Shape Of Unit Cell Research Articles

DFT-based investigation of polyetherketoneketone materials for surface modification for dental implants

BackgroundPolyetherketoneketone (PEKK) is a high-performance thermoplastic polymer with unique structural and mechanical properties that make it a promising candidate for surface modification of dental implants. This study was conducted to investigate the feasibility of PEKK for this purpose using the Cambridge Serial Total Energy Package (CASTEP) code based on density functional theory (DFT).MethodsThis study examined the ground state energy, structural properties, thermodynamic behavior, cohesive energy, refractive index, stress analysis, mechanical properties, and anisotropic behavior of PEKK.ResultsThis study found that PEKK has a complex crystal structure with an orthorhombic unit cell shape, triclinic lattice type, and a centered structure. It also has a 2D layered structure owing to the presence of carbonyl groups, which provides a large surface area for interaction with biological tissues. Thermodynamic analysis showed that PEKK exhibited bond elongation and structural changes at 380 °C, indicating thermal degradation. The cohesive energy of PEKK was calculated to be – 440 eV, indicating its stability and structural integrity. PEKK has a complex refractive index, with real and imaginary components that affect its optical properties. Stress analysis showed that PEKK is resistant to shear deformation and has high hydrostatic stress, which contributes to its stability and biocompatibility.ConclusionThe mechanical properties of PEKK, including its high stiffness, resistance to volume change under pressure, and ability to accommodate natural movements, make it suitable for surface modification of dental implants.

Closed-form effective out-of-plane elastic properties of regular and non-regular hexagonal lattice plates

This study derives closed-form expressions for the effective out-of-plane elastic properties of regular and non-regular hexagonal lattice plates. The derivation utilizes the homogenization method based on equivalent strain energy and the Kirchhoff plate theory. Rigorous accuracy assessments of the closed forms are conducted through comparisons with the existing literature and direct finite element analysis. A detailed parametric study is also conducted using the obtained closed forms to provide insights into the relationships between the effective elastic properties and the unit-cell shape. Lastly, general forms for some effective properties applicable to out-of-plane and in-plane situations are presented for hexagonal lattices.

Disruption of polar order in lead zirconate titanate by composition-modulated artificial superlattice

Lead zirconate titanate (Pb (Zrx, Ti1−x)O3: PZT) is a well-known ferroelectric compound, in which long-range polar order is usually developed. In the present study, it was clarified by distortion-corrected atomic-scale scanning transmission electron microscopy imaging that long-range polar order is disrupted in PZT by utilizing composition-modulated superlattice. Shape of unit cell was unusual both in the Pb(Zr0.65Ti0.35)O3 (PZT65) and Pb(Zr0.30Ti0.70)O3 (PZT30) layers, which was due to mutual in-plane lattice constraint. By taking account of this, first-principles calculations clarified that multiple directions can be energetically favorable for lead-ion displacement, which explains a reason why long-range polar order was disrupted.

Pentamodes: Effect of unit cell topology on mechanical properties

Pentamodes (first conceived theoretically by Milton and Cherkaev) are a very interesting class of mechanical metamaterials that can be used as building blocks of structures withdecoupled bulk and shear moduli. The pentamodes usually are composed of double cone-shaped struts with the middle diameter being large and the end diameters being tiny (ideally approaching zero). The cubic diamond geometry was proposed by Milton and Cherkaev as a suitable geometry for the unit cell and has since been used in the majority of the works on pentamodes. In this work, we aim to evaluate the degree to which the base unit cell design contributes to high bulk to shear modulus ratio, also known as Figure Of Merit(FOM). In addition to the diamond unit cell, three other well-known unit cell types are considered, and the effect of small diameter size and the ratio of large-to-small diameter, α, on the FOM is evaluated. The results showed that regardless of the base unit cell shape, the FOM value is highly dependent on the d (the smaller diameter size of double-cone) value, while its dependence on the D (the greater diameter of double-cone) value is very weak. For d/h∝0.05 (h representing the linkage length), figures of merit in the range of 103 could be reached for all the studied topologies.

