Simple Lattice Structures Research Articles

Study on the residual stress of simple cubic lattice structure produced by selective laser melting

Lattice structures become the focus for scholars to research due to its unique lightweight, high impact resistance and ideal noise reduction. Selective laser melting has become a very effective and convenient method for preparing lattice structures of excellent quality. However, it is imperative to acknowledge that rapid heating and cooling processes inherent to the method can generate excessive residual stresses within the lattice structures, thereby significantly compromising their mechanical properties. To address this issue, the present study seeks to elucidate the patterns and characteristics of distribution of residual stresses and deformations within simple cubic lattice structures, employing a combination of experimental techniques and finite element analysis. The fabrication of these simple cubic lattice structures is accomplished through selective laser melting. The investigation encompasses both two methods, involving X-ray measurements at discrete points on the structure, and finite element simulations to depict the overall stress distribution. The results show that the residual stress and deformation are more likely concentrated on the initial surface to be processed, and residual stress on the substrates is bigger than that on bars. Specifically, the biggest stress concentrates on the Z-bars, up to 1393 MPa. However, in terms of the overall state of stress distribution in the structure, the residual stress on the substrate is slightly higher than that on the lattice structure.

Design of the Elastic Modulus of porous lattice structures composed of cells with continuously variable cross section carrying structures

BackgroundPorous bone implants have a wide range of applications for their low elastic modulus and good connectivity. It is necessary to explore an elastic modulus control method that can significantly regulate the elastic modulus under the condition of maintaining a constant porosity. MethodsFor achieving continuously changing elastic modulus of porous lattice structure, the simple cubic lattice structures were selected as research object, and the distribution of cross-sectional sizes of its carrying structures were set as variable continuous curves. The prediction model for the elastic modulus was established based on the elasticity mechanics and the equal mass assumption. Then, the prediction model is enhanced through compression simulation of the unit cell structure. Finally, the accuracy of prediction model is validated by compression experiments. FindingsThe results indicate that the distribution of cross-sectional size of the carrying structures has a significant impact on the elastic modulus of unit cell structures under the constraint of equal mass. By adjusting the characteristic parameters of distribution curves, the elastic modulus can be changed within a large range. InterpretationVariable cross-section can effectively change the elastic modulus of porous structures while ensuring constant porosity. This method has important value in decoupling the influence of geometric parameters on the elastic modulus of porous structures.

An Exploration of the Phonon Frequency Spectrum and Born–von Karman Periodic Boundary Conditions in 1D and 2D Lattice Systems Using a Computational Approach

Periodic boundary conditions (PBCs) are a pivotal concept in the treatment of ideal lattices of infinite extent as a finite lattice. Most undergraduate texts that delve into the analytical treatment of lattice dynamics solve the problem in the reciprocal space with an implicit assumption of PBCs. While the traditional approach centered in the reciprocal or [Formula: see text]-space is elegant for simple one-dimensional lattice structures, the method becomes mathematically cumbersome for more complex lattices with real-world applications, such as a honeycomb lattice involving a [Formula: see text] secular determinant. In this work, we have explored the solution of lattice dynamics in direct space numerically, by constructing unit cells through an explicit implementation of Born–von Karman PBCs and solving the lattice dynamical equations in the displacement–time domain using the fourth-order Runge–Kutta algorithm. The Fast Fourier Transform technique is then used to obtain the phonon frequency spectrum corresponding to the computed instantaneous displacements. The fidelity of the model is validated by the agreement of the computational results obtained for the phonon spectrum at high symmetry points in the Brillouin zone with the analytical values for the given problem. Initially, the dynamics and the phonon spectrum are explored for monatomic and diatomic linear lattices which serve to act as introductory cases for the approach before investigating the 2D monatomic square and honeycomb lattices using the nearest and next-nearest neighbor approximations. A short-range force constant model employing the central forces and angular forces is used for the monatomic square lattice to account for the interatomic interactions. Our computational approach is expected to be physically more intuitive for a student for visualizing the periodicity of a given lattice and understanding its related dynamics. The approach demonstrates the usage of Born–von Karman PBCs in constructing a unit cell that effectively captures the dynamics of a lattice system, complementing the traditional secular determinant formalism. The work also illustrates an instance of how the computer programming can be used as a tool to empower the students to explore abstract concepts in physics. A honing of programming and computational skills of students enables them to interact with dynamic models in physics and gain deeper insight into the real-world applications of physics principles. Target group of this work is the students and educators at undergraduate level who seek a thorough and didactic comprehension of lattice dynamics.

