Periodic Cell Structure Research Articles

A review of structural diversity design and optimization for lattice metamaterials

Metamaterials are a type of groundbreaking engineered materials with unique properties not found in natural substances. Lattice metamaterials, which have a periodic lattice cell structure, possess exceptional attributes such as a negative Poisson’s ratio, high stiffness-to-weight ratios, and outstanding energy dissipation capabilities. This review provides a comprehensive examination of lattice metamaterials. It covers their various structures and fabrication methods. The review emphasizes the crucial role of homogenization methods and multi-scale modeling in assessing metamaterial properties. It also highlights the advancement of topology optimization through advanced computational techniques, such as finite element analysis simulations and machine learning algorithms.

Reliable Methods for Classification, Characterization, and Design of Cellular Structures for Patient-Specific Implants.

In our research, our goal was to develop a characterization method that can be universally applied to periodic cell structures. Our work involved the accurate tuning of the stiffness properties of cellular structure components that can significantly reduce the number of revision surgeries. Up to date porous, cellular structures provide the best possible osseointegration, while stress shielding and micromovements at the bone-implant interface can be reduced by implants with elastic properties equivalent to bone tissue. Furthermore, it is possible to store a drug inside implants with a cellular structure, for which we have also prepared a viable model. In the literature, there is currently no established uniform stiffness sizing procedure for periodic cellular structures but also no uniform designation to identify the structures. A uniform marking system for cellular structures was proposed. We developed a multi-step exact stiffness design and validation methodology. The method consists of a combination of FE (Finite Element) simulations and mechanical compression tests with fine strain measurement, which are finally used to accurately set the stiffness of components. We succeeded in reducing the stiffness of test specimens designed by us to a level equivalent to that of bone (7-30 GPa), and all of this was also validated with FE simulation.

Programmable Auxeticity in Hydrogel Metamaterials via Shape-Morphing Unit Cells.

Mechanical metamaterials recruit unique mechanical behavior that is unavailable in bulk materials from a periodic unit cell structure with a specific geometry. However, such metamaterials can typically not be reconfigured once manufactured. Herein, the authors introduce shape morphing of a hydrogel metamaterial via spatio‐selective integration of responsive actuating elements to reconfigure the mesoscale unit cell geometry to reach programmable auxeticity on the macroscale. Via thermal control, the unit cell angle of a honeycomb structure can be precisely programmed from 68° to 107°. This results in negative, zero, or positive Poisson's ratio under applied tensile strain. The geometrical reconfiguration with resulting programmable auxeticity is predicted and verified by finite element (FE) simulation. This concept of shape‐morphing hydrogel metamaterials via the addition of actuating struts into otherwise passive architectures offers a new strategy for reconfigurable metamaterials and extends applications of hydrogels in general. It can be readily extended to other architectures and may find applications in mechanical computing as well as soft robotics.

Evaluation of mechanical properties of periodic cell structures with a bistable microscopic deformation mechanism

Evaluation of mechanical properties of periodic cell structures with a bistable microscopic deformation mechanism

Guided wave structure of spoof surface plasmon polaritons with ring cavities

The confined capability of the spoof surface plasmon polaritons (SSPPs) can be regulated by the periodic cell structure of the SSPP waveguide. In this paper, to further enhance the confinement to the SSPP interface fields and reduce the lateral dimension of the SSPP guided wave structure, the periodic unit loaded with rectangular ring cavities on both sides of the metal strip is proposed. The experimental results show that at a given periodic cell height, the proposed guided wave structure have a lower asymptotic frequency and steep sideband characteristics. That indicates it has good low-pass guided wave performance. Meanwhile, this structure is beneficial to device integration.

