scholarly journals Designing Metasurfaces with Canonical Unit Cells

Crystals ◽  
2020 ◽  
Vol 10 (10) ◽  
pp. 938
Author(s):  
Dominik Barbarić ◽  
Zvonimir Šipuš
Keyword(s):  
Cell Types ◽  
Unit Cell ◽  
Design Approach ◽  
Optimization Approach ◽  
Cell Geometry ◽  
Full Wave ◽  
Unit Cells ◽  
Approximate Expressions ◽  
Surface Sheet ◽  
Selection Of

Among different approaches to designing metasurfaces, surface sheet impedance is proving to be a straightforward path for many applications. Recent publications have proposed several methods for optimizing this design approach, enabling rapid metasurface development. Upon finding the requirements using the sheet impedance approach, design continues with the selection of unit cell geometry. This choice is usually based on approximate expressions that have been published throughout the years. We review the approximate expressions for metasurface unit cell design, with consideration of their applicability to certain applications, namely polarization-dependent beam-shaping metasurfaces. We evaluate the accuracy of the approximate expressions against simulation results from a full-wave electromagnetic solver, and propose an optimization approach to correct the proposed design for the observed error. The applicability of different unit cell types is discussed, especially considering the limitations of technological processes typically used in metasurface production. A prototype was developed to verify the validity of this design approach.

Structure, Process, and Material Influences for 3D Printed Lattices Designed With Mixed Unit Cells

2020 ◽  
Author(s):  
Gabriel Briguiet ◽  
Paul F. Egan
Keyword(s):  
Elastic Modulus ◽  
Mechanical Testing ◽  
Mechanical Response ◽  
Cell Types ◽  
Unit Cell ◽  
Ultraviolet Curing ◽  
Mechanical Responses ◽  
Lattice Design ◽  
Unit Cells ◽  
3D Printed

Abstract Emerging 3D printing technologies are enabling the design and fabrication of novel architected structures with advantageous mechanical responses. Designing complex structures, such as lattices, with a targeted response is challenging because build materials, fabrication process, and topological design have unique influences on the structure’s mechanical response. Changing any factor may have unanticipated consequences, even for simpler lattice structures. Here, we conduct mechanical compression experiments to investigate varied lattice design, fabrication, and material combinations using stereolithography printing with a biocompatible polymer. Mechanical testing demonstrates that a higher ultraviolet curing time increases elastic modulus. Material testing demonstrated that anisotropy does not strongly influence lattice mechanics. Designs were altered by comparing homogenous lattices of single unit cell types and heterogeneous lattices that combine two types of unit cells. Unit cells for heterogeneous structures include a Cube design for a high elastic modulus and Cross design for improved shear response. Mechanical testing of three heterogeneous layouts demonstrated how unit cell organization influences mechanical outcomes, therefore enabling the tuning of an elastic modulus that surpasses the law of averages designed for application-dependent mechanical needs. These findings provide a foundation for linking design, process, and material for engineering 3D printed structures with preferred properties, while also facilitating new directions in design automation and optimization.

Data-Driven Multiscale Topology Optimization Using Multi-Response Latent Variable Gaussian Process

2020 ◽  
Author(s):  
Liwei Wang ◽  
Siyu Tao ◽  
Ping Zhu ◽  
Wei Chen
Keyword(s):  
Topology Optimization ◽  
Gaussian Process ◽  
Latent Variable ◽  
Distance Measure ◽  
Material Design ◽  
Cell Types ◽  
Unit Cell ◽  
Data Driven ◽  
Single Class ◽  
Unit Cells

Abstract The data-driven approach is emerging as a promising method for the topological design of the multiscale structure with greater efficiency. However, existing data-driven methods mostly focus on a single class of unit cells without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of inherent ordering or “distance” measure between different classes of unit cells in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) to creating multi-response LVGP (MRLVGP) for the unit cell libraries of metamaterials, taking both qualitative unit cell concepts and quantitative unit cell design variables as mixed-variable inputs. The MRLVGP embeds the mixed variables into a continuous design space based on their collective effect on the responses, providing substantial insights into the interplay between different geometrical classes and unit cell materials. With this model, we can easily obtain a continuous and differentiable transition between different unit cell concepts that can render gradient information for multiscale topology optimization. While the proposed approach has a broader impact on the concurrent topological and material design of engineered systems, we demonstrate its benefits through multiscale topology optimization with aperiodic unit cells. Design examples reveal that considering multiple unit cell types can lead to improved performance due to the consistent load-transferred paths for micro- and macrostructures.