Effects of the unit-cell size and arrangement on the compressive behaviors of lattice structures in powder bed fusion additive manufacturing

Lattice structures demonstrate a unique compressive behavior wherein the compressive strength increases and converges to a specific value as the number of unit-cell arrangements and overall dimensions of the lattice structure increase. In this study, the effects of the unit-cell size and cell arrangement on the compressive behavior of lattice structures were investigated to determine the convergence of compression characteristics at specific unit-cell configurations. Simple cubic lattice structures were designed and manufactured using powder bed fusion techniques. The lattice structures were characterized using universal testing machines. Experimental results revealed that the convergence of compressive strength was influenced by the size of the unit cell: the number of arrangements at which a specific compressive strength was reached increased as the unit-cell sizes decreased. Furthermore, specific convergence points were determined for different unit-cell sizes, providing valuable insights into the compressive strength behavior of lattice structures. This study emphasizes the significance of considering both unit-cell arrangements and overall dimensions when designing standard specimens for compression testing. Additionally, the methodology developed in this study can be applied to obtain an optimal configuration for desired strength characteristics.

A Machine Learning Study on High Thermal Conductivity Assisted to Discover Chalcogenides with Balanced Infrared Nonlinear Optical Performance.

Exploration of novel nonlinear optical (NLO) chalcogenides with high laser-induced damage thresholds (LIDT) is critical for mid-infrared (mid-IR) solid-state laser applications. High lattice thermal conductivity (κL ) is crucial to increasing LIDT yet often neglected in the search for NLO crystals due to lack of accurate κL data. A machine learning (ML) approach to predict κL for over 6000 chalcogenides is hereby proposed. Combining ML-generated κL data and first-principles calculation, a high-throughput screening route is initiated, and ten new potential mid-IR NLO chalcogenides with optimal bandgap, NLO coefficients, and thermal conductivity are discovered, in which Li2 SiS3 and AlZnGaS4 are highlighted. Big-data analysis on structural chemistry proves that the chalcogenides having dense and simple lattice structures with low anisotropy, light atoms, and strong covalent bonds are likely to possess higher κL . The four-coordinated motifs in which central cations show the bond valence sum of +2 to +3 and are from IIIA, IVA, VA, and IIB groups, such as those in diamond-like defect-chalcopyrite chalcogenides, are preferred to fulfill the desired structural chemistry conditions for balanced NLO and thermal properties. This work provides not only an efficient strategy but also interpretable research directions in the search for NLO crystals with high thermal conductivity.

Effects of cell orientation on compressive behaviour of electron beam powder bed fusion Ti6Al4V lattice structures

Electron beam powder bed fusion (EBPBF) is suitable for making porous (or lattice) structures for medical implant applications. However, it is challenging for a lattice structure with a high porosity level to have sufficient strength, while lattice structures with sufficient strength are required for orthopedic applications. Furthermore, strength anisotropy needs to be understood for the design of femoral stems as load direction (LD) is location dependent. The present study aims to understand the effects of cell orientation on the compressive behavior of simple cubic lattice structures built using EBPBF and Ti6Al4V alloy, with [001]//LD or [111]//LD. It has been found that the apparent yield strength (σy-L) of [001] lattices is 1.8 times higher than that of [111] lattices, by experimental determination and also by numerical simulation. Simulation has shown that, with the [001]//LD condition, σ1 in vertical load supporting struts is low when the structure yields. But locally, σ1 (>1,000 MPa) is positive and high for the [111]/LD condition when yielding of the structure occurs with the load value only 57% of the value that is required for causing yielding in the [001]//LD condition. The predictive yield strength values by simulation of both [001] and [111] lattices have been found to be slightly lower than the experimentally determined values. Explanation for this will be provided by considering the effect of the struct effective diameter with EBPBF strut irregularity on the strength of the lattice structures.

