Periodic Metamaterials Research Articles

Correction to: Attenuation of vibrations in a drone camera by periodic resonator metamaterials: experimental analysis

Correction to: Attenuation of vibrations in a drone camera by periodic resonator metamaterials: experimental analysis

Attenuation of vibrations in a drone camera by periodic resonator metamaterials: experimental analysis

Attenuation of vibrations in a drone camera by periodic resonator metamaterials: experimental analysis

Tiling-based lattice generation for structural property exploration

Advancements in additive manufacturing enable the development of artificial lattice structures with unique properties not found in natural materials. Specifically, filament-based lattices are known for having a lightweight yet strong nature, exhibiting auxetic behavior and excellent energy absorption capabilities. Recent research has focused on developing algorithms and frameworks to manipulate cell geometry and material properties to achieve unusual properties. However, the exploration of the full design space is hampered in practice primarily due to restrictions on cell tiling variation. Here, for the first time, a Tiling-Based Lattice Generation (TBLatGen) framework is presented that relies on various tiling operations and stochastic changes in internal cell geometry. By utilizing reflections, rotations, glide reflections, translations, and combinations of these operations, lattice structures are tiled to achieve an extensive range of properties. For instance, achieving Poisson's ratios ranging over at least ±20 using a minimal set of design parameters is demonstrated, a range unprecedented in prior studies. Experimental testing of a physical prototype validates the auxetic behavior of one newly proposed tiled lattice structure. Beyond this, the proposed TBLatGen framework is anticipated to be applicable to general periodic metamaterials, enabling the design and discovery of new structures exhibiting exceptional mechanical, thermal, electrical, or magnetic properties.

3D Printing of Periodic Porous Metamaterials for Tunable Electromagnetic Shielding Across Broad Frequencies

HighlightsThe stable periodic porous shielding materials were prepared by combining the strategies of 3D printing and metamaterial design.The relationship between porous material structure and electromagnetic interference shielding efficiency (EMI SE) effectiveness was deeply explored, revealing the important structural parameters for realizing tunable EMI SE property.The optimized design of the periodic porous shielding box achieves effective EMI shielding in a wide wavelength range (over 2.4 GHz).

An Extensive Parametric Analysis and Optimization to Design Unidimensional Periodic Acoustic Metamaterials for Noise Attenuation

The presented research delineates an extensive study aimed at obtaining and comparing optimal designs and geometries for one-dimensional periodic acoustic metamaterials to attenuate noise within the audible frequency range of 20 Hz to 20 kHz. Various periodic designs, encompassing diverse geometric parameters and shapes—from Basic-Periodic to Semi-Periodic, Tapered-Diverging, and Tapered-Converging unit cells of repeated patterns—are examined to identify the most effective configurations for this application. A thorough parametric analysis is executed employing FE-Bloch’s theorem across these four configurations to determine their bandgaps and to identify the most effective geometry. A normalization process is utilized to extend the domain of the analysis and the range of the system parameters studied in this work, totaling 202,505 design cases. Finally, the optimal design is identified based on achieving the best bandgaps coverage. The study concludes with the presentation of frequency domain acoustic pressure responses at multiple sensing points along the filters, validating the performance and the obtained bandgaps through these optimal geometries.

Compression behavior of sheet-network triply periodic minimal surface metamaterials as a function of density grading

This study involved the fabrication and experimental testing of five distinct geometries of triply periodic minimal surface (TPMS) cellular structures characterized by uniform and relative density grading. The specific geometries examined were Schoen-Gyroid, Schwarz-Diamond, Schoen-I-WP, Schwarz-Primitive, and Fischer-Koch S. The experimental tests focused on subjecting these structures to compression loads. Samples were produced with a masked stereolithography (MSLA) printer. The samples had initial and end volume fractions (VFs) ranging from 20% to 60% in increments of 10%, with five varied relative densities. The Taguchi method is utilized to determine the optimal testing parameters, while the Analysis of Variance (ANOVA) test is employed to examine the data. The novelty of this paper is to comprehensively investigate the structural efficiency and versatility of TPMS for various applications by optimizing five different functionally graded TPMSs. The ANOVA findings highlighted the substantial impacts of Initial VF, Final VF, and TPMS type on the observed fluctuations in stress at the first peak. The Initial VF made a significant contribution, demonstrating 28.8% higher effectiveness than the Final VF. The TPMS type had a statistically significant effect on the amount of energy absorbed, revealing that different lattice types have abilities to absorb energy.