A MICRO APPROACH TO VALIDATE THE GURSON YIELD CRITERIA AT MACRO LEVEL

In the present work, an effort has been made to validate Gurson yield criteria at the macro level with an equivalent numerical model at the micro level. The continuum body at macroscale has been assumed as periodically arranged stackable unit cells each containing a single void at microscale. A hexagonal cylinder containing a spherical void is considered as the shape of the unit cell; for simplicity, the hexagonal cylinder is modeled as a circular cylinder which allows simpler axisymmetric loading. Furthermore, due to symmetry, only a quarter of the geometry is required to model. A good comparison between both models is obtained for the different void radii.

Research on the element structure and surface current distribution of metasurface based on characteristic mode analysis

Scientific research has shown that the geometric structure of the metasurface has a significant impact on its ability to control the propagation of electromagnetic waves. The control of surface current can be achieved by designing the shape of the metasurface unit cell. In this paper, the traditional metasurface is studied using characteristic mode analysis, and a modified metasurface is proposed, which consists of 4 × 4 hexagonal rings with an asymmetric concave interior. The modified metasurface controls the distribution of surface current by increasing the path of surface current, thus lowering the frequency of modal significance. In addition, due to the special asymmetric concave interior, the frequency difference of different modal currents increases, leading to the expansion of the operating bandwidth of modal currents. A metasurface antenna is fabricated and measured for proof of concept. With a size of 0.69λL × 0.69λL × 0.06λL (λL is the wavelength in free space at the lowest operating frequency), the designed antenna achieves a −10 dB impedance band of 40%, 3 dB axial ratio band of 19.4%, and boresight gain of 8 dBi.

Transient Thermal Performance of Phase-Change Material Infused in Cellular Materials Based on Different Unit Cell Topologies

Abstract Phase change material (PCM) employment in thermal management and energy storage applications is limited due to their inherently low thermal conductivity. Significant enhancement in the thermal performance of PCMs can be obtained when infused in porous media with high porosity and high solid-phase thermal conductivity. Earlier studies typically employ high porosity aluminum foams obtained via a conventional manufacturing process, commonly known as foaming. A typical representative unit cell of metal foams obtained via foaming process can be of tetrakaidecahedron shape. The conventional manufacturing process of high porosity metal foams offers limited flexibility over unit cell shape, porosity, and pore density. Metal additive manufacturing advancements have the potential to address this manufacturing limitation and provides freedom in the above design domain. To this end, we have explored four different unit cell topologies, viz., octet, tetrakaidecahedron, face-diagonal cube, and cube, for their role in enhancing the transient thermal performance when infused with PCMs. An enthalpy-porosity method has been employed to model the phase-change process for wide range of variables. It has been found that the presence of solid media results in significant enhancement in PCM's thermal performance, and the Octet-shaped unit cell outperformed the other unit cell topologies explored in this study.

Effect of unit cell shape and structure volume fraction on the mechanical and vibration properties of 3D printed lattice structures

Lattice structures have been proven to be one of the best choices since their inception, for various structural and other commercial applications, for enhanced mechanical properties, especially in the case of vibration isolation, where band gaps play a vital role. In the present study, additively manufactured 3D printed lattices are prepared with the help of fused deposition modelling (FDM) under various design variations such as Diamond, Kelvin, and Octa formations. Further, three variations in the form of cell density have been used in all the designs, such as low, medium, and high density. The effect of the design variations on Young’s modulus, ultimate compressive strength, and plateau stress have been studied, and comparative analysis amongst the designs has been carried out. In the case of the diamond foam, the Young’s modulus of 54.84, 79.43, and 63.13 MPa has been obtained for low, medium, and high density, respectively. However, in the case of Octa formation with a high-density apology, highest value of young modulus is obtained, which is 174.94 MPa. But the plateau stress is the best in the case of high-density diamond topology and least in the case of high-density Octa formation. In addition, the diamond foam with the medium density has shown the best compressive strength, i.e., 5.003 MPa. Moreover, vibration analysis properties were explored; interestingly, it has been seen that the transmissivity of the medium-form structures for all shapes is higher than the others whereas the natural frequency of the Diamond and Octa shapes is lower. Hence the shape and form of the lattice have a significant effect on the final properties of the lattices and lattice structures contribute to structural integrity in terms of better properties and enhanced behaviour.

