Metamaterial Architectures Research Articles

Harnessing structural hierarchy and multi-material approaches to improve crushing performance of re-entrant honeycombs

This study proposes to improve the crushing performance of re-entrant honeycombs by considering both mechanistic and material ingredients. First, a set of novel hierarchical configurations possessing hexachiral auxetic subordinate cells was designed by replacing the solid cell walls of the conventional re-entrant honeycomb. Then the voids of the modified re-entrant honeycombs and the proposed hierarchical metamaterials were filled with a flexible material by using a multi-material 3D printer. Parametric numerical analyses were performed using validated Finite Element models to identify optimal metamaterial architectures. A set of samples, including traditional and developed configurations, were 3D printed and subjected to uniaxial compression loading. The deformation mechanism, compressive strength, and energy absorption of the samples were compared at different strain levels. The results show that introducing hexachiral hierarchies along the ribs prolongs the duration of plastic deformation and keeps the auxeticity of the samples at larger strains. This provides a stable and long post-yield plateau in the compressive stress-strain curve that brings considerable improvement in energy absorption and compressive strength. In addition, multi-material approaches with the combination of rigid photopolymer and flexible rubber-like material also contribute to stabilizing the deformation mechanism of both conventional and developed hierarchical re-entrant auxetic configurations. The proposed hierarchical auxetic structures present more specific compressive strength and specific energy absorption (up to ~150 %) compared to conventional re-entrant auxetic honeycombs. Overall, the proposed hybrid designed strategies can be leveraged to manipulate the collapse mechanism and improve crushing performance.

Mechanical performance of solid and sheet network-based stochastic interpenetrating phase composite materials

Nature-inspired architected materials premise effective property combinations that are well beyond the limits of classical engineering materials. The current study expands the concept of architected, interpenetrating phase composites (IPC) with regular periodic inner phase reinforcements to the realm of stochastic designs. Schoen's Wrapped Package minimal surface (IWP) is used as base reinforcement phase structure, while implicit functions are employed for the creation of stochastic solid and sheet topologies. The study is performed for various reinforcement volume fractions as low as 20 and up to 40%, using a resin-based 3D printer for the specimen fabrication. The strong directional dependence of the uniaxial properties of regular IWP-based designs is highlighted, while their linear and nonlinear material attributes are compared with the ones of stochastic architectures. It is shown that stochastic, sheet-based single phase and IPC material architectures can yield comparable effective mechanical properties or outperform the energy absorption capacity of regular designs at low volume fraction reinforcements. The stochasticity of the strain fields is experimentally verified through digital image correlation (DIC), associating the arising failure modes with the regular or stochastic nature of the inner reinforcement phase. Moreover, functionally graded stochastic architectures are engineered and characterized, establishing a fundamental control of the deformation and resulting stress-strain response along a desired material direction. The high-performing effective material attributes, combined with the directional independence premised by the stochasticity of the IPC metamaterial architectures constitute objectives beyond the performance limits of regular cellular materials, opening new frontiers in the design of advanced structural applications.

Towards biomimetic, lattice-based, tendon and ligament metamaterial designs

The engineering of tendon and ligament tissue biocompatible restoration materials constitutes a long-standing engineering challenge, from the chemical, biological and mechanical compatibility analysis and design perspective. Their mechanics are inherently anisotropic, exceeding the potential limits of common, non-architected engineering materials. In the current contribution, the design of advanced material or “metamaterial” architectures that can emulate the mechanical properties observed in native tendon and ligament tissues is analytically, experimentally, and numerically investigated. To that scope, anisotropic metamaterial designs that are based on rectangular cuboid architectures with and without inner body-centered strengthening cores are considered. Thereupon, the metamaterial design specifications required for the approximation of the highly anisotropic tissue performance, namely of the characteristic normal, shear and Poisson's ratio attributes are studied. It is shown that certain strengthened, anisotropic body-centered cuboid lattice architectures allow for substantial effective metamaterial stiffness along the primal tissue loading direction, upon a rather low shear loading resistance. The previous mechanical attributes come along with Poisson's ratio values well above unity and moderate relative density values, furnishing a combination of material characteristics that is highly desirable in restoration praxis. The analytically and numerically guided anisotropic metamaterial performance is experimentally reproduced both for the case of uniaxial and shear loads, using a microfabrication stereolithography additive manufacturing technique. The obtained scanning electron microscopy images highlight the fabrication feasibility of the identified metamaterial architectures, in scales that are directly comparable with the ones reported for the natural tissues, having feature sizes in the range of some 10ths of micrometers and elastic attributes within the range of clinical observation.