Theoretical study on the tendency of heat capacity of nanostructures using modified Debye's method

ABSTRACT As one of the most important basic properties of thermal physics, the theoretical study of specific heat capacities impacts numerous fields. With the recent rapid discovery of nanomaterials, the specific heat capacity of nanostructures has attracted more and more attention. In recent years, relevant theoretical explanations continue to grow, but it is undeniable that theoretical models have to keep up with the new discoveries. This paper provides new theoretical approaches to properly scrutinise some of these phenomena. Two modified Debye's models are constructed and investigated, based on the assumptions of simple cubic lattice structures and the lattice vibration of structures under low temperatures (1.5–15 K). While the first model focuses on the limited degree of freedom for nanostructures, the second model retains the trend of Debye's model taking into account the sound velocity under the influence of boundary conditions. We further notify that the first model fits well with the experimental data qualitatively and the second one successfully explains the proportional relationship between the heat capacity of nanostructures of various shapes and sizes, respectively. Hence, these two models can form a basis to stimulate further theoretical developments to come.

DLP Fabrication of Zirconia Scaffolds Coated with HA/β-TCP Layer: Role of Scaffold Architecture on Mechanical and Biological Properties

In order to merge high-mechanical properties and suitable bioactivity in a single scaffold, zirconia porous structures are here coated with a hydroxyapatite layer. The digital light processing (DLP) technique is used to fabricate two types of scaffolds: simple lattice structures, with different sizes between struts (750, 900 and 1050 µm), and more complex trabecular ones, these latter designed to better mimic the bone structure. Mechanical tests performed on samples sintered at 1400 °C provided a linear trend with a decrease in the compressive strength by increasing the porosity amount, achieving compressive strengths ranging between 128–177 MPa for lattice scaffolds and 34 MPa for trabecular ones. Scaffolds were successfully coated by dipping the sintered samples in a hydroxyapatite (HA) alcoholic suspension, after optimizing the HA solid loading at 20 wt%. After calcination at 1300 °C, the coating layer, composed of a mixture of HA and β-TCP (β-TriCalcium Phospate) adhered well to the zirconia substrate. The coated samples showed a proper bioactivity, well pronounced after 14 days of immersion into simulated body fluid (SBF), with a more homogeneous apatite layer formation into the trabecular samples compared to the lattice ones.

Hybrid Ti6Al4V/Silk Fibroin Composite for Load-Bearing Implants: A Hierarchical Multifunctional Cellular Scaffold.

Despite the tremendous technological advances that metal additive manufacturing (AM) has made in the last decades, there are still some major concerns guaranteeing its massive industrial application in the biomedical field. Indeed, some main limitations arise in dealing with their biological properties, specifically in terms of osseointegration. Morphological accuracy of sub-unital elements along with the printing resolution are major constraints in the design workspace of a lattice, hindering the possibility of manufacturing structures optimized for proper osteointegration. To overcome these issues, the authors developed a new hybrid multifunctional composite scaffold consisting of an AM Ti6Al4V lattice structure and a silk fibroin/gelatin foam. The composite was realized by combining laser powder bed fusion (L-PBF) of simple cubic lattice structures with foaming techniques. A combined process of foaming and electrodeposition has been also evaluated. The multifunctional scaffolds were characterized to evaluate their pore size, morphology, and distribution as well as their adhesion and behavior at the metal–polymer interface. Pull-out tests in dry and hydrated conditions were employed for the mechanical characterization. Additionally, a cytotoxicity assessment was performed to preliminarily evaluate their potential application in the biomedical field as load-bearing next-generation medical devices.

Topological Pumping in a Floquet-Bloch Band.

Constructing new topological materials is of vital interest for the development of robust quantum applications. However, engineering such materials often causes technological overhead, such as large magnetic fields, spin-orbit coupling, or dynamical superlattice potentials. Simplifying the experimental requirements has been addressed on a conceptual level-by proposing to combine simple lattice structures with Floquet engineering-but there has been no experimental implementation. Here, we demonstrate topological pumping in a Floquet-Bloch band using a plain sinusoidal lattice potential and two-tone driving with frequencies ω and 2ω. We adiabatically prepare a near-insulating Floquet band of ultracold fermions via a frequency chirp, which avoids gap closings en route from trivial to topological bands. Subsequently, we induce topological pumping by slowly cycling the amplitude and the phase of the 2ω drive. Our system is well described by an effective Shockley model, establishing a novel paradigm to engineer topological matter from simple underlying lattice geometries. This approach could enable the application of quantized pumping in metrology, following recent experimental advances on two-frequency driving in real materials.

