastomeric Lattices

Additive manufacturing is catalyzing a new class of volumetrically varying lattice structures in which the dynamic mechanical response can be tailored for a specific application. Simultaneously, a diversity of materials is now available as feedstock including elastomers, which provide high viscoelasticity and increased durability. The combined benefits of complex lattices coupled with elastomers is particularly appealing for anatomy-specific wearable applications such as in athletic or safety equipment. In this study, Siemens' DARPA TRADES-funded design and geometry-generation software, Mithril, was leveraged to design vertically-graded and uniform lattices, the configurations of which offer varying degrees of stiffness. The designed lattices were fabricated in two elastomers using different additive manufacturing processes: (a) vat photopolymerization (with compliant SIL30 elastomer from Carbon) and (b) thermoplastic material extrusion (with Ultimaker™ TPU filament providing increased stiffness). Both materials provided unique benefits with the SIL30 material offering compliance suitable for lower energy impacts and the Ultimaker™ TPU offering improved protection against higher impact energies. Moreover, a hybrid lattice combination of both materials was evaluated and demonstrated the simultaneous benefits of each, with good performance across a wider range of impact energies. This study explores the design, material, and process space for manufacturing a new class of comfortable, energy-absorbing protective equipment to protect athletes, consumers, soldiers, first responders, and packaged goods.

Properties Evaluations of Topology Optimized Functionally Graded Lattice Structures Fabricated by Selective Laser Melting

Owning to their lightweight characteristic and high performance, functionally graded lattice structures (FGLSs) show great potential in orthopedics, automotive industries and aerospace applications. Here, two types of uniform lattice structures (ULSs) with RD = 0.50 and 0.20, and two types of FGLSs with RD = 0.30-0.50 and RD = 0.20-0.40, were designed by topology optimization and fabricated by SLM technology. Subsequently, their surface morphology, compressive deformation behavior and energy absorption abilities were evaluated by use of the finite element method (FEM) and compression tests. From these results, both elastic modulus and yield strength of specimens decreased with the lowering of the RD value. ULSs had a uniform deformation behavior with bending and bulking of struts, while FGLSs presented a mixed deformation behavior of different layers. Additionally, the energy absorption capability (Wv) of specimens was proportional to the RD value. When the value of RD increased from 0.20 to 0.50, the Wv of specimens increased from 0.3657 to 1.7469 MJ/m3. Furthermore, mathematical models were established successfully to predict the mechanical properties of FGLSs with percentage deviations < 10%. This work provides a comprehensive understanding regarding how to design and manufacture FGLSs with the properties desired for satisfying the demand of different application scenarios.

Flexural properties of 3D printed graded lattice reinforced cementitious composites using digital image correlation

Three-dimensional (3D) printed polymer-reinforced cementitious composites are expected to be used to improve the ductility of cement-based materials. However, research on the maximum flexural capacity and failure mode of lattice-reinforced cementitious composites remains insufficient. In this study, six types of cells with different volume fractions are designed, and mainly undergo bending and tensile deformation. According to the load characteristics during a three-point bending test, five kinds of graded lattice structures are designed. Moreover, a skin-lattice structure and uniform lattice structure are designed, and plain cement mortar is set to comprehensively evaluate the bending mechanical properties of graded lattice-reinforced cementitious composites. The crack evolution and failure mode of these composites under three-point bending load are studied using digital image correlation (DIC). The results show that compared with the uniform lattice, the graded lattice can improve the maximum bending capacity of cement-based materials, improve their cracking characteristics and failure modes during the bending process, and enhance their toughness while reducing the amount of required material. Compared with the plain cement mortar specimen, the graded lattice-reinforced specimen with the largest bending peak load is found to have a 175% increase in the bending peak load and a significant increase in the bending bearing capacity.

Observation of the Sign Reversal of the Magnetic Correlation in a Driven-Dissipative Fermi Gas in Double Wells.

We report the observation of the sign reversal of the magnetic correlation from antiferromagnetic to ferromagnetic in a dissipative Fermi gas in double wells, utilizing the dissipation caused by on-site two-body losses in a controlled manner. We systematically measure dynamics of the nearest-neighbor spin correlation in an isolated double-well optical lattice, as well as a crossover from an isolated double-well lattice to a one-dimensional uniform lattice. In a wide range of lattice configurations over an isolated double-well lattice, we observe a ferromagnetic spin correlation, which is consistent with a Dicke type of correlation expected in the long-time limit. This work demonstrates the control of quantum magnetism in open quantum systems with dissipation.