Inverse metamaterial design combining genetic algorithms with asymptotic homogenization schemes

In the current work, a numerical method for the inverse engineering of metamaterials is elaborated. The method is based on the combination of asymptotic homogenization schemes with genetic algorithms and it makes use of the complete set of parameters contained in the target compliance tensor. As such, it can be used to compute lattice unit-cell patterns that meet target macroscale elastic, shear, Poisson’s ratio and normal to shear strain coupling performances for the first time. The elaborated formulation applies to both constant and variable target relative density metamaterial designs, identifying metamaterial architectures within and beyond orthotropy. Different relevant case-study examples are provided, highlighting the potential of the formulation to capture a wide range of effective metamaterial behaviors. The accuracy of the results is additionally verified through commercial code, dedicated Abaqus finite element models, as well as through experimental testing of 3D-printed, periodic metamaterial samples. The scheme has a substantially low computational cost, so that a wide range of inverse engineering tasks can be performed within a computing time of a few minutes, using regular power, personal computing machines.

Multi-stable acoustic metamaterials with re-configurable mass distribution

This article proposes a design strategy for acoustic metamaterial lattices which leverages the characteristic multi-stability and kinematic amplification of the internal architecture to realize a re-configurable effective mass distribution, enabling a corresponding frequency band structure of extreme tunability. The approach builds metamaterial lattices from bi-stable elastic elements featuring the typical two-bar inertial amplification mechanism, whose deformation axis is uniquely misaligned with that of its elastic support such that the realized amplification is configuration-specific. Conveniently, a change in the configuration does not simultaneously alter the element dimensions and, therefore, the size/shape of the finite metamaterial structure remains constant. Moreover, as the multi-stability and kinematic amplification are each based on geometry, scaling the resulting metamaterial structure is expected to be straightforward. The dynamic performance of 1D/2D metamaterial architectures exhibiting the proposed design strategy is analytically determined via Bloch wave analysis and supported by numerical demonstration of the corresponding finite structures.

High-performance large-scale simulation of multi-stable metastructures

In this paper, we have developed a solver based on the message-passing interface (MPI) to enable rapid large-scale simulation of generic metastructures composed of bi- or multi-stable elements. The in-house solver has been thoroughly validated against a commercial numerical solver (Abaqus) and the well-established serial codes from the previous studies. We can achieve up to 4th-order solution accuracy with fully explicit Runge-Kutta (RK) methods, exceeding what many commercial structural analysis tools provide. With our parallel code dedicated to solving specific problem types, the absolute computational speed can be improved by three orders of magnitude, enabling the investigation of a large parameter space. More importantly, the in-house implementation enables an effective distribution of the computational load following the intrinsic structural periodicity, thus achieving efficient parallel scalability. To demonstrate our code's capability to handle massively large problems previously unattainable with existing solvers, we investigate the amplitude-dependent energy transmissibility of bi-stable metabeams and the stability of the transition wave's propagation speed. The achieved numerical and computational performance gains drastically expand the accessible analysis domains of general nonlinear metamaterial and metastructure architectures, thus opening up the potential to uncover new dynamics and enable practical implementations. Program summaryProgram Title:NM̂3 (Nonlinear MetaMaterials MPI) solverCPC Library link to program files:https://doi.org/10.17632/8f4n99jccf.1Developer's repository link:https://github.com/wonnie87/NMCubeLicensing provisions: MITProgramming language: FortranNature of problem:NM̂3 enables massively parallel simulations of strongly nonlinear metamaterials and metastructures, including 1D multi-stable lattice with coupled pendula (discrete sine-Gordon model), 1D lattice with quartic on-site potentials (discrete ϕ-4 model), and metabeam with a bi-stable microstructure.Solution method: Up to the 4th-order explicit Runge-Kutta (RK) methods are implemented in NM̂3. The Newmark-β (implicit) method with constant average acceleration is also available if unconditional numerical stability is desired.Additional comments including restrictions and unusual features: Running NM̂3 requires installation of Python (with NumPy library), MPI, and HDF5. A Python script is used to generate input files. The code use MPI system calls to allow a massive parallelization among the compute processes. The code uses HDF5 file format for data storage.