scholarly journals Dual Graded Lattice Structures: Generation Framework and Mechanical Properties Characterization

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1528
Author(s):  
Khaled G. Mostafa ◽  
Guilherme A. Momesso ◽  
Xiuhui Li ◽  
David S. Nobes ◽  
Ahmed J. Qureshi
Keyword(s):  
Mechanical Properties ◽  
Relative Density ◽  
Lattice Structure ◽  
Cell Types ◽  
Functionally Graded ◽  
Unit Cell ◽  
Lattice Structures ◽  
Unit Cells ◽  
Mechanical Properties Characterization ◽  
Graded Lattice

Additive manufacturing (AM) enables the production of complex structured parts with tailored properties. Instead of manufacturing parts as fully solid, they can be infilled with lattice structures to optimize mechanical, thermal, and other functional properties. A lattice structure is formed by the repetition of a particular unit cell based on a defined pattern. The unit cell’s geometry, relative density, and size dictate the lattice structure’s properties. Where certain domains of the part require denser infill compared to other domains, the functionally graded lattice structure allows for further part optimization. This manuscript consists of two main sections. In the first section, we discussed the dual graded lattice structure (DGLS) generation framework. This framework can grade both the size and the relative density or porosity of standard and custom unit cells simultaneously as a function of the structure spatial coordinates. Popular benchmark parts from different fields were used to test the framework’s efficiency against different unit cell types and grading equations. In the second part, we investigated the effect of lattice structure dual grading on mechanical properties. It was found that combining both relative density and size grading fine-tunes the compressive strength, modulus of elasticity, absorbed energy, and fracture behavior of the lattice structure.

An Optimal Method for Periodic Structures Design

2017 ◽  
Author(s):  
Emanuele Riva ◽  
Gabriele Cazzulani ◽  
Edoardo Belloni ◽  
Francesco Braghin
Keyword(s):  
Periodic Structures ◽  
Mechanical Impedance ◽  
Cell Geometry ◽  
Optimal Method ◽  
Unit Cells ◽  
Geometrical Constraints ◽  
Dimensional Parameters ◽  
Specific Frequency ◽  
The Waves ◽  
Selection Of

Periodic structures provide filtering behavior for vibrations, as a result of the repetition in space of unit blocks, or unit cells. In general, they are characterized by an internal mechanical impedance mismatch, so that waves are reflected and transmitted every time a discontinuity is present. The global behavior given by waves superposition is their cancellation, only for specific frequency ranges, generally called stop-bands or band-gaps. The variation of non-dimensional parameters shows how these attenuation regions move in the frequency domain: the correspondent diagrams are the main tools for the design problem and are known as band-maps. The selection of the geometrical, physical and elastic properties of the unit cell is therefore dependent on the designer experience and nothing can be said about the optimality of the proposed solution. Numerical methods are used for the selection of the best cell geometry, in order to get optimal attenuation. Generally, this is a time consuming approach. In this paper, an new method is presented, based on how the waves are reflected and transmitted at cells interface. Both beam and rod case studies are investigated. The algorithm allows matching between band-gap central frequency and the desired value, while the designed attenuation is optimal there, under certain physical and geometrical constraints. Moreover, the design of the bandgap location has been decoupled from the design of the magnitude of attenuation. This approach is purely analytic, therefore the computational efforts required are minimum. In order to validate the analytical model, a passive periodic beam has been manufactured. Its real frequency response is therefore compared to the expected one.

scholarly journals Ab-initiophasing using nanocrystal shape transforms with incomplete unit cells

IUCrJ ◽  
2013 ◽  
Vol 1 (1) ◽  
pp. 19-27 ◽  
Author(s):  
Haiguang Liu ◽  
Nadia A. Zatsepin ◽  
John C. H. Spence
Keyword(s):  
Single Unit ◽  
Dynamic Range ◽  
Cell Types ◽  
Critical Issue ◽  
Unit Cell ◽  
Crystal Shape ◽  
Transform Method ◽  
Unit Cells ◽  
Projection Approximation ◽  
Diffraction Patterns