Emergent disorder and mechanical memory in periodic metamaterials

Ordered mechanical systems typically have one or only a few stable rest configurations, and hence are not considered useful for encoding memory. Multistable and history-dependent responses usually emerge from quenched disorder, for example in amorphous solids or crumpled sheets. In contrast, due to geometric frustration, periodic magnetic systems can create their own disorder and espouse an extensive manifold of quasi-degenerate configurations. Inspired by the topological structure of frustrated artificial spin ices, we introduce an approach to design ordered, periodic mechanical metamaterials that exhibit an extensive set of spatially disordered states. While our design exploits the correspondence between frustration in magnetism and incompatibility in meta-mechanics, our mechanical systems encompass continuous degrees of freedom, and thus generalize their magnetic counterparts. We show how such systems exhibit non-Abelian and history-dependent responses, as their state can depend on the order in which external manipulations were applied. We demonstrate how this richness of the dynamics enables to recognize, from a static measurement of the final state, the sequence of operations that an extended system underwent. Thus, multistability and potential to perform computation emerge from geometric frustration in ordered mechanical lattices that create their own disorder.

Discrete heat equation for a periodic layered system with allowance for the interfacial thermal resistance: General formulation and dispersion analysis.

Discrete heat equations for the multilayered periodic systems with allowance for the thermal resistance between the layers and corresponding dispersion relations in ω-k space have been derived and analyzed. The discrete equations imply a finite velocity of thermal disturbances and guarantee the positiveness of the solutions. Analytical expressions for the attenuation distance, and phase and group velocities have been obtained as functions of frequency and thermal resistance between the discrete layers. These functions demonstrate unusual behavior at high frequency compared to the continuum case. Furthermore, the maximum allowed frequency and wave number for the discrete heat equation are limited, whereas there are no such limits in a continuum. The discrete equation contains an infinite hierarchy of continuous partial differential equations, which starts with the Fourier law, proceeds with the hyperbolic equation, the Guyer-Krumhansl (or Jeffreys type) equation, and then with higher-order equations. The partial differential equations with a finite number of terms are only approximations of the discrete equation, which implies that on the ultrashort space and timescales the discrete approach is preferable. This work provides a relatively simple, easy-to-adopt, conceptual tool, together with analytical expressions allowing one to study ultrafast wavelike heat conduction regimes in periodic multilayered metamaterials.

Origami-based bidirectional self-locking system for energy absorption

When a periodic cellular structure is subjected to high-intensity loading, lateral splashing can occur, significantly decreasing macro mechanical properties. Periodic structures with self-locking properties can overcome this inherent flaw and achieve excellent performance characteristics, including high energy absorption efficiency. In this regard, thin-walled periodic self-locking dissipative structures have been extensively studied recently. Most existing bend-dominated self-locking dissipative systems are two-dimensional and can only achieve self-locking under specific loading conditions. This paper describes a three-dimensional origami-based bidirectional self-locking system that can achieve self-locking under normal and shear loading. Furthermore, a plastic hinge model revealed the energy absorption mechanism of the origami-based cells, whose specific energy absorption (SEA) is higher than that of other existing bend-dominated self-locking cells. The bidirectional self-locking of the origami-based system was demonstrated through compression, bending and impact tests. This origami-based system has high energy absorption efficiency, and the novel bidirectional self-locking mechanism can significantly broaden the design space for periodic dissipative metamaterials.