Acoustic metamaterials with independently tunable mass, damping, and stiffness

Over the past decades, metamaterials—whose engineered internal architecture grants unusual or extraordinary macroscopic response—have garnered increasing attention from researchers as the desire to shape material behavior beyond natural limitations (e.g., chemistry) arises within several areas of materials science and engineering. The bulk of reported acoustic metamaterial architectures are passive such that their properties and functions are fixed at fabrication. Nevertheless, a tuning capacity is desirable to expand the range of response, in general, and to allow for adaptation in the face of changing service requirements. Despite the diversity of proposed tuning strategies, most target the stiffness parameter alone, leaving the inertial and dissipative properties unaffected. In this presentation, we present a novel implementation of (geometric) bi-stability and kinematic amplification to independently tune the value and distribution of the effective mass, stiffness, and viscous damping within acoustic metamaterials, which impacts the dynamic response. Through analytical and numerical investigations of a 1D system, we show that the corresponding frequency band structure depends on the specific configurations of bi-stable elements within the unit cell. As the number of bi-stable elements per unit cell increases, so to do the number of unique dynamic responses to which to tailor the system. The proposed strategy significantly expands the property set available for tuning acoustic metamaterial performance post-fabrication.

Double negative bend headed I-shaped metamaterial based Terahertz optical power splitter

Terahertz (THz) technology has piqued the interest of many researchers due to the fascinating characteristics of THz waves. Two new metamaterial array architectures are proposed in this paper to investigate power splitting via backward wave propagation. The first array pattern is a rectangular array arrangement, which is defined analytically and suggested as a power splitter in the TE (transverse electric) mode. From the proposed rectangular metamaterial array pattern, another cavity array structure was proposed which successfully increased DNG (double negative) response inside the metamaterial device and produced better splitting performance in the DNG condition. The unit cell and array patterns had almost identical effective parameter results, but some of them changed because the air-dielectric-metal combination was increased. The power splitter is demonstrated at the 0.91 THz frequency range where it shows the effective permittivity is −6, permeability is −6, and the refractive index is −6. At 0.94 THz, the DNG backward wave divider has negative effective parameters with an effective permittivity of −5.8, permeability of −5.8, and refractive index of −5.8.Both of the analytical structure patterns are proposed for optical power splitter and divider applications, which are used in various microwave circuits, such as mixers, balanced amplifiers, and antenna arrays.

Multiphase lattice metamaterials with enhanced mechanical performance

We describe here the quasi-static crushing behavior of novel classes of multiphase (hybrid) hierarchical lattice metamaterials. The first class is represented by a hybrid architecture combining a hierarchical honeycomb with polyurethane foam filler, while the second is a multiphase structure produced by injecting an alginate hydrogel into the hierarchical voids of the honeycomb metamaterial. Twelve different auxetic (i.e. negative Poisson’s ratio) and non-auxetic metamaterial architectures have been 3D printed and subjected to edgewise compression crushing loading. A parametric numerical analysis has been also performed using validated finite element models to identify best metamaterial architecture configurations. Configurations filled with the hydrogel showed a significant stabilization of the deformation mechanism during large deformation edgewise compression. The use of metamaterials designs with internal slots and round in the ribs also filled by polyurethane rigid semi-reticulated foam feature however significant increases in terms of specific stiffness, mean crushing force, strength and energy absorption. The enhancement is particularly evident for the hybrid lattice metamaterials auxetic configurations.

The role of polymer mechanochemistry in responsive materials and additive manufacturing

The use of mechanical forces to chemically transform polymers dates back decades. In recent years, the use of mechanochemistry to direct constructive transformations in polymers has resulted in a range of engineered molecular responses that span optical, mechanical, electronic and thermal properties. The chemistry that has been developed is now well positioned for use in materials science, polymer physics, mechanics and additive manufacturing. Here, we review the historical backdrop of polymer mechanochemistry, give an overview of the existing toolbox of mechanophores and associated theoretical methods, and speculate as to emerging opportunities in materials science for which current capabilities are seemingly well suited. Non-linear mechanical responses and internal, amplifying stimulus–response feedback loops, including those enabled by, or coupled to, microstructured metamaterial architectures, are seen as particularly promising. Polymer mechanochemistry converts mechanical forces in materials to chemical reactions through the response of functional groups known as mechanophores. This Review discusses the colorimetric, mechanical, chemical and electronic responses of mechanophores that may be useful in materials for strain sensing and strengthening, soft devices and additive manufacturing.