Pore-scale numerical simulation of the thermal performance for phase change material embedded in metal foam with cubic periodic cell structure

Pore-scale numerical simulation is conducted to study the thermal performance of composite change phase material (PCM). The low melting point paraffin wax R56 is selected as PCM. Aluminum foam with cubic periodic cell structure is designed, which not only possesses high thermal conductivity, high porous structure and low relative density but also can be rapidly manufactured by the new manufacturing technology. Hence it is an excellent candidate used as metal matrix of composites. The pore-scale numerical method is used to calculate the temperature variation and trace the melting evolution of composite PCM. The effects of geometrical parameters of metal foam such as porosities and pore densities on the thermal behavior of composite PCM are numerically investigated. It is observed from numerical results that the effects of aluminum foam on the thermal performance of composite PCM are very pronounced. Compared with the pure paraffin, the melting time for composite PCM is greatly shortened to 24.1% of that of pure paraffin. Also the effective thermal conductivity of composite PCM is drastically improved, e.g., the effective thermal conductivity can be enhanced about 123 times as much as that of pure paraffin. By comparing with the different porosities and pore densities composite PCMs, the geometrical parameters of aluminum foam have the distinct effects on the thermal performance of composite PCMs, e.g., the melting rate for composite PCMs with the low porosity or high pore density is higher as compared to the composite PCMs with the high porosity or low pore density. By analyzing the temperature-time history, it is demonstrated that there is local thermal non-equilibrium phenomenon between aluminum skeleton and paraffin during the melting process and local thermal non-equilibrium gradually weakens as the reduction of temperature difference between aluminum skeleton and paraffin.

A 3D investigation of thermoacoustic fields in a square stack

The thermoviscous behavior of the oscillating gas within the porous medium of a thermoacoustic refrigerator enables the conversion of sound into heat in the process of typical standing-wave thermoacoustic refrigeration systems. Several nonlinear mechanisms, such as harmonics generation, self-induced streaming and possible turbulence, cause complicated flow behavior and influence the performance of such devices. Few analytical and numerical approximations (Cao et al., 1996; Worlikar and Knio, 1996; Worlikar et al., 1998) describe the flow field and the energy flux density in standing devices comprising stacks of parallel plates, but almost no 3-D simulation has been developed that models the large-amplitude excitations and enables the prediction of the oscillating-flow behavior within a porous medium made of square channels. Here, we build on existing effort (Abd El-Rahman and Abdel-Rahman, 2014) and report a computational fluid dynamics analysis of a Helium-filled half-wavelength thermoacoustic refrigerator. The finite volume method is used, and the solid and gas domains are represented by large numbers of hexahedral elements. The calculations assume a 3-D periodic cell structure to reduce the computational cost and apply the dynamic mesh technique to account for the adiabatically oscillating wall boundaries. The simulation uses an implicit time integration of the full unsteady compressible flow equations along with the conjugate heat transfer algorithm. For the sake of simulation, the geometry and operating conditions closely follow the experimental setup of Lotton et al. (2009) [5]. A typical run involves about 200,000 computational cells, whereas the working frequency and the applied drive ratio are 592.5Hz and 2.0%, respectively. The stationary system response is predicted and the numerical values are compared to theory. The results show good agreement with theoretical behavior in the linear regime of drive ratios up to 2.0% while a maximum cooling effect of 10 degrees is captured between the stack ends. This simulation provides an interesting tool for understanding the transient flow behavior, mean energy-flux density and flow streaming, and helps building 3-D computational fluid dynamics models for thermoacoustic devices.

Finite Element Models Used to Determine the Equivalent In-plane Properties of Honeycombs

This paper presents some general two- and three-dimensional finite element models capable to obtain accurate equivalent in-plane orthotropic mechanical properties of honeycombs using the homogenization method. For that, the models are developed on a representative volume element with appropriate periodic boundary conditions and three load cases: two pure axial loads and a pure in-plane shearing load. The developed models use beam, solid 2D and 3D, and also shell type finite elements. The proposed models are validated using analytical relationships from literature and can be extended to more complicated geometries where no analytical relationships for homogenizations exist. For this reason, some aspects regarding their proper use, depending on the purpose of the analysis, are presented. It is shown that similar models can be used for different periodic cell structures as chiral and anti-chiral honeycomb structures. The developed finite element models can also be used conveniently for parametric and sensitivity analyses because the total number of degrees of freedom is relatively small compared to a complete model.