Toward Fatigue-Tolerant Design of Additively Manufactured Strut-Based Lattice Metamaterials

Abstract The advent of additive manufacturing (AM) has enabled the prototyping of periodic and non-periodic metamaterials (a.k.a. lattice or cellular structures) that could be deployed in a variety of engineering applications where certain combinations of performance features are desirable. For example, these structures could be used in a variety of naval engineering applications where lightweight, large surface area, energy absorption, heat dissipation, and acoustic bandgap control are desirable. Furthermore, combining the multifunctional design optimization of these structures with progressive degradation due to cyclic loading could lead to fatigue-activated attritable systems with potentially tailorable performances not yet in reach by current conventional systems. Nevertheless, in order to deploy these complex geometry structures their multiphysics response has to be well understood and characterized. The objective of the current effort is to describe an initial approach for designing a uniaxial metamaterial specimen for fatigue testing as the first step toward the design of multi-axial fatigue test coupons. In order to compare bending- and stretching-dominated structures, two strut-based lattices made of Ti-6Al-4V alloy consisting of the octet and tetrakaidecahedron (or Kelvin) cells are examined. The specimens are designed to fail in the central area of the specimen where edge effects are minimized. Finite element results of the relevant structural mechanics are implemented and exercised to compare the performance of the eight relevant geometries and to evaluate the effect of relative density on fatigue life.

A non-conformal domain decomposition method utilizing rotating subdomains and non-matching grids for periodic metamaterial simulation

Electromagnetic metamaterials possess characteristics such as having large-scale, periodic, multi-media, and complex geometric structures, making them highly suitable for simulation using the finite element domain decomposition method (DDM). This work proposes a non-conformal DDM for simulating finite-period metamaterials, achieving simulation with a minimal number of domains while significantly reducing computational resource consumption. First, the computational domain of the periodic metamaterial is partitioned into several non-conformal hexahedral subdomains. Subsequently, a limited number of non-repetitive subdomain models with non-matching grids are constructed, leveraging the three-dimensional rotational and translational properties of these subdomains to facilitate simulation. By eliminating the necessity to construct models for every subdomain, a substantial reduction in memory consumption is achieved. Second, an iteration method for solving the matrix equations of subdomains is enhanced by introducing a multifrontal block incomplete Cholesky decomposition preconditioner, thereby enhancing the computational efficiency of matrix equations with a large number of unknowns. Meanwhile, parallel computing techniques are employed to accelerate the proposed method. Finally, we integrate the aforementioned method into a solver and leverage it to develop an electromagnetic simulation tool tailored for metamaterials. The tool is employed to simulate metamaterial structures of varying scales, resulting in notable reductions in both memory and time consumption while maintaining accuracy comparable to commercial software.

Crashworthiness study of aluminum foam-filled tubular lattice structures based on triply periodic minimal surface metamaterials under lateral crushing

Owing to their superior energy absorption capabilities and lightweight characteristics, both aluminum foam and tubular lattice structures based on triply periodic minimal surfaces (named T-TLS) had attracted a lot of attention. However, they had never functioned together in combination. Accordingly, aluminum foam was filled into T-TLS to form foam-filled T-TLS with the aim of enhancing the energy absorption performance, and their mechanical properties under lateral crushing were experimentally and numerically studied. Quasi-static lateral crushing experiments were firstly performed on the empty T-TLS, cylindrical foam filler, and foam-filled T-TLS to obtain deformation modes, force–displacement responses, and crashworthiness parameters. The experimental results indicated that filling aluminum foam changed the deformation mode from a four-hinge mode to a six-hinge mode. Moreover, foam-filled T-TLS displayed significantly enhanced energy absorption performance attributed to the interaction between T-TLS and aluminum foam, as evidenced by higher energy absorption (EA) and specific energy absorption (SEA). Subsequently, validated finite element (FE) models of foam-filled T-TLS were developed to further reveal their crushing responses and crashworthiness performances. Numerical results revealed evident influences of relative densities of T-TLS and foam filler on the deformation mode and energy absorption performance. The competition in stiffness between T-TLS and foam filler led to three distinct deformation modes. Finally, a multi-objective optimization was carried out to derive optimized configurations for foam-filled T-TLS subjected to lateral crushing. In comparison with the baseline designs, the optimal results demonstrated enhanced crashworthiness, with the SEA value increasing by 40.6 to 97.3%.