Soft Topological Metamaterials with Pronounced Polar Elasticity in Mechanical and Dynamic Behaviors

We realize soft topological mechanical metamaterials with pronounced polar elastic responses (i.e., softer on one edge than the other) in both the quasistatic and dynamic regimes. Numerical simulations and experimental results confirm the presence of directional dependence in metamaterial response at low and high strain rates, despite the use of lossy elastomer as bulk media. The metamaterials exhibit means to tailor the location of topologically protected uniaxial mechanical stiffnesses by virtue of both loading orientation and geometric changes to the lattice architecture. High-speed video recordings show strong topologically protected asymmetric wave propagation for the soft metamaterials subjected to impact. The results indicate a class of metamaterial architectures possessing polar elastic behavior and confirm the persistence of the response in lossy media.

Compact localized states of open scattering media: a graph decomposition approach for an ab initio design.

We study the compact localized scattering resonances of periodic and aperiodic chains of dipolar nanoparticles by combining the powerful equitable partition theorem (EPT) of a graph theory with the spectral dyadic Green's matrix formalism for the engineering of embedded quasi-modes in non-Hermitian open scattering systems in three spatial dimensions. We provide the analytical and numerical design of the spectral properties of compact localized states in electromagnetically coupled chains and establish a connection with the distinctive behavior of bound states in the continuum. Our results extend the concept of compact localization to the scattering resonances of open systems with an arbitrary aperiodic order beyond tight-binding models, and are relevant for the efficient design of novel photonic and plasmonic metamaterial architectures for enhanced light-matter interaction.

Theory of the Hall effect in three-dimensional metamaterials

We apply homogenization theory to calculate the effective electric conductivity and Hall coefficient tensor of passive three-dimensionally periodic metamaterials subject to a weak external static homogeneous magnetic field. We not only allow for variations of the conductivity and the Hall coefficient of the constituent material(s) within the metamaterial unit cells, but also for spatial variations of the magnetic permeability. We present four results. First, our findings are consistent with previous numerical calculations for finite-size structures as well as with recent experiments. This provides a sound theoretical justification for describing such metamaterials in terms of effective material parameters. Second, we visualize the cofactor fields appearing in the homogenization integrals. Thereby, we identify those parts of the metamaterial structures which are critical for the observed effective metamaterial parameters, providing a unified view onto various previously introduced single-constituent/multiple-constituent and isotropic/anisotropic architectures, respectively. Third, we suggest a novel three-dimensional non-magnetic metamaterial architecture exhibiting a sign reversal of the effective isotropic Hall coefficient. It is conceptually distinct from the original chainmail-like geometry, for which the sign reversal is based on interlinked rings. Fourth, we discuss two examples for metamaterial architectures comprising magnetic materials: yet another possibility to reverse the sign of the isotropic Hall coefficient and an approach to conceptually break previous bounds for the effective mobility.

Three-dimensional poroelastic metamaterials with extremely negative or positive effective static volume compressibility

Recently, three-dimensional poroelastic metamaterials have been introduced that show an unusual isotropic increase of their effective volume when increasing the hydrostatic pressure of the surrounding air. This behavior corresponds to a negative effective static volume compressibility. Here, we present significantly simplified metamaterial architectures, which are composed of just one rather than eight hollow sealed functional elements within each cubic unit cell. On cubic symmetry microstructured polymer samples made by 3D laser printing, we measure a negative effective compressibility of about κeff=−4.7%∕bar under pressure control. This value is six times larger than previous values. Furthermore, we present related modified architectures with an extremely large positive effective compressibility of about κeff=5.0%∕bar. Finally, we show that, in principle, the positive effective metamaterial compressibility can exceed the isothermal compressibility of the surrounding air of κ=101%∕bar under ambient conditions.