Effect of Architected Structural Members on the Viscoelastic Response of 3D Printed Simple Cubic Lattice Structures.

Three-dimensional printed polymeric lattice structures have recently gained interests in several engineering applications owing to their excellent properties such as low-density, energy absorption, strength-to-weight ratio, and damping performance. Three-dimensional (3D) lattice structure properties are governed by the topology of the microstructure and the base material that can be tailored to meet the application requirement. In this study, the effect of architected structural member geometry and base material on the viscoelastic response of 3D printed lattice structure has been investigated. The simple cubic lattice structures based on plate-, truss-, and shell-type structural members were used to describe the topology of the cellular solid. The proposed lattice structures were fabricated with two materials, i.e., PLA and ABS using the material extrusion (MEX) process. The quasi-static compression response of lattice structures was investigated, and mechanical properties were obtained. Then, the creep, relaxation and cyclic viscoelastic response of the lattice structure were characterized. Both material and topologies were observed to affect the mechanical properties and time-dependent behavior of lattice structure. Plate-based lattices were found to possess highest stiffness, while the highest viscoelastic behavior belongs to shell-based lattices. Among the studied lattice structures, we found that the plate-lattice is the best candidate to use as a creep-resistant LS and shell-based lattice is ideal for damping applications under quasi-static loading conditions. The proposed analysis approach is a step forward toward understanding the viscoelastic tolerance design of lattice structures.

Simple optimal lattice structures for arbitrary loadings

This paper identifies four categories of optimal truss lattice structures (TLSs) that together provide ultimate stiffness for arbitrary multi-loading scenarios in the low volume fraction limit. Each category consists of 7 periodic sets of straight bars, forming periodic parallelepiped unit cells. Compared to other optimal TLSs, the identified TLSs most probably have the simplest possible geometries with the least number of bar sets. Macroscopic properties of a TLS are estimated using a superposition model, and an optimization problem is solved to determine the exact geometries of the optimal TLSs. Systematic optimization results, run for thousands of random multi-loading conditions, are compared to (postulated) theoretical bounds for both truss and plate lattice structures. The results clearly demonstrate near-optimality of the identified TLSs (relative difference mostly within machine precision except in few cases up to 0.1%) for any loading scenarios in linear elasticity. At the same time, the optimal anisotropic TLSs always have inferior stiffness to the corresponding optimal plate lattice structures and this inferiority is bounded between 1 (single uniaxial load) and a factor of 3 (optimal isotropy).

Transient analysis of nonlinear locally resonant metamaterials via computational homogenization

In this paper, the transient computational homogenization scheme is extended to allow for nonlinear elastodynamic phenomena. The framework is used to analyze wave propagation in a locally resonant metamaterial containing hyperelastic rubber-coated inclusions. The ability to properly simulate realistic nonlinearities in elasto-acoustic metamaterials constitutes a step forward in metamaterial design as, so far, the literature has focused only on academic nonlinear material models and simple lattice structures. The accuracy and efficiency of the framework are assessed by comparing the results with direct numerical simulations for transient dynamic analysis. It is found that the band gap features are adequately captured. The ability of the framework to perform accurate nonlinear transient dynamic analyses of finite-size structures is also demonstrated, along with the significant computational time savings achieved.

Generalization of exactly-solvable model to exhibit solid-fluid phase transition in crystal structures with two particles in a primitive cell

In our previous paper (Komatsu 2015 J. Stat. Mech. P08020), we investigated an interacting-particle model with infinite-range cosine potentials, and derived the partition function which shows solid-fluid phase transition by exact calculation. However, we could treat only simple lattice structures in which more than one stable point exists in a primitive cell such as the triangular or face-centered cubic lattice. In the present paper, we generalize our previous scheme to more complicated lattice structures with two particles in a primitive cell. Generalization to more complicated lattice structures is straightforward.