Analysis of Helmholtz resonator wall elasticity effects on the performance of periodic acoustic metamaterial

In this paper, a metamaterial made of a porous layer with embedded periodic Helmholtz resonators is studied and the effects of the resonator wall elasticity on the acoustic attenuation performance of the metamaterial are investigated numerically. The analytical transmission loss results using the parallel transfer matrix method show good agreement with finite element results for the rigid wall case. Elastic materials with different thicknesses are considered for the wall of the neck and the top, lateral and bottom walls of the resonator cavity. It is shown that the transmission loss of the metamaterial degrades when the bottom wall of the resonator cavity is elastic. The elasticity of the bottom wall has a significant impact on the performance of the metamaterial. This analysis will help for better design of acoustic metamaterials with periodic Helmholtz resonators.

Modal analysis of waveguide for the study of frequency bandgaps of a bounded periodic medium

A novel method based on waveguide modal analysis is presented to evaluate the effectiveness in terms of frequency bandgaps of bounded periodic metamaterials. The effect of the size of the bounded medium, i.e., the number of periodic unit cells, on the frequency bandgaps predicted by Floquet–Bloch theory in the infinite case is investigated and quantified. The waveguides considered in this work have a bounded cross-section and an infinite longitudinal axis simulated by Perfectly Matched Layers. Its useful area is made of a bounded 1D or 2D-periodic matrix-inclusion metamaterial. In the 2D-periodic case, an approach combining the waveguide modal analysis with the Floquet–Bloch transform is further proposed. Applying the proposed method, the SH-waves propagating in a waveguide are studied by using the finite element method. The discrete spectrum of the waveguide and the associated attenuated or trapped wave modes are calculated and analyzed, which provides, within a semi-analytic framework, an exact characterization regarding the attenuation coefficient and the frequency bandgaps of the studied bounded periodic medium. More particularly, effectiveness indicators are defined to compare the width and the position of frequency bandgaps between the bounded and infinite cases as a function of the cell number. Last but not least, the proposed method is also successfully applied to bounded periodic media with local resonators to characterize their filtering and attenuation effectiveness, which shows its interest in such a case of great practical interest.

Vibration mitigation using finite graded metamaterials: a rod with attached local resonators

The paper concerns the analysis of vibration transmission and mitigation in a finite rod performing axial vibrations with attached multiple damped resonators. The resonators are not assumed to be periodically spaced or to have similar dynamic properties. The behaviour is analysed in terms of waves travelling between the discontinuities. Reflection and transmission coefficients of the rod with one local resonator attached are utilised in the analysis. Values of these coefficients for each of the attached resonators, along with the boundary conditions and field transfer function, are used to derive analytical expressions for the displacement of the finite rod at any point. Once the displacement is determined, the transmission loss is calculated. Moreover, the eigenfrequencies of the graded metamaterial finite rod are identified using the phase closure principle. The influence of the mass, the damping and the location of the resonators on the vibration attenuation are investigated. Numerical examples are presented. Good agreement is noted between the results of the analytical studies and finite element simulations in COMSOL. It is shown that the graded metamaterial rod can provide better vibration attenuation as compared to the conventional periodic metamaterial.