Cell Patterning: Controllable Patterning of Different Cells Via Optical Assembly of 1D Periodic Cell Structures (Adv. Funct. Mater. 19/2015)

Cell Patterning: Controllable Patterning of Different Cells Via Optical Assembly of 1D Periodic Cell Structures (Adv. Funct. Mater. 19/2015)

Controllable Patterning of Different Cells Via Optical Assembly of 1D Periodic Cell Structures

Flexible patterning of different cells into designated locations with direct cell–cell contact at single‐cell patterning precision and control is of great importance, however challenging, for cell patterning. Here, an optical assembly method for patterning of different types of cells via direct cell–cell contact at single‐cell patterning precision and control is demonstrated. Using Escherichia coli and Chlorella cells as examples, different cells are flexibly patterned into 1D periodic cell structures (PCSs) with controllable configurations and lengths, by periodically connecting one type of cells with another by optical force. The patterned PCSs can be flexibly moved and show good light propagation ability. The propagating light signals can be detected in real‐time, providing new opportunities for the detection of transduction signals among patterned cells. This patterning method is also applicable for cells of other kinds, including mammalian/human cells.

Numerical Analysis of Heat Transfer and Pressure Drop in Metal Foams for Different Morphological Models

Because of their light weight, open porosity, high surface area per unit volume, and thermal characteristics, metal foams are a promising material for many industrial applications involving fluid flow and heat transfer. The pressure drop and heat transfer in porous media have inspired a number of experimental and numerical studies, and many models have been proposed in the literature that correlate the pressure gradient and the heat transfer coefficient with the mean cell size and porosity. However, large differences exist among results predicted by different models, and most studies are based on idealized periodic cell structures. In this study, the true three-dimensional microstructure of the metal foam is obtained by employing x-ray computed microtomography (XCT). This is the “real” structure. For comparison, ideal Kelvin foam structures are developed in the free-to-use software “surface evolver” surface energy minimization program. These are “ideal” structures. Pressure drop and heat transfer are then investigated in each structure using the CFD module of COMSOL® Multiphysics code. A comparison between the numerical predictions from the real and ideal geometries is carried out. The predictions showed that heat transfer characteristics are very close for low values of Reynolds number, but larger Reynolds numbers create larger differences between the results of the ideal and real structures. Conversely, the differences in pressure drop at any Reynolds number are nearly 100%. Results from the models are then validated by comparing them with experimental results taken from the literature. The validation suggests that the ideal structure poorly predicts the heat transfer and pressure drops.

A Miniaturized Frequency Selective Surface Based on Square Loop Aperture Element

We propose a miniaturized band-pass frequency selective surface (FSS) with periodic unit cell structure. The proposed FSS is realized by symmetrically bending the edges of the square loop aperture element, by which our proposed FSS increases the resonant length, and, hence, reduces its size. In this FSS, each unit cell has a dimension of 0.0538λ × 0.0538λ, whereλrepresents the wavelength of the corresponding resonant frequency. Both the theoretical analysis and simulation results demonstrate that our proposed FSS, having high polarization stability and angle stability, can achieve smaller size in comparison with the previously proposed structures.