Deep learning algorithms for design of periodic structures and dispersion curves calculation

Periodic structure is useful and powerful tool for the wave manipulation. The development of design and analysis of periodic structures using traditional methods (analysis of eigenfrequencies by the finite element method) takes quite a lot of time. Machine learning and deep learning algorithms can speed up the development and subsequent analysis of periodic structures. In this work, we consider a particular case of the propagation of torsional waves in cylindrical objects, the calculation of their dispersion curves, and methods for generating the design of a unit cell of periodic structure by a given bandgap configuration. To achieve this goal, autoencoders and diffusion models were used. A dataset of unit cell shapes and their dispersion curves were used as training data. First, the dispersion curves were analysed to form a bandgap configuration, which was then fed to the input of the neural network. The neural network generates unit cell shape as the output data. Information about dispersion curves is also very important for the analysis of periodic structures. To calculate the dispersion curves, the possibility of using deep learning methods is considered - the problem is the opposite of the previous one. According to the given form, the neural network should calculate dispersion curves. The paper presents the results of applying this method for calculating dispersion curves.

Experimental investigation of mechanical stiffness in lattice structures fabricated with PLA using fused deposition modelling

The objective of the paper is to design and characterise with polylactic acid (PLA) material three cellular structures in the form of lattices which are diagonal-octet-centred shapes for two sizes 6x6x6 and 12x12x12 with a compression test to examine their stiffness using FDM technology compared to polyjet technology.The study used two analytical approaches to investigate lattice structures: experimental analysis and theoretical analysis. Experimental methods such as compression tests were conducted to determine the characteristics of lattice structures. In addition, theoretical analysis was conducted using Hook's law and Ashby's Gibson model to predict appropriate behaviour. The combination of experimental and theoretical methods provided a comprehensive understanding of lattice structures and their properties.The experimental study examined the impact of the shape and size of a lattice structure on the stiffness and lightness of objects 3D printed with FDM technology by PLA material. The research revealed that the 6x6x6 diagonal lattice structure size provided a good balance between stiffness and lightness. While the 6x6x6 byte structure was even lighter, with a mass ratio of 2.09 compared to the diagonal structure, it was less rigid, with a ratio of 0.43, making the diagonal structure more suitable for certain applications. The study highlights the importance of considering both the shape and size of the lattice structure when designing 3D-printed objects with specific mechanical properties; the chosen structure could be a good choice for applications where stiffness and lightness are important.The limitations of the research lie in its limited scope, focusing primarily on the effect of shape (octet-diagonal centred) and unit cell size on Young's modulus of PLA material. Other aspects of 3D printing, such as material selection and thermal properties, were not considered. Furthermore, the results obtained are specific to the printing parameters and experimental conditions chosen, which limits their generalizability to other 3D printing configurations or methods. However, these results have important implications for optimising the PLA printing process. They enable the identification of optimal parameters, such as unit cell shape and size, to produce stiffer, higher-quality structures. In addition, the research is helping to improve the mechanical properties of 3D-printed lattice parts, paving the way for more efficient manufacturing methods and stronger components.Our analysis can be used as a decision aid for the design of FDM lattice parts. Indeed, we can choose the diagonal structure of 6x6x6, which would provide favourable stiffness for functional parts.The paper explores the compression test of lattice structures using FDM technology, which presents a new direction for additive manufacturing. The study takes an experimental approach to evaluate the reliability of various additive manufacturing technologies for creating lattice structures. The study results provide insight into the most reliable technology for producing lattice structures.