Elastic architected mechanical metamaterials with negative stiffness effect for high energy dissipation and low frequency vibration suppression

In this research, mechanical metamaterials with negative stiffness (NS) effect were architected and fabricated for high energy dissipation and low frequency vibration suppression. Periodic cellular metamaterials formed by connecting multiple NS elements in series exhibited hysteresis and lengthy sawtooth loading and unloading plateaus, which made them desirable for use in energy dissipation applications. And the key point was that the deformation of these metamaterials was completely reversible. To determine the underlying cause of hysteresis, the mechanical behavior with phase-transition characteristics was analyzed. Then, a finite element model was built, and the numerical simulation results were compared to the experimental test findings of the metamaterials, and the two were in good agreement, verifying the validity of the model. Furthermore, the influences of structural parameters on mechanical characteristics were systematically investigated and discussed utilizing the numerical models that had undergone experimental validation. The energy dissipation effect resulting from the phase transformation mechanisms could also be applied to the field of vibration control. Corresponding hammer tests were performed to explore the dynamic behavior of the NS metamaterials. The results show that the proposed metamaterials exhibit excellent vibration suppression performance, especially for low frequency vibration mitigation.

Detecting bifurcations in 2D periodic metamaterials from images

Architectured materials are often used for their high strength-to-weight ratio. For this matter, they are designed with high porosity which makes them sensitive to buckling under compressive loading. This buckling is usually predicted by numerical computations but very few experiments are available to confront these numerical results. Experimentally, the onset of instabilities is usually determined by following the global force applied onto the sample. However, this detection might be hindered by the presence of various defects which may locally trigger the instabilities. A very simple technique is proposed herein to detect instabilities in periodic architectured materials using standard imaging techniques. It is shown to be applicable at a local scale, thereby allowing for a local instability detection.

Inverse design of mechanical springs with tailored nonlinear elastic response utilizing internal contact

This work employs a contact-aware topology optimization approach for the design of nonlinear springs with a broad range of prescribed load–displacement responses in both tension and compression. By leveraging the third medium contact approach to model internal contact, this method enables the utilization of collision between parts to achieve the desired load–displacement response while minimizing material consumption. The effectiveness of the proposed computational design approach is demonstrated using axially loaded springs as a benchmark, but the proposed method is also applicable to more general cases, including the design of periodic nonlinear material microstructures and metamaterials.

Bayesian optimisation of hexagonal honeycomb metamaterial

Periodic mechanical metamaterials, such as hexagonal honeycombs, have traditionally been designed with uniform cell walls to simplify manufacturing and modelling. However, recent research has suggested that varying strut thickness within the lattice could improve its mechanical properties. To fully explore this design space, we developed a computational framework that leverages Bayesian optimisation to identify configurations with increased uniaxial effective elastic stiffness and plastic or buckling strength. The best topologies found, representative of relative densities with distinct failure modes, were additively manufactured and tested, resulting in a 54% increase in stiffness without compromising the buckling strength for slender architectures, and a 63% increase in elastic modulus and a 88% increase in plastic strength for higher volume fractions. Our results demonstrate the potential of Bayesian optimisation and solid material redistribution to enhance the performance of mechanical metamaterials.

Electro-momentum coupling tailored in piezoelectric metamaterials with resonant shunts

Local microstructural heterogeneities of elastic metamaterials give rise to non-local macroscopic cross coupling between stress–strain and momentum–velocity, known as Willis coupling. Recent advances have revealed that symmetry breaking in piezoelectric metamaterials introduces an additional macroscopic cross coupling effect, termed electro-momentum coupling, linking electrical stimulus and momentum and enabling the emergence of exotic wave phenomena characteristic of Willis materials. The electro-momentum coupling provides an extra degree of freedom for controlling elastic wave propagation in piezoelectric composites through external electrical stimuli. In this study, we present how to tune the electro-momentum coupling arising in 1D periodic piezoelectric metamaterials with broken inversion symmetry through shunting the inherent capacitance of the individual piezoelectric layers with a resistor and an inductor in series forming a resistor–inductor–capacitor circuit. Guided by the effective elastodynamic theory and homogenization method for piezoelectric metamaterials, we derived a closed-form expression of the electro-momentum coupling in shunted piezoelectric metamaterials. Moreover, we demonstrate the ability to tailor the electro-momentum coupling coefficient and control the amplitudes and phases of the forward and backward propagating waves, yielding tunable asymmetric wave responses. The results of our study hold promising implications for applications involving asymmetric wave phenomena and programmable metamaterials.