A micropolar anisotropic constitutive model of cancellous bone from discrete homogenization

Cosserat models of cancellous bone are constructed, relying on micromechanical approaches in order to investigate microstructure-related scale effects on the macroscopic properties of bone. The derivation of the effective mechanical properties of cancellous bone considered as a cellular solid modeled as two-dimensional lattices of articulated beams is presently investigated. The cell walls of the bone microstructure are modeled as Timoshenko thick beams. The asymptotic homogenization technique is involved to get closed form expressions of the equivalent properties versus the geometrical and mechanical microparameters, accounting for the effects of bending, axial, and transverse shear deformations. Considering lattice microrotations as additional degrees of freedom at both the microscopic and macroscopic scales, an anisotropic micropolar equivalent continuum model is constructed, the effective mechanical properties of which are identified. The effective elastic moduli of various periodic cell structures are computed in situations of low and high effective densities to assess the impact of the transverse shear deformation. The stress distribution in a cracked bone sample is computed based on the effective micropolar model, highlighting the regularizing effect of the Cosserat continuum in comparison to a classical elasticity continuum model.

Heat sink applications of extruded metal honeycombs

Linear Cellular Alloys (LCAs) are metal honeycombs that are extruded using powder metal-oxide precursors and chemical reactions to obtain near fully dense metallic cell walls. Either ordered periodic or graded cell structures can be formed. In this work, the performance of heat sinks fabricated from stochastic cellular metals is compared to that of LCA heat sinks. Flash diffusivity experiments are performed to determine the in situ thermal properties of cell wall material. The pressure drop for unidirectional fluid flow in the honeycomb channels and the total heat transfer rate of LCA heat sinks are experimentally measured. These measurements are compared to values predicted from a finite difference code and commercial computational fluid dynamics (CFD) software.

Yield surfaces of various periodic metal honeycombs at intermediate relative density

Initial yield surfaces are derived for several periodic metal honeycomb cell structures with sufficiently high relative density that failure occurs by plastic yielding. Both in-plane stress states (normal stresses perpendicular to cell axes, with in-plane shear) and triaxial stress states with one principal stress direction along the cell axes are considered. Beam/column and plate/shell yield criteria are adopted to address general in-plane loading and 3D triaxial loading, respectively, accounting for combined cell wall stretching and bending as appropriate. Cell wall behavior is assumed to be elastic-perfectly plastic. The initial yield surfaces for different periodic cell structures are systematically compared. Some issues related to the initial yield surfaces of various honeycombs are discussed, including dependencies on relative density and in-plane and out-of-plane applied stresses, as well as the influence of joints between cell walls.

Simulations of flow through open cell metal foams using an idealized periodic cell structure

A new approach to modeling the flow through a porous medium with a well defined structure is presented. This approach entailed modeling an idealized open cell metal foam based on a fundamental periodic unit of eight cells and solving the flow through the three-dimensional cellular unit. To model an infinitely large matrix, periodic boundary conditions were set on the walls parallel to the flow direction, while a pseudo-periodic boundary condition with a prescribed volumetric flow rate was set over the inlet–outlet pair of the unit cell. The pressure drop data of the flow through the cellular unit were then compared on a length-normalized basis against experimental data. The pressure drop values predicted by the simulations were consistently 25% lower than the values obtained in the experiments on a similar foam and under identical flow conditions. One explanation for the discrepancy between the two sets of data is the lack of pressure drop increasing wall effects in the simulations. The increase in the pressure drop from wall effects in the simulation was quantified.

Temperature gradients and frictional energy dissipation in the sliding of hydroxylated α-alumina surfaces

The dynamics of friction and energy dissipation of a small nanoscale hydroxylated alumina surface sliding across a large identical surface were investigated by molecular dynamics (MD) simulations. The energy released into both the sliding and stationary surfaces and the energy transfer from the sliding interface to the bulk were investigated by monitoring the temperature of the surfaces and their sublayers. Steady state temperature gradients are found for the sublayers of each surface as a result of the balance between the heat released from the sliding friction and heat transfer to the bulk. The MD simulations show periodic friction energy release from the interface to the surfaces, giving rise to periodic changes in the temperature of the surface sublayers. This temperature depends on the sliding velocity. The periodicity in the friction energy release arises from the periodic unit cell structures of the surfaces. Atomic-level vibrational motions and interdigitation of the surface atoms give rise to the frictional energy of the sliding surfaces. Velocity distributions are determined for atoms within different surface layers and they become more Boltzmann-like the further the layers are from the interface and if the sliding is fast and not in the stick–slip regime. Tribological properties for continuous sliding across the same regime of the bottom surface, by using periodic boundary conditions, differ from those for sliding across a large bottom surface.

