Antonio Palermo

Composite 3D-printed metastructures for low-frequency and broadband vibration absorption

Significance Architected material used to control elastic wave propagation has thus far relied on two mechanisms for forming band gaps, or frequency ranges that cannot propagate: (i) Phononic crystals rely on their structural periodicity to form Bragg band gaps, but are limited in the low-frequency ranges because their unit cell size scales with wavelength; and (ii) Metamaterials overcome this size dependence because they rely on local resonances, but the resulting band gaps are very narrow. Here, we introduce a class of materials, elastic metastructures, that exploit resonating elements to broaden and lower Bragg gaps while reducing the mass of the system. This approach to band-gap engineering can be used for low-frequency vibration absorption and wave guiding across length scales. Architected materials that control elastic wave propagation are essential in vibration mitigation and sound attenuation. Phononic crystals and acoustic metamaterials use band-gap engineering to forbid certain frequencies from propagating through a material. However, existing solutions are limited in the low-frequency regimes and in their bandwidth of operation because they require impractical sizes and masses. Here, we present a class of materials (labeled elastic metastructures) that supports the formation of wide and low-frequency band gaps, while simultaneously reducing their global mass. To achieve these properties, the metastructures combine local resonances with structural modes of a periodic architected lattice. Whereas the band gaps in these metastructures are induced by Bragg scattering mechanisms, their key feature is that the band-gap size and frequency range can be controlled and broadened through local resonances, which are linked to changes in the lattice geometry. We demonstrate these principles experimentally, using advanced additive manufacturing methods, and inform our designs using finite-element simulations. This design strategy has a broad range of applications, including control of structural vibrations, noise, and shock mitigation.

Engineered metabarrier as shield from seismic surface waves

Resonant metamaterials have been proposed to reflect or redirect elastic waves at different length scales, ranging from thermal vibrations to seismic excitation. However, for seismic excitation, where energy is mostly carried by surface waves, energy reflection and redirection might lead to harming surrounding regions. Here, we propose a seismic metabarrier able to convert seismic Rayleigh waves into shear bulk waves that propagate away from the soil surface. The metabarrier is realized by burying sub-wavelength resonant structures under the soil surface. Each resonant structure consists of a cylindrical mass suspended by elastomeric springs within a concrete case and can be tuned to the resonance frequency of interest. The design allows controlling seismic waves with wavelengths from 10-to-100 m with meter-sized resonant structures. We develop an analytical model based on effective medium theory able to capture the mode conversion mechanism. The model is used to guide the design of metabarriers for varying soil conditions and validated using finite-element simulations. We investigate the shielding performance of a metabarrier in a scaled experimental model and demonstrate that surface ground motion can be reduced up to 50% in frequency regions below 10 Hz, relevant for the protection of buildings and civil infrastructures.

Designing perturbative metamaterials from discrete models

Identifying material geometries that lead to metamaterials with desired functionalities presents a challenge for the field. Discrete, or reduced-order, models provide a concise description of complex phenomena, such as negative refraction, or topological surface states; therefore, the combination of geometric building blocks to replicate discrete models presenting the desired features represents a promising approach. However, there is no reliable way to solve such an inverse problem. Here, we introduce ‘perturbative metamaterials’, a class of metamaterials consisting of weakly interacting unit cells. The weak interaction allows us to associate each element of the discrete model with individual geometric features of the metamaterial, thereby enabling a systematic design process. We demonstrate our approach by designing two-dimensional elastic metamaterials that realize Veselago lenses, zero-dispersion bands and topological surface phonons. While our selected examples are within the mechanical domain, the same design principle can be applied to acoustic, thermal and photonic metamaterials composed of weakly interacting unit cells.A perturbative method is proposed for the systematic design of mechanical metamaterials, where each element of the discrete model is associated with individual geometric features of the metamaterial, through the weak interaction between the unit cells.