A nature-inspired gradable elliptic-cell lattice structure based on cypress wood texture; theoretical and experimental analysis for mechanical properties

The accessibility and commercialization of additive manufacturing allow scientists to design affordable, light weighted cellular-graded structures with customized mechanical properties. This study introduced a new functionally graded lattice structure inspired by the porous wood texture of cypress. This structure can simultaneously alter the relative density and unit cell shapes by gradual cell size grading and its porosity in each repetition which can provide graded properties along the particular axis and in each structural point. Different mechanical properties and geometrical features are easily achievable by altering the unit cell’s shape and dimensions. Elastic modulus, Poisson’s ratio, and specific energy absorption values depend on ellipses radii in cell scales, layers of lattices, and structures. Porosity and surface-to-volume ratio are calculated with high accuracy for different structures, which can be optimized for biomaterial and bioimplant substitution. Numerical simulation is carried out as two perpendicular uniaxial compressions for extracting the structural properties. In addition, an experimental test on the polymeric specimen, made by the DLP technique, validates the results, which shows good agreement with numerical ones. Designs of experiments were set up to determine the parameters’ main and interaction effects on the mechanical properties. RSM function is evaluated for two radii as factors in three levels in both unit cells and layers. Linear tessellation of a layer and parallel array of two perpendicular sets results in a highly porous, ultra-light, weighted structure.

Theory of plasmon-polaritons in binary metallic supercrystals

We present a theory of optical excitations in binary plasmonic supercrystals that are made out of two types of metal nanoparticles. Compared to monodisperse supercrystals, binary crystals have a larger number of plasmonic bands. Their dispersion is governed by the lattice symmetry, unit cell parameters, and shape and material composition of the nanoparticle building blocks. We develop a quantum description of the plasmon polaritons in supercrystals that starts from the dipole and quadrupole excitations of the nanoparticles, their interaction, and their coupling to photons. We show how to use group theory to analyze the plasmon- and photon-induced supercrystal states and their interaction. Plasmon-polaritons of binary metallic supercrystals are in the regime of ultrastrong and deep strong light-matter interaction; i.e., the coupling strength is on the same order as the photon energy. One consequence of the strong interaction is that quadrupolar plasmon modes and photons with energies well above the plasmon energies have to be taken into account to calculate the polariton dispersion. A cesium chloride crystal of two nanoparticles with different dipole and quadrupole energies serves as the example structure to show how the plasmon-polariton dispersion depends on the properties of the nanoparticles and supercrystal structure. The tools presented here can be used to predict and analyze any type of optically active excitation in supercrystals. The results show how to differentiate the optical properties of binary nanoparticle supercrystals into properties that inflexibly depend on lattice symmetry and properties that can be finely tuned by choosing the nanoparticle composition and shape.

Shape optimization method for strength design problem of microstructures in a multiscale structure

AbstractIn this paper, we propose a solution to a shape optimization problem for the strength design of periodic microstructures in multiscale structures. Two maximum stress minimization problems are addressed: minimization of maximum microstructural stress and minimization of maximum macrostructural stress. The homogenization method is used to bridge the macrostructure and the microstructure and to calculate local microstructural stress. By replacing the maximum stress value with a Kreisselmeier‐Steinhauser function, the difficulty of nondifferentiability of maximum stress is avoided. Each strength design problem is formulated as a distributed parameter optimization problem subject to an area constraint including the whole microstructure. The shape gradient functions for both problems are derived using Lagrange's undetermined multiplier method, the material derivative method, and the adjoint variable method. The H1 gradient method is used to determine the unit cell shapes of the microstructure, while reducing the objective function and maintaining smooth design boundaries. In the numerical examples, the optimal shapes obtained for minimization of the maximum local stress of the microstructure and the macrostructure are compared and discussed. The results confirm the effectiveness of the microstructure shape optimization method for the two strength design problems of multiscale structures.

