Unit Cell Design Research Articles

Hard- and Soft-Coded Strain Stiffening in Metamaterials via Out-of-Plane Buckling Using Highly Entangled Active Hydrogel Elements.

Metamaterials show elaborate mechanical behavior such as strain stiffening, which stems from their unit cell design. However, the stiffening response is typically programmed in the design step and cannot be adapted postmanufacturing. Here, we show hydrogel metamaterials with highly programmable strain-stiffening responses by exploiting the out-of-plane buckling of integrated pH-switchable hydrogel actuators. The stiffening upon reaching a certain extension stems from the initially buckled active hydrogel beams. At low strain, the beams do not contribute to the mechanical response under tension until they straighten with a resulting step-function increase in stiffness. In the hydrogel actuator design, the acrylic acid concentration hard-codes the configuration of the metamaterial and range of possible stiffening onsets, while the pH soft-codes the exact stiffening onset point after fabrication. The utilization of out-of-plane buckling to realize subsequent stiffening without the need to deform the passive structure extends the application of hydrogel actuators in mechanical metamaterials. Our concept of out-of-plane buckled active elements that stiffen only under tension enables strain-stiffening metamaterials with high programmability before and after fabrication.

Designing three-dimensional lattice structures with anticipated properties through a deep learning method

Lattice structures have been a hot topic recently owing to their superior mechanical properties, which are significantly influenced by the unit cell structure. By leveraging the power of deep learning, inverse design can be conducted on the unit cell structure based on the mechanical properties of its lattice structure. Assisted by deep learning, this study introduces a novel data-driven approach to design three-dimensional (3D) unit cells for lattice structures with anticipated properties. The approach can be efficiently and accurately applied to various unit cell structures. An auto-encoder is trained to extract the geometric features from unit cell point clouds. The effective mechanical properties of the lattice structures are calculated by combining the homogenization method and the finite element method. Subsequently, a mapping relationship between mechanical properties and geometric features is established through the multi-layer perceptron neural network. The models are ultimately employed to design 3D unit cells given anticipated properties of lattice structures. The results show that the mechanical properties of the generated unit cells satisfy the anticipated values. The applications of proposed method are demonstrated in orthopedic implants, new hybrid unit cells, and functionally gradient structures. Furthermore, the method can be extended to unit cell design across diverse domains.

Design and Implementation of Different Unit Cells for Reconfigurable Intelligent Surface

Recently, great attention has been given to the idea of a smart environment. It often involves the use of reconfigurable intelligent surfaces (RIS) for the management of electromagnetic wave reflections as the world awaits the emergence of 6G. Changeable intelligent surfaces may enhance the creation of wireless communication. The design and analysis of several unit cell reflections are presented in this work. The first design relies on the Switching Technique which involves switching on and off to acquire the phase as well as the coefficient of reflection to accommodate 6G standards. The unit cells design is configured to operate in the millimeter band and X band. In the second design, the radius of the circular patch was changed to adjustment of the phase and reflection coefficient. The use of Floquet technique is employed in investigating the scattering characteristics of a unit cell's constituent elements based on the assumption that every element consists of an extremely iterating periodic structure. To determine the optimal force reflection and the transformation phase, the return loss alongside reflection phase graphs of each resonant component were examined. The simulation results indicate that the first design exhibits a reflection phase shift range of -180 to 90 and a reflection magnitude over 0.93 at a frequency of 11GHz. In contrast, the second design demonstrates a reflection phase shift range of -135 to 135 and a reflection magnitude surpassing 0.9 at a frequency of 28GHz. The analysis and simulation of the design models were carried out using the CST model.

Comparative study on the process, anisotropy, and mechanical performance of laser powder bed fusion fabricated truss-lattice structures with different unit cell designs

Lattice structures to fabricate bone implants can avoid stress-shielding effects and promote bone-in-growth. However, the performance of bones varies in different body parts, creating a barrier to manufacture an appropriate lattice structure for bone implant. Here, the formability, anisotropy, energy absorption abilities, stress distribution, and deformation mode of the laser powder bed fusion (LPBF) processed face-centered cubic (FCC), Octet, and Kelvin lattice structures were systematically compared through experiments and finite element analysis. The results show that the Kelvin lattice structure had the optimal comprehensive mechanical performance. This research has potential value for the design and manufacturing of specific bone implants.