X-ray free electron lasers are used in measuring diffraction patterns from nanocrystals in the `diffract-before-destroy' mode by outrunning radiation damage. The finite-sized nanocrystals provide an opportunity to recover intensity between Bragg spots by removing the modulating function that depends on crystal shape,i.e.the transform of the crystal shape. This shape-transform dividing-out scheme for solving the phase problem has been tested using simulated examples with cubic crystals. It provides a phasing method which does not require atomic resolution data, chemical modification to the sample, or modelling based on the protein databases. It is common to find multiple structural units (e.g.molecules, in symmetry-related positions) within a single unit cell, therefore incomplete unit cells (e.g.one additional molecule) can be observed at surface layers of crystals. In this work, the effects of such incomplete unit cells on the `dividing-out' phasing algorithm are investigated using 2D crystals within the projection approximation. It is found that the incomplete unit cells do not hinder the recovery of the scattering pattern from a single unit cell (after dividing out the shape transforms from data merged from many nanocrystals of different sizes), assuming that certain unit-cell types are preferred. The results also suggest that the dynamic range of the data is a critical issue to be resolved in order to apply the shape transform method practically.

scholarly journals Improving the accuracy of analytical relationships for mechanical properties of additively manufactured lattice structures

2020 ◽  
Author(s):  
Reza Hedayati ◽  
Naeim Ghavidelnia ◽  
Mojtaba Sadighi ◽  
Bodaghi
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Cell Types ◽  
Timoshenko Beam Theory ◽  
Unit Cell ◽  
Lattice Structures ◽  
Starting Point ◽  
Unit Cells ◽  
Order Of Magnitude ◽  
The Difference

Porous implants must satisfy several physical and biological requirements in order to be promising materials for orthopedic application: they should have the proper levels of stiffness, permeability, and fatigue resistance and in proximity to how much they are in bone tissues. In recent years, several experimental, numerical, and analytical studies have been carried out on the influence of unit cell geometry on such properties. Even though experimental and numerical techniques can effectively study and predict the behavior of different micro-structure, they lack the ease the analytical relationships provide for such predictions. Even though it is well-known that Timoshenko beam theory gives much better accuracy in predicting the deformation of a beam (and as a result lattice structures), many of the already-existing relationships in the literature have been derived based on Euler-Bernoulli beam theory. The question that arises here is that can there be a convenient way to convert the already-existing relationships based on Euler-Bernoulli to relationships based on Timoshenko beam theory without the need to rewrite all the derivations from the starting point. In this paper, this question is addressed and answered, and a simple approach is presented. This technique is applied to six unit cells for which Euler-Bernoulli analytical relationships could be found in the literature, but Timoshenko theories could not be found: BCC, hexagonal packing, rhombicuboctahedron, diamond, truncated cube, and truncated octahedron. The results of this study demonstrated that converting analytical relationships based on Euler-Bernoulli to equivalent Timoshenko ones can decrease the difference between the analytical and numerical values for one order of magnitude which is a significant improvement in accuracy of the analytical formulas. The methodology presented in this study is not only beneficial to the already-existing analytical relationships but also facilitates derivation of accurate analytical relationships for other, yet unexplored, unit cell types.

Bayesian removal of noise for increased sensitivity in vector pattern recognition lattice imaging of interfaces

1993 ◽  
Vol 51 ◽  
pp. 994-995
Author(s):  
L. Fei ◽  
P. Fraundorf
Keyword(s):  
Pattern Recognition ◽  
Perfect Crystal ◽  
Unit Cell ◽  
Ion Milling ◽  
Beam Radiation ◽  
Major Interest ◽  
Unit Cells ◽  
Mapping Process ◽  
Increased Sensitivity ◽  
Electron Microscopes