Equilibrium and Non-Equilibrium Lattice Dynamics of Anharmonic Systems.

In this review, motivated by the recent interest in high-temperature materials, we review our recent progress in theories of lattice dynamics in and out of equilibrium. To investigate thermodynamic properties of anharmonic crystals, the self-consistent phonon theory was developed, mainly in the 1960s, for rare gas atoms and quantum crystals. We have extended this theory to investigate the properties of the equilibrium state of a crystal, including its unit cell shape and size, atomic positions and lattice dynamical properties. Using the equation-of-motion method combined with the fluctuation-dissipation theorem and the Donsker-Furutsu-Novikov (DFN) theorem, this approach was also extended to investigate the non-equilibrium case where there is heat flow across a junction or an interface. The formalism is a classical one and therefore valid at high temperatures.

A Study on the Shape and Dimensional Accuracy of Additively Manufactured Titanium Lattice Structures for Orthopedic Purposes

The deviation between the designed lattice structures and the 3D-printed ones has been studied in this research. Three types of lattice structures were designed using the SpaceClaim application in the ANSYS software and then fabricated using Direct Metal Laser Sintering (DMLS) via EOS M 290 3D printer. Considering the orthopedic application, Ti6Al4V alloy of grade 23 was selected as a material for all samples of the structures. A thorough comparison was done on the volume, mass, and porosity to effectively map the possible deviations between the designed and the printed version. The shape accuracy of the 3D printing process was discussed during the study. As the complexity of the shape of the unit cell increases, the accuracy of the printing process becomes lower. Dimensional accuracy in the XY plane is higher than accuracy in the Z plane. Simple unit cell shape was proven to be more accurate in the 3D printing process.

Flexural wave propagation in periodic Micropolar-Cosserat panels: Spectral Element Formulation

In this research, a perspective of the dispersion relation of flexural waves on periodic structures is proposed. The rotational theory of micro-elements is stem to explore the favorable impact of size effect on structures through the localization of the strain energy. The panels are modelled as a one-dimensional (1-D) Micropolar–Cosserat (MC) continuum to explore the effect of length-scale or micro-rotational waves of solids. The spectral element formulation of a panel and the transfer matrix of the unit cell is presented within the framework of the state-space method. The propagation constant in the eigenvalue domain is established based on the Bloch–Floquet theorem to account for the periodicity of the panel. The MC theory in analyzing the band-gap (stop-band) and pass-band characteristics of the unit cell panels is validated by a commercial finite element software package-COMSOL Multiphysics. The mode shape of unit cell for the start and end point of band-gap is further analyzed within the realms of finite element method (FEM) analysis. The appropriate limiting condition reverts MC spectral element into Timoshenko (TM) beam model. The comparison of Timoshenko beam model with the spectral element of 1-D plane-stress (PS) analysis is also investigated. It is observed that the shear wave of the MC model is coupled with a micro-rotational wave of micro-elements, unlike the classical continuum framework. The response of the finite structure subjected to various frequencies is presented too. Presence of vibration attenuation in the specified band-gap (BG) is justified through the elemental dynamic stiffness (DS) matrix of unit cells. This reduced the level of vibration at the specific frequency range within the attenuation band or disintegrates it into two bands. The attenuation bandwidth and its location is significantly affected by the modulation of both geometry and material properties of the beam. Investigation of flexural wave propagation based on the proposed 1-D MC beam theory shows good agreement with the two-dimensional (2-D) plane-stress FEM analysis.