Modeling and finite element simulation of sustainable coronary stent with a variation in unit cell design

Modeling and finite element simulation of sustainable coronary stent with a variation in unit cell design

Multifunctional Design of Triply Periodic Minimal Surface Structures for Temporary Pediatric Fixation Devices

Fracture fixation and limb deformity correction in pediatric orthopedics often use temporary metallic fixation devices. These devices’ higher stiffness compared to cortical bone leads to stress shielding, causing significant bone density reduction, periprosthetic loosening, and bone growth interference. The 3D‐printed triply periodic minimal surface (TPMS) structures present a promising engineering solution to match bone stiffness while ensuring reliable implant strength. In this study, finite‐element modeling and experimental testing are employed to identify optimal multifunctional TPMS‐based lattices that meet the required design constraints of 1) stiffness in the range of cortical bone, 2) strength in the range of cortical bone, 3) minimum osteointegration to facilitate the implant removal after healing, and 4) manufacturability with limited defect sensitivity. Six different types of TPMS structures in Ti–6Al–4V material manufactured via laser powder bed fusion are evaluated for their ability to target the lower and upper bounds of pediatric cortical bone stiffness. Lattices based on the Primitive unit cell design are superior, demonstrating the highest strength/stiffness ratio, best manufacturability, and potentially reduced osteointegration due to larger pore size, smaller surface area, and smallest negative Gaussian curvature compared to other investigated TPMS types.

Low-loss vanadium dioxide-enabled mmWave tunable reflective electromagnetic surface with complementary unit cells for wave manipulation

This study presents a novel implementation of vanadium dioxide (VO2) phase change material in an electromagnetic (EM) surface with beam steering capabilities. For the first time, we present the design, fabrication, and measurement of a globally actuated, VO2-based beamforming reflective EM surface. We propose a design featuring complementary unit cells that enable beam steering with a single excitation, marking a pioneering use of low-loss VO2 in creating a complementary EM surface for the mmWave band. The unit cells incorporating VO2 exhibit low-loss characteristics, with −0.92 and −1.9 dB in the hot state and −0.49 and −0.25 dB in the cold state, respectively. We incorporate both positive and negative phase variants alongside two temperature-independent phase unit cells. The complementary design enables us to utilize two beam operating states, effectively exploiting the otherwise unused cold state. We experimentally demonstrated beamforming at ±5° and ±10° from the broadside. In the case of ±10°, the measured gains at 35 GHz in the cold and hot states were 19.4 and 20.3 dB, respectively, which aligned well with the simulated gains of 20.9 and 21.5 dB. Manipulation of the electromagnetic wave direction with a single excitation has the potential for imaging, sensing, and communication applications. The complementary unit cell design methodology can be further adapted for mmWave beamforming, absorbing, and cloaking reconfigurable EM surfaces. Furthermore, the use of VO2 can be extended up to sub-THz frequencies due to the wideband, low-loss characteristics compared with conventional reconfigurable devices, such as PIN diodes or MEMS switches.

A compact quad-square negative-index metamaterial: Design, simulation, and experimental validation for microwave applications

This research provides a detailed explanation of the design, simulation, and experimental of quad-square metamaterial-based negative-index unit cells for S-band applications. The Computer Simulation Technology 2022 licensee version was utilized to design and obtain numerical results for the unit cell. The proposed unit cell for the metamaterial has dimensions of 5 × 5 × 1.57 mm3. The substrate chosen was FR-4, resulting in a substantial effective medium ratio value of 19.07. A series of systematic parametric studies were conducted to optimize the quad square metamaterial structure. Key parameters, such as substrate types, unit cell arrays, thicknesses of substrate, and split gaps, were varied to determine their impact on the structure. The validated equivalent circuit result was compared to the simulated results, showing a significant agreement. The demonstrated correlation between simulation and experimental data highlights the dependability of the proposed quad-square metamaterial, positioning it as a viable option for a range of electromagnetic applications, such as communication systems, sensors, and imaging devices.