The multiple source feedback of supersonic jet screech. IV. Space–time diagrams and the fast/slow waves of transitory wave theory

In Part II [J. Acoust. Soc. Am. 108, 2588 (2000)] the space–time wave diagrams of multiple (point) source screech were elucidated, showing the condition for perfect, or nearly so, reinforcement of the feedback sound at the nozzle. In the transitory wave theory [J. Acoust. Soc. Am. 106, 2194 (1999)] the velocity modulation of a transitory instability wave as it traverses the periodic cell structure results in a continuous phased array which was resolved into fast (approx. sonic) upstream and slow downstream source waves (of constant sinuous amplitude, apart from the envelope factor), only the former radiating strongly, in the upstream direction. The two points of view are reconciled by constructing fast and slow waves in the space–time diagrams by: (a) introducing intermediate negative sources: (b) taking the sources at half strength and adding virtual sources at the zero positions on the fast wave traces, of the same sign as adjacent sources: (c) taking the other half-strength sources and adding virtual sources of opposite sign, the sources then being of the same sign along the slow wave traces. The implications of the need to introduce negative sources in the point source array are discussed.

The multiple source feedback of supersonic jet screech, I: Theory—frequency

Screech sound, generated by the interaction of jet instability waves with the spatially periodic cell structure of choked or ‘‘off-design’’ supersonic jets, feeds back to initiate new instability waves at the nozzle. The interaction produces a phased array of effective point sources distance s apart, with a single equivalent (centroidal) source at distance n′s from the nozzle. The feedback criteria discussed at the last Meeting yield frequency f=fPRφ, where fPR=(U/s)⋅1/(1+M) for perfect reinforcement at the nozzle; U,M=instability wave velocity, Mach number; φ=(N+p+ν+I)/n′→1 with n′s≡(N+μ+ν)s, νs=distance of equivalent source from nearest cell end at (N+μ)s from the nozzle, N=integer, |μ|≤1/2, and I=−1, 0, or +1. Exact for any number of symmetrically disposed source strengths, numerical solutions show it to be a good approximation for arbitrary strengths and for inclusion of differing source distances (with weighted equivalent source). The mean s is appropriate for unequal source spacing; but then perfect reinforcement cannot occur. With perfect reinforcement unlikely, the 1953 hypothesis that f→fPR is confirmed as a simple and useful approximation.

Feedback criteria for edge tones and the multiple sources of choked jet screech

Screech sound is generated by the interaction of jet instability waves with the spatially periodic cell structure of a choked supersonic jet, the sound initiating new instability waves at the nozzle. Its frequency is important because of possible structural damage to high-performance aircraft. It was hypothesized that the interaction resulted in a phased array of point sources, with an effective source at distance h′ from the nozzle. This reduced the phase feedback criterion to that of edge tones with frequency f=(U/h′)(N+p)/(1+M), where U, M are, respectively, the velocity and Mach number of the instabilty waves, N is an integer, and p an ideally fixed constant, 0≤p≤1. It was hypothesized that N takes the value yielding maximum feedback for maximum jet instability for edge tones, and that closest to perfect reinforcement, f→fPR=(U/s)/(1+M), s=cell length, for screech. Multiple-source feedback is now considered, allowing for a different (effective) first cell length. The preceding concepts are fully confirmed for screech, but N is not limited to integer values. As illustrated by experimental results, and though f→fPR, absolutely perfect reinforcement is unlikely to occur.