Limits of the Kelvin Voigt Model for the Analysis of Wave Propagation in Monoatomic Mass-Spring Chains

In this study, the effect of energy dissipation on harmonic waves propagating in one-dimensional monoatomic linear viscoelastic mass-spring chains is investigated. In particular, first dispersion laws in terms of wavenumber, attenuation, and wave propagation velocities (phase, group, and energy) for a generic viscoelastic mass-spring chain are derived from the homologous linear elastic (LE) expressions in force of the correspondence principle. A new formula for the energy velocity is introduced to account for energy dissipation. Next, such relations are specified for the Kelvin Voigt (KV) and the standard linear solid (SLS) rheological models. The analysis of the KV mass-spring chain in the high-frequency regime proves that the so-called wavenumber-gap is not related to energy dissipation, as assumed in previous studies, but is due to the nonphysical rigid behavior of the model at high frequencies. The SLS mass-spring chain, in fact, does not show any wavenumber-gap and at high frequencies recovers the wavenumber dispersion curve of the LE system. The behavior of the energy velocity for the different mass-spring chains confirms this conclusion.

Acoustic properties of porous microlattices from effective medium to scattering dominated regimes

Microlattices are architected materials that allow for an unprecedented control of mechanical properties (e.g., stiffness, density, and Poissons coefficient). In contrast to their quasi-static mechanical properties, the acoustic properties of microlattices remain largely unexplored. This paper analyzes the acoustic response of periodic millimeter-sized microlattices immersed in water using experiments and numerical simulations. Microlattices are fabricated using high-precision stereolithographic three-dimensional printing in a large variety of porosities and lattice topologies. This paper shows that the acoustic propagation undergoes a frequency dependent transition from a classic poroelastic behaviour that can be described by Biots theory to a regime that is dominated by scattering effects. Biots acoustic parameters are derived from direct simulations of the microstructure using coupled fluid and solid finite elements. The wave speeds predicted with Biots theory agree well with the experimental measures. Within the scattering regime, the signals show a strong attenuation and dispersion, which is characterized by a cut-off frequency. The strong dispersion results in a frequency dependent group velocity. A simplified model of an elastic cylindrical scatterer allows predicting the signal attenuation and dispersion observed experimentally. The results in this paper pave the way for the creation of microlattice materials for the control of ultrasonic waves across a wide range of frequencies.

Large scale metasurfaces for seismic waves control

Elastic metamaterials are artificial composites with subwavelength resonant particles hosted in a medium able to manipulate the propagation of elastic waves. When the resonant particles are placed at the free surface of the medium to form a resonant “metasurface,” the localization mechanism and the direction of surface waves can be fully controlled. In this talk, we discuss the use of resonant metasurfaces to control the propagation of vertically and horizontally polarized surface waves and their possible application for seismic waves mitigation. By combining analytical, numerical, and experimental studies, we describe the interaction of Rayleigh waves with a metasurface of vertical resonators and design large-scale resonant barriers to deviate damaging seismic Rayleigh waves into the medium bulk. Additionally, we investigate the effect of material stratification on the metasurface dynamics by analyzing the propagation of surface waves in unconsolidated granular media with depth-dependent stiffness profile. Finally, we describe the interaction of Love waves guided by a stratified medium with a metasurface of horizontal resonators and design large-scale resonant metalenses to redirect their propagation.

A metamaterial design method applied to topologically protected mechanical metamaterials

Mass-spring models provide a straightforward way to describe complex dynamic behavior of mechanical systems, such as topologically protected and backscattering-free surface phonons. Such discrete models also provide a means to translate these properties, based on the unique class of electronic materials of topological insulators, to the mechanical domain. This talk will discuss a systematic design process to take such a mass-spring model and implement its functionality directly into a metamaterial. The design method uses combinatorial searches plus gradient-based optimizations to determine the configuration of the metamaterial’s building blocks that replicates the behavior of the target mass-spring model. A key aspect of the design method is the use of “perturbative metamaterials”—i.e., metamaterials with weakly interacting unit cells. The weak coupling enables the design space to be divided into smaller sub-spaces that can be independently tuned, which results in an exponential speed-up of the design pro...

A simple beam model to analyse the durability of adhesively bonded tile floorings in presence of shrinkage

A simple beam model for the evaluation of tile debonding due to substrate shrinkage is presented. The tile-adhesive-substrate package is modeled as an Euler-Bernoulli beam laying on a two-layer elastic foundation. An effective discrete model for inter-tile grouting is introduced with the aim of modelling workmanship defects due to partial filled groutings. The model is validated using the results of a 2D FE model. Different defect configurations and adhesive typologies are analysed, focusing the attention on the prediction of normal stresses in the adhesive layer under the assumption of Mode I failure of the adhesive.