A Terahertz Programmable Digital Metasurface Based on Vanadium Dioxide

Metasurfaces can realize the flexible manipulation of electromagnetic waves, which have the advantages of a low profile and low loss. In particular, the coding metasurface can flexibly manipulate electromagnetic waves through controllable sequence encoding of the coding units to achieve different functions. In this paper, a three-layer active coding metasurface is designed based on vanadium dioxide (VO2), which has an excellent phase transition. For the designed unit cell, the top patterned layer is composed of two split square resonant rings (SSRRs), whose gaps are in opposite directions, and each SSRR is composed of gold and VO2. When VO2 changes from the dielectric state to the metal state, the resonant mode changes from microstrip resonance to LC resonance, correspondingly. According to the Pancharatnam-Berry (P-B) phase, the designed metasurface can actively control terahertz circularly polarized waves in the near field. The metasurface can manipulate the order of the generated orbital angular momentum (OAM) beams: when the dielectric VO2 changes to metal VO2, the order l of the OAM beams generated by the metasurface changes from −1 to −2, and the purity of the generated OAM beams is relatively high. It is expected to have important application values in terahertz wireless communication, radar, and other fields.

Architecture Design of High‐Performance Piezoelectric Energy Harvester with 3D Metastructure Substrate

AbstractPiezoelectric energy harvesters (PEHs) have drawn considerable attention due to their unique ability to convert ambient mechanical energy to electrical energy. These devices are widely implemented in numerous applications such as wearable technology, structural health monitoring, and renewable energy systems. In this work, a novel approach that seamlessly integrates arbitrary metastructures into the substrate layer of cantilever beam‐based PEHs is presented. The corresponding performance of each PEH design is evaluated via an experimentally validated finite element model. This is the first systematic study to explore 3D metastructures with various unit cell configurations, unit cell numbers, and porosity levels. Compared with the existing PEH designs, implementation of a 3D auxetic metastructure with 85% porosity single unit cell design can demonstrate a substantial enhancement in output power, reaching 48.16 mW, and a high normalized power density (NPD) of 2.1131 µW mm−3 g−2 Hz−1. Results show that there are competing requirements for improving the performance of PEHs. On one hand, low metastructure stiffness is preferred to achieve high power output at low resonant frequency. On the other hand, metastructures designs with low stiffness may induce excessive distortion in the substrate layer, leading to mechanical energy loss. This deformation mechanism adversely affects the mechanical to electrical energy conversion efficiency. Detailed guidelines for designing and manufacturing high‐performance PEHs are discussed in this work.

Design and Measurement of a Two-Dimensional Beam-Steerable Metasurface for Ka-Band Communication Systems

This study introduces a steerable metasurface reflector designed for the Ka-band, enabling one-dimensional and two-dimensional beam steering. The paper elaborates on the design considerations, manufacturing process, and experimental findings. The unit cell design incorporates a Varactor diode as the tuning element, facilitating a dynamic phase range exceeding 300° with minimal metasurface beam steering losses. Notably, the experimental results are in good agreement with the simulation outcomes. The advantages of employing this metasurface reflector include rapid beam steering, cost-effective production implementation, support for both one-dimensional and two-dimensional beam steering, low reflection loss, high-resolution beam steering, and continuous beam steering capabilities.

A reflective textile metasurface for indoor signal coverage enhancement

The design of a reflective metasurface solely based on flexible textile material is presented for indoor signal coverage enhancement in a specific scenario – reflecting and reallocating radio frequency energy that would have leaked through a large window area. The proposed reflective metasurface design, reflective metasurface is composed of layers of square conductive textile patches and dielectric textile substrates. For the unit cell design, a reflective phase difference of up to 90° can be achieved via varying the size of the conductive patches. Meanwhile, a phase difference of up to 180° can be achieved by the alignment of conductive patches on different textile substrate layers, which is an ideal design philosophy for textile material. The proposed metasurface, consisting of 12 × 12 unit cells, can achieve a main reflected beam pointing in the direction of ±35° and a secondary reflected beam at ±63°. Simulated results show that the reflected beams remain relatively stable under the crumpling conditions often seen for curtains. A prototype of the design was fabricated and tested in a real-world scenario. A maximum signal strength enhancement of 15 dB and an average enhancement of 5.97 dB in a wide range of directions can be achieved with the reflective metasurface applied.