Interface structure is of major interest in microscopy. With high resolution transmission electron microscopes (TEMs) and scanning probe microscopes, it is possible to reveal structure of interfaces in unit cells, in some cases with atomic resolution. A. Ourmazd et al. proposed quantifying such observations by using vector pattern recognition to map chemical composition changes across the interface in TEM images with unit cell resolution. The sensitivity of the mapping process, however, is limited by the repeatability of unit cell images of perfect crystal, and hence by the amount of delocalized noise, e.g. due to ion milling or beam radiation damage. Bayesian removal of noise, based on statistical inference, can be used to reduce the amount of non-periodic noise in images after acquisition. The basic principle of Bayesian phase-model background subtraction, according to our previous study, is that the optimum (rms error minimizing strategy) Fourier phases of the noise can be obtained provided the amplitudes of the noise is given, while the noise amplitude can often be estimated from the image itself.

scholarly journals Extraneous E-Cadherin Engages the Deterministic Process of Somatic Reprogramming through Modulating STAT3 and Erk1/2 Activity

Cells ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 284
Author(s):  
Yu-Hao Liu ◽  
Chien-Chang Chen ◽  
Yi-Jen Hsueh ◽  
Li-Man Hung ◽  
David Hui-Kang Ma ◽  
...  
Keyword(s):  
Stochastic Process ◽  
Molecular Mechanism ◽  
Activity Ratio ◽  
Cell Types ◽  
Deterministic Process ◽  
Modes Of Action ◽  
Molecular Events ◽  
Different Cell Types ◽  
Selection Of ◽  
E Cadherin

Although several modes of reprogramming have been reported in different cell types during iPSC induction, the molecular mechanism regarding the selection of different modes of action is still mostly unknown. The present study examined the molecular events that participate in the selection of such processes at the onset of somatic reprogramming. The activity of STAT3 versus that of Erk1/2 reversibly determines the reprogramming mode entered; a lower activity ratio favors the deterministic process and vice versa. Additionally, extraneous E-cadherin facilitates the early events of somatic reprogramming, potentially by stabilizing the LIF/gp130 and EGFR/ErbB2 complexes to promote entry into the deterministic process. Our current findings demonstrated that manipulating the pSTAT3/pErk1/2 activity ratio in the surrounding milieu can drive different modes of action toward either the deterministic or the stochastic process in the context of OSKM-mediated somatic reprogramming.

scholarly journals Prediction of Effective Thermal Conductivities of Four-Directional Carbon/Carbon Composites by Unit Cells with Different Sizes

2021 ◽  
Vol 11 (3) ◽  
pp. 1171
Author(s):  
Chang Xu ◽  
Zhihong Sun ◽  
Guowei Shao
Keyword(s):  
Carbon Fiber ◽  
Longitudinal Direction ◽  
Unit Cell ◽  
Carbon Composites ◽  
Temperature Boundary ◽  
The Matrix ◽  
Unit Cells ◽  
Experimental Values ◽  
Different Diameters ◽  
Thermal Conductivities

Two-unit cells developed to predict the effective thermal conductivities of four-directional carbon/carbon composites with the finite element method are proposed in this paper. The smaller-size unit cell is formulated from the larger-size unit cell by two 180° rotational transformations. The temperature boundary conditions corresponding to the two-unit cells are derived, and the validity is verified by the temperature and heat flux distributions at specific positions of the larger-size unit cell and the smaller-size unit cell. The thermal conductivities of the carbon fiber bundles and carbon fiber rods are measured firstly. Then, combined with the properties of the matrix, the effective thermal conductivities of the four-directional carbon/carbon composites are numerically predicted. The results in transverse direction predicted by the larger-size unit cell and the smaller-size unit cell are both higher than experimental values, which are 5.8 to 6.2% and 7.3 to 8.2%, respectively. In longitudinal direction, the calculated thermal conductivities of the larger-size unit cell and the smaller-size unit cell are 6.8% and 6.2% higher than the experimental results, respectively. In addition, carbon fiber rods with different diameters are set to clarify the influence on the effective thermal conductivities of the four-directional carbon/carbon composites.

Pressure dependence of unit cell geometry of single crystalline TbNi2B2C

1998 ◽  
Vol 305 (3-4) ◽  
pp. 209-212 ◽  
Author(s):  
Ulf Jaenicke-Rössler ◽  
Gernot Zahn ◽  
Peter Paufler ◽  
Holger Bitterlich ◽  
Günter Behr
Keyword(s):  
Pressure Dependence ◽  
Unit Cell ◽  
Cell Geometry ◽  
Single Crystalline
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