Phonon softening and slowing-down of charge density wave fluctuations in BaNi2As2

BaNi$_2$As$_2$ is a nonmagnetic analogue of the iron pnictide superconductors, and in its tetragonal state exhibits an incommensurate charge-density-wave (IC-CDW) and a sizable elastoresistance. In this work, phonons in BaNi$_2$As$_2$ associated with the IC-CDW and uniform in-plane lattice distortions are investigated using high-resolution inelastic X-ray scattering. The in-plane transverse acoustic phonons reveal no softening at temperatures where the elastoresistance increases strongly, indicating the latter to be electronically driven. Systematic phonon measurements reveal the IC-CDW occurs in two stages upon cooling: underdamped phonons first soften to zero energy well above the IC-CDW ordering temperature, then the resulting quasielastic IC-CDW fluctuations gradually slow down and coalesce into the static IC-CDW order. A possible origin for our observations is the IC-CDW in tetragonal BaNi$_2$As$_2$ being uniaxial, which provides an additional Ising degree of freedom favorable for disordered IC-CDW modulations, and accounts for the elastoresistance through a weak coupling to the lattice.

Lattice uniformities inducing unbounded convergence

A net (xγ)γ∈Γ in a locally solid Riesz space (X,τ) is said to be unbounded τ-convergent to x if |xγ−x|∧u⟶τ0 for all u∈X+. We recall that there is a locally solid linear topology uτ on X such that unbounded τ-convergence coincides with uτ-convergence. It turns out that uτ is characterised as the weakest locally solid linear topology which coincides with τ on all order bounded subsets. It is with this motivation that we introduce, for a uniform lattice (L,u), the weakest lattice uniformity u⁎ on L that coincides with u on all the order bounded subsets of L. It is shown that if u is the uniformity induced by the topology of a locally solid Riesz space (X,τ), then the u⁎-topology coincides with uτ. This allows comparing results of this paper with earlier results on unbounded τ-convergence. It will be seen that despite the fact that in the setup of uniform lattices most of the machinery used in the techniques of [24] is lacking, the concept of ‘unbounded convergence’ well fittingly generalizes to uniform lattices. We shall also answer Questions 3.3, 5.10 of [24] and Question 18.51 of [22].

Influence of Density Gradient on the Compression of Functionally Graded BCC Lattice Structure.

In this paper, five grading functional gradient lattice structures with a different density perpendicular to the loading direction were proposed, and the surface morphology, deformation behavior, and compression properties of the functional gradient lattice structures prepared by selective laser melting (SLM) with Ti-6Al-4V as the building material were investigated. The results show that the characteristics of the laser energy distribution of the SLM molding process make the spherical metal powder adhere to the surface of the lattice structure struts, resulting in the actual relative density of the lattice structure being higher than the designed theoretical relative density, but the maximum error does not exceed 3.33%. With the same relative density, all lattice structures with density gradients perpendicular to the loading direction have better mechanical properties than the uniform lattice structure, in particular, the elastic modulus of LF, the yield strength of LINEAR, and the first maximum compression strength of INDEX are 28.99%, 16.77%, and 14.46% higher than that of the UNIFORM. In addition, the energy absorption per unit volume of the INDEX and LINEAR is 38.38% and 48.29% higher, respectively, than that of the UNIFORM. Fracture morphology analysis shows that the fracture morphology of these lattice structures shows dimples and smooth planes, indicating that the lattice structure exhibits a mixed brittle and ductile failure mechanism under compressive loading. Finite element analysis results show that when the loading direction is perpendicular to the density gradient-forming direction, the higher density part of the lattice structure is the main bearing part, and the greater the density difference between the two ends of the lattice structure, the greater the elastic modulus.

A Novel and Elliptical Lattice Design of Flocking Control for Multi-Agent Ground Vehicles

Flocking control of multi-agent ground vehicles recently attracted rising attention because of its strength in extending 1D platooning to coordinated 2D movements. However, the uniform interaction ranges and the non-defined orientation of the flocking lattice make flocking control of ground vehicles face some key issues. To achieve cooperative motions of connected and automated vehicles (CAVs), this letter proposed a novel and elliptical lattice to extend the existing flocking theory with a uniform hexagon lattice. The proposed elliptical lattice is designed based on the characteristics of the vehicle heading direction, velocity, minimum safety distance, and lane width to analytically adapt to vehicle driving environments. Moreover, a new flocking control law considering road boundaries’ (permanent) repulsive forces is developed to ensure the desired formation at a steady state. Simulation results show that the proposed elliptical lattice of flocking control can be applied to realize cooperative driving of multi-agent CAVs with the desired formation on the road.