Effects of design and manufacturing deviations on compressive properties of glass sponge lattice structures manufactured by selective laser melting

Bio-inspiration offers researchers innovative perspectives and methodologies, stimulating the advancement of high-performance, high-durability, and added-value materials, structures, and products. Inspired by the lightweight, high-strength, and highly stable glass sponges (GSs), five types of glass sponge lattice structures (GSLSs) were successfully designed and manufactured by selective laser melting (SLM) with Ti6Al4V. By conducting a comparative analysis of unit cell design and manufacturing deviations, we assess their impact on the compressive properties of GSLSs. Notably, the original GSLS with circle-/grid-like heterogeneous geometries exhibits outstanding overall compression performance, including stability, stress dispersion and unique cell-by-cell and layer-by-layer fracture mechanisms among GSLSs, which are attributable to their reinforced diagonal struts and heterogeneous unit cells. Hence, three strategies for unit cell design and optimization were proposed. These discoveries guide the future design and optimization of lattice structures (LSs) and offer potential applications for GSLSs in aerospace, biomedicine, automobiles, architecture, and wearable products.

Bio-Inspired Pressure-Dependent Programmable Mechanical Metamaterial with Self-Sealing Ability.

Self-sealing is one of the fascinating functions in nature that enables living material systems to respond immediately to damage. A prime plant model is Delosperma cooperi, which can rapidly self-seal damaged succulent leaves by systematically deforming until the wound closes. Inspired by this self-sealing principle, a novel programmable mechanical metamaterial has been developed to mimic the underlying damage management concept. This material is able to react autonomously to changes in its physical condition caused by an induced damage. To design this ability into the programmable metamaterial, a permeable unit cell design has been developed that can change size depending on the internal pressure. The parameter space and associated mechanical functionality of the unit cell design is simulated and analyzed under periodic boundary conditions and various pressures. The principles of self-sealing behavior in designed metamaterials are investigated, crack closure efficiency is identified for different crack lengths, the limitations of the proposed approach are discussed, and successful crack closure is experimentally demonstrated in the fabricated metamaterial. Although this study facilitates the first step on the way of integrating new bio-inspired principles in the metamaterials, the results show how programmable mechanical metamaterials might extend materials design space from pure properties to life-likeabilities.

Design Optimization of Lattice Structures Under Impact Loading for Additive Manufacturing

Abstract Additive manufacturing (AM) has enabled the production of intricate lattice structures with excellent performance and minimal mass. Design approaches that consider static loading, including lattice-based topology optimization (TO), have been well-researched recently. However, to date, there appears to be no widely accepted method of optimizing lattice structures for high-strain rate loading, especially when the design for additive manufacturing (DFAM) principles are considered. This study proposes a computational framework for the design of lattice structures under specified impact loading. To manage dimensionality while achieving sufficient generality, a heuristic design space is developed that relies on traditional TO to govern the design's macrostructure and standard dimensioning to govern its mesostructure. DFAM principles are then incorporated into a Bayesian optimization scheme wrapped around traditional TO to achieve manufacturable designs that absorb high-impact loading. Because this approach does not require analytical gradient information, the framework can be used to optimize directly on complex objectives, such as injury metrics calculated from the acceleration curve. A series of case studies is formulated around a mass-performance tradeoff and involves individual unit cell design as well as full-part design. The proposed design parameterization is found to enable sufficient flexibility to achieve consistently good performance regardless of AM build orientation.

Monolayer actively tunable dual-frequency switch based on photosensitive silicon metamaterial

We propose a monolayer actively tunable dual-frequency switch in the terahertz (THz) range based on photosensitive silicon (PSi) metamaterial. The designed unit cell consists of hollow cross-shaped slots and four L-shaped slots made of a perfect electric conductor (PEC), with PSi embedded in both the cross-shaped and four L-shaped slots of identical dimensions. The PEC serves as the dielectric substrate. By varying the intensity of the pump beam to adjust the conductivity of the PSi, tuning of the transmittance at the resonant frequencies of the entire structure is achieved, enabling the switch to function in both ON and OFF states. Under vertical incidence of THz waves in the range of 1 THz to 3 THz, in the absence of pump beam, the PSi is in an insulating state with a conductivity of approximately 1 S/m. The proposed terahertz dual-frequency switch is in the ON state, with transmittances of 97.0% at the first resonance frequency (f1=1.736THz) and 98.3% at the second resonance frequency (f2=2.176THz), and group delays of 4.397 ps and 2.540 ps, respectively. When the pump beam intensity is 294.6 μj/cm2, the PSi is in a metallic state with a conductivity of approximately 1 × 105 S/m. The switch is in the OFF state, with zero transmittance in the range of 1 THz to 3 THz and a group delay of 0.327 ps. The calculated modulation degrees of amplitude at f1 and f2 for this terahertz dual-frequency switch are both 100%, demonstrating a high-performance switch. The two resonant frequencies f1 and f2 of the terahertz dual-frequency switch are generated by weakly coupled superposition between the embedded cross-shaped and four L-shaped PSi resonators (CSPR and FLSPR), exhibiting polarization-insensitive characteristics under vertical incidence of THz waves. We believe that this compact structure of terahertz metamaterial dual-frequency switch holds great application prospects in terahertz filtering, slow light devices, terahertz modulation, and the future 6G communication field.