Large deformation response of additively-manufactured FCC metamaterials: From octet truss lattices towards continuous shell mesostructures

Starting with the statically-determinate solid octet truss lattice, the large strain compression response of different metamaterial architectures is analyzed through finite element analysis and compression experiments on additively-manufactured stainless steel specimens. Simulation results clearly demonstrate that for a relative density of 20% the conventional solid octet-truss lattice has a lower specific energy absorption capability than some simple periodic shell structures. The analysis of the closed-packed hollow sphere assembly subject to hydrostatic compression reveals that the constituent hollow spheres initially transform into rhombic dodecahedra, which results in significant strengthening at the macroscopic level. Unlike the octet-truss with solid struts, hollow octet truss structures remain stable for hydrostatic, confined and uniaxial compression at the lowest relative density considered. Its strength, in particular at small plastic strains, is substantially improved when substituting the geometric hollow truss joints for hollow spheres. The continuous shell mesostructures defined by the Hybrid (hollow) Truss-Sphere (HTS) and the hollow octet truss assembly exhibited the highest strength and energy absorption potential at 20% relative density for the high and low strain-hardening materials considered, respectively. Moreover, it is found that the HTS metamaterial exhibits the highest relative Young's and bulk moduli among all four architectures considered. It is also shown computationally that hollow rhombic dodecahedral mesostructures could provide nearly twice the strength and energy absorption of the conventional octet truss.

Repulsion of polarized particles near a magneto-optical metamaterial

We show that a particle emitting in close proximity to a magneto-optical metamaterial substrate can experience a repulsive force if the magnetization is found along the surface plane. An analytical condition for the existence of such a repulsive force is obtained within the near-field approximation. Significantly, the repulsive force can be tuned by varying the filling fraction in a stack of two alternating layers of a metallic magneto-optical material and a dielectric. Potential applications can be envisaged for nanomechanical devices, particularly since similar metamaterial architectures have already been developed experimentally.

Parallel Hall effect from three-dimensional single-component metamaterials

We propose a class of three-dimensional metamaterial architectures composed of a single doped semiconductor (e.g., n-Si) in air or vacuum which lead to an unusual effective behavior of the classical Hall effect. Using an anisotropic structure, we numerically demonstrate a Hall voltage that is parallel—rather than orthogonal—to the external static magnetic-field vector (“parallel Hall effect”). The sign of this parallel Hall voltage can be determined by a structure parameter. Together with the previously demonstrated positive or negative orthogonal Hall voltage, we demonstrate four different sign combinations.

Manipulating waves with LEGO® bricks: A versatile experimental platform for metamaterial architectures

In this letter, we discuss a versatile, fully reconfigurable experimental platform for the investigation of phononic phenomena in metamaterial architectures. The approach revolves around the use of 3D laser vibrometry to reconstruct global and local wavefield features in specimens obtained through simple arrangements of LEGO® bricks on a thin baseplate. The agility by which it is possible to reconfigure the brick patterns into a nearly endless spectrum of topologies makes this an effective approach for rapid experimental proof of concept, as well as a powerful didactic tool, in the arena of phononic crystals and metamaterials engineering. We use our platform to provide a compelling visual illustration of important spatial wave manipulation effects (waveguiding and seismic isolation), and to elucidate fundamental dichotomies between Bragg-based and locally resonant bandgap mechanisms.

Theory-Guided Design of Organic Electro-Optic Materials and Devices

Integrated (multi-scale) quantum and statistical mechanical theoretical methods have guided the nano-engineering of controlled intermolecular electrostatic interactions for the dramatic improvement of acentric order and thus electro-optic activity of melt-processable organic polymer and dendrimer electro-optic materials. New measurement techniques have permitted quantitative determination of the molecular order parameters, lattice dimensionality, and nanoscale viscoelasticity properties of these new soft matter materials and have facilitated comparison of theoretically-predicted structures and thermodynamic properties with experimentally-defined structures and properties. New processing protocols have permitted further enhancement of material properties and have facilitated the fabrication of complex device structures. The integration of organic electro-optic materials into silicon photonic, plasmonic, and metamaterial device architectures has led to impressive new performance metrics for a variety of technological applications.

Metamaterial based telemetric strain sensing in different materials

We present telemetric sensing of surface strains on different industrial materials using split-ring-resonator based metamaterials. For wireless strain sensing, we utilize metamaterial array architectures for high sensitivity and low nonlinearity-errors in strain sensing. In this work, telemetric strain measurements in three test materials of cast polyamide, derlin and polyamide are performed by observing operating frequency shift under mechanical deformation and these data are compared with commercially-available wired strain gauges. We demonstrate that hard material (cast polyamide) showed low slope in frequency shift vs. applied load (corresponding to high Young's modulus), while soft material (polyamide) exhibited high slope (low Young's modulus).