Free vibration analysis of curved lattice sandwich beams

In this paper, the effects of initial curvature and lattice core shape on the bending vibration of sandwich beams are investigated. The three-dimensional (3D) sandwich beam is simulated by combining a two-dimensional (2D) cross-sectional analysis with a one-dimensional (1D) nonlinear beam analysis. The sandwich beam is composed of two identical isotropic faces covering a lattice core. Four different lattice core structures are used to take into account the effect of core unit cell shape on the dynamic properties of the sandwich beam. The nonlinear governing equations of the sandwich beam are Discretized using a time-space scheme. Numerical results show that the lattice unit cell shape affects both in-plane and out of plane stiffness values and hence changes the dynamic behavior of the beam. Furthermore, it is observed that by changing the density ratio of the beam, modes veer away from each other at a specific value of density ratio for specific unit cell types. Moreover, the initial curvature of the beam is shown to affect the dynamics of the beam especially lower modes. Finally, it is obtained that the dynamics of the beam is different when it is initially curved or curved due to an applied end follower moment.

Numerical Investigation of Impact Behavior of Strut-Based Cellular Structures Designed by Spatial Voronoi Tessellation

Porous materials have significant advantages, such as their light weight and good specific energy absorption. This paper presents the designs of two ordered Voronoi structures, a truncated octahedron (Octa) and a rhombic dodecahedron (Dodeca), based on spatial Voronoi tessellation. Through a numerical analysis, the dynamic behavior, deformation and energy absorption of the two porous structures under different impact energies were explored. According to the energy-absorption index, the effects of porosity, rotating unit cell and unit-cell shape on the energy absorption of the porous structures were quantitatively evaluated. The study shows that, for Dodeca and Octa structures subjected to various impact energies, the force-displacement curves exhibit three modes. The porosity, rotational unit cell and unit-cell shape play a crucial role in affecting the impact resistance of porous structures. The work in this paper proposes an effective way to improve the energy-absorption capacity of porous structures under different impact energies. At the same time, a new understanding of the deformation mechanism of Octa and Dodeca was obtained, which is significant for the impact-resistance design and energy-absorption evaluation of porous structures.

Utilizing interdigital and supershape geometries for the design of frequency selective surfaces with high angular and polarization stabilities

In this research article, the superformula is used to design the geometry of a frequency selective surface (FSS) unit cell, which resembles the shapes found in nature. The designed shape of unit cell is like petals, which may take different form by varying the values of six parameters. The proposed FSS unit cell has both angular and polarization stabilities of incident wave. For the miniaturization of FSS and decrease of resonance frequency, interdigital capacitances (IDCs) are devised in the FSS structure, which do not deteriorate angular and polarization stabilities. The dimensions of the unit cell are 10 mm × 10 mm and the resonance frequency is specified as 3.5 GHz. An equivalent circuit is derived for the unit cell to evaluate its frequency responses. Its performance as the transmission coefficient is obtained by the equivalent circuit and full-wave simulation. The effects of variations of the geometrical dimensions of the FSS unit cell on its performance are studied. A prototype model of proposed FSS is fabricated and measured. The performance of its equivalent circuit, full-wave computer simulation results and measured data are compared and are shown to be in good agreement.

Envelope Function Analysis of Quasicrystals

Quasicrystals have attracted a growing interest in material science because of their unique properties and applications. Proper determination of the atomic structure is important in designing a useful application of these materials, for which a difficult phase problem of the structure factor must be solved. Diffraction patterns of quasicrystals consist of a periodic series of peaks, which can be reduced to a single envelope. Knowing the distribution of the diffraction image into series, it is possible to recover information about the phase of the structure factor without using time-consuming iterative methods. By the inverse Fourier transform, the structure factor can be obtained (enclosed in the shape of the average unit cell, or atomic surface) directly from the diffraction patterns. The method based on envelope function analysis was discussed in detail for a model 1D (Fibonacci chain) and 2D (Penrose tiling) quasicrystal. First attempts to apply this technique to a real Al-Cu-Rh decagonal quasicrystal were also made.