Auxetic lattice structures consisting of an enhanced trigram frame unit cell with superior stiffness

Superior stiffness is deemed essential for structures intended for several applications. The stiffness enhancement can be achieved by adopting structures that deform based on the stretching-dominated mechanism instead of the bending-dominated mechanism. This paper proposes a novel auxetic unit cell design and two distinct lattice structures dominated by stretching when subjected to quasi-static compressive and tensile loadings. The structures are manufactured via the fused deposition modeling (FDM) 3D printing method with the use of polylactic acid (PLA) filament as the patent material. The investigation also includes theoretical analyses and finite element (FE) simulations, all yielding consistent results. Response Surface Methodology (RSM) is also employed to understand the influence of three geometric parameters. Besides, single-objective optimization is conducted to maximize the stiffness through geometry design, and multi-objective approaches are implemented to improve the stiffness while simultaneously reducing relative density. Finally, different unit cells, which deform based on the stretching-dominated mechanism, are selected to represent their respective classifications, enabling a comparison of their potential stiffness capacity with the designed structures in this study. Remarkably, it is highlighted that the proposed unit cells and structures outperform others in terms of specific stiffness, making them a promising choice for use in structural engineering.

Micro- and Macro-Scale Topology Optimization of Multi-Material Functionally Graded Lattice Structures

Lattice structures are becoming an increasingly attractive design approach for the most diverse engineering applications. This increase in popularity is mainly due to their high specific strength and stiffness, considerable heat dissipation, and relatively light weight, among many other advantages. Additive manufacturing techniques have made it possible to achieve greater flexibility and resolution, enabling more complex and better-performing lattice structures. Unrestricted material unit cell designs are often associated with high computational power and connectivity problems, and highly restricted lattice unit cell designs may not reach the optimal desired properties despite their lower computational cost. This work focuses on increasing the flexibility of a restricted unit cell design while achieving a lower computational cost. It is based on a two-scale concurrent optimization of the lattice structure, which involves simultaneously optimizing the topology at both the macro- and micro-scales to achieve an optimal topology. To ensure a continuous optimization approach, surrogate models are used to define material and geometrical properties. The elasticity tensors for a lattice unit cell are obtained using an energy-based homogenization method combined with voxelization. A multi-variable parameterization of the material unit cell is defined to allow for the synthesis of functionally graded lattice structures.

Gain enhancement in octagonal shaped frequency reconfigurable antenna using metasurface superstrate

Abstract A novel, high-gain reconfigurable antenna with a metasurface (MS) superstrate-based configuration is proposed in this research article. The design utilizes a concentric octagonal-shaped patch as a base antenna. Four SMP1345-079LF PIN diode switches are incorporated in the base antenna to facilitate frequency reconfiguration. When all four of the diodes are in OFF condition, the designed antenna resonates at 5.8 GHz. Switching ON the diodes switches the resonating frequency to 5 GHz. A novel MS unit cell of shape like ‘8’ has been designed and analyzed. The designed unit cell exhibits properties of the metamaterial in the operating frequencies. An MS superstrate of a 5 × 5 array has been designed and connected to the base antenna through Teflon rods. Further, the proposed reconfigurable antenna with MS has been analyzed for air and foam medium (medium between antenna and superstrate). The proposed structure offers better performance for the air medium with a gain enhancement of 4.23 dBi and 1.55 dBi at 5 GHz and 5.8 GHz respectively. Fabrication and testing processes are undertaken to validate the proposed antenna’s performance.

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.