M320 超音波共鳴法による格子型金属構造体の弾性率評価(GS3 材料力学(3),修士研究発表セッション)

M320 超音波共鳴法による格子型金属構造体の弾性率評価(GS3 材料力学(3),修士研究発表セッション)

Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice

Dirac points are central to many phenomena in condensed-matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators. At a Dirac point, two energy bands intersect linearly and the electrons behave as relativistic Dirac fermions. In solids, the rigid structure of the material determines the mass and velocity of the electrons, as well as their interactions. A different, highly flexible means of studying condensed-matter phenomena is to create model systems using ultracold atoms trapped in the periodic potential of interfering laser beams. Here we report the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum bandgap inside the Brillouin zone at the positions of the two Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to change the positions of the Dirac points inside the Brillouin zone. When the anisotropy exceeds a critical limit, the two Dirac points merge and annihilate each other-a situation that has recently attracted considerable theoretical interest but that is extremely challenging to observe in solids. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials in which the topology of the band structure is crucial, but also provide an avenue to exploring many-body phases resulting from the interplay of complex lattice geometries with interactions.

A new particle‐tracking approach to simulating transport in heterogeneous fractured porous media

Particle‐tracking methods are often used to model contaminant transport in fractured porous media because they are straightforward to implement for fracture networks and are able to take into account the matrix effect without mesh generation. While classical methods assume infinite matrix or regularly spaced fractures, we have developed a stochastic method adapted to solute transport in complex fracture networks associated with irregular matrix blocks. Diffusion times in the matrix blocks are truncated by the finite size of the blocks. High ratios of matrix diffusion to fracture advection, small fracture apertures, and small blocks favor the transfer of particles to nearby fractures through matrix diffusion. Because diffusion occurs on both sides of the originating fracture before particles reach one of the neighboring fractures, transfer times to both neighboring fractures are strongly affected by the network configurations on both sides of the fracture. This new particle‐tracking method is able to deal with complex fracture networks by considering heterogeneous configurations on both sides of the fracture. We finally show on simple Sierpinski lattice structures that neglecting the finite size of the matrix blocks may lead to orders of magnitude overestimations of the transfer times.

Miniaturized Transmission Lines Based on Hybrid Lattice-Ladder Topology

This paper introduces hybrid structures with unit cells that are a combination of lattice and ladder topologies. These unit cells dramatically increase the quality factor, miniaturization, and maximum frequency of synthetic transmission lines. Also, it is shown that lattice topologies in general are less vulnerable to the effect of parasitics, such as self resonance of loading capacitors or mutual inductance between different cells. The underlying theory is studied, and simple formulas are given for predicting the behavior of these lines. A few examples are presented that, based on full-wave simulations, show the large gain in miniaturization, quality factor, or bandwidth compared to the simple ladder or lattice structures. Measured results for a fabricated synthetic line are presented that show a miniaturization factor of n=?{?eff?eff}=16.5 for Z 0=50 ? and a very small dispersive behavior from dc to 2.5 GHz.

Nanoscale Electronic Inhomogeneity in In2Se3 Nanoribbons Revealed by Microwave Impedance Microscopy

Driven by interactions due to the charge, spin, orbital, and lattice degrees of freedom, nanoscale inhomogeneity has emerged as a new theme for materials with novel properties near multiphase boundaries. As vividly demonstrated in complex metal oxides (see refs 1-5) and chalcogenides (see refs 6 and 7), these microscopic phases are of great scientific and technological importance for research in high-temperature superconductors (see refs 1 and 2), colossal magnetoresistance effect (see ref 4), phase-change memories (see refs 5 and 6), and domain switching operations (see refs 7-9). Direct imaging on dielectric properties of these local phases, however, presents a big challenge for existing scanning probe techniques. Here, we report the observation of electronic inhomogeneity in indium selenide (In(2)Se(3)) nanoribbons (see ref 10) by near-field scanning microwave impedance microscopy (see refs 11-13). Multiple phases with local resistivity spanning 6 orders of magnitude are identified as the coexistence of superlattice, simple hexagonal lattice and amorphous structures with approximately 100 nm inhomogeneous length scale, consistent with high-resolution transmission electron microscope studies. The atomic-force-microscope-compatible microwave probe is able to perform a quantitative subsurface electrical study in a noninvasive manner. Finally, the phase change memory function in In(2)Se(3) nanoribbon devices can be locally recorded with big signals of opposite signs.

Simple metals under pressure

The alkali metals have long been regarded as ‘simple metals’ because of their simple lattice structures under ordinary conditions. New calculations predict that under pressure lithium will have a paired, molecular-like structure, similar to hydrogen, that may even be insulating. This unexpected finding may lead to a revised understanding of these simple metals.