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Drying of fine hair and fibers induces dramatic capillary-driven deformation, with important implications on natural phenomena and industrial processes. We recently observed peculiar self-assembly of hair bundles into various distinct patterns depending on the interplay between the bundle length and the liquid drain rate. Here, we propose a mechanism for this pattern selection, and derive and validate theoretical scaling laws for the polymorphic self-assembly of polygonal hair bundles. Experiments are performed by submerging the bundles into a liquid bath, then draining down the liquid. Depending on the interplay between the drain rates and the length of the fibers, we observe the bundles morphing into stars (having concave sides), polygons (having straight edges and rounded corners), or circles. The mechanism of self-assembly at the high drain regime is governed by two sequential stages. In the first stage of the high drain rate regime, the liquid covers the outside of the bundles, and drainage from inside the bundle does not play a role in the self-assembly due to the high viscous stress. The local pressure at the corners of the wet bundles compresses the fibers inward blunting the corners, and the internal lubrication facilitates fiber rearrangement. In the second stage, the liquid is slowly draining from within the fiber spacing, and the negative capillary pressure at the perimeter causes the fibers to tightly pack. In the slow drainage regime, the first stage is absent, and the fibers slowly aggregate without initial dynamic rearrangement. Understanding the mechanism of dynamic elastocapillarity offers insights for studying the complicated physics of wet granular drying.

Millions of years of evolution have allowed animals to develop unusual locomotion capabilities. A striking example is the legless-jumping of click beetles and trap-jaw ants, which jump more than 10 times their body length. Their delicate musculoskeletal system amplifies their muscles’ power. It is challenging to engineer insect-scale jumpers that use onboard actuators for both elastic energy storage and power amplification. Typical jumpers require a combination of at least two actuator mechanisms for elastic energy storage and jump triggering, leading to complex designs having many parts. Here, we report the new concept of dynamic buckling cascading, in which a single unidirectional actuation stroke drives an elastic beam through a sequence of energy-storing buckling modes automatically followed by spontaneous impulsive snapping at a critical triggering threshold. Integrating this cascade in a robot enables jumping with unidirectional muscles and power amplification (JUMPA). These JUMPA systems use a single lightweight mechanism for energy storage and release with a mass of 1.6 g and 2 cm length and jump up to 0.9 m, 40 times their body length. They jump repeatedly by reengaging the latch and using coiled artificial muscles to restore elastic energy. The robots reach their performance limits guided by theoretical analysis of snap-through and momentum exchange during ground collision. These jumpers reach the energy densities typical of the best macroscale jumping robots, while also matching the rapid escape times of jumping insects, thus demonstrating the path toward future applications including proximity sensing, inspection, and search and rescue.

Waveguides for mechanical signal transmission in the megahertz to gigahertz regimes enable on-chip phononic circuitry, which brings new capabilities complementing photonics and electronics. Lattices of coupled nano-electromechanical drumhead resonators are suitable for these waveguides due to their high Q-factor and precisely engineered band structure. Here, we show that thermally induced elastic buckling of such resonators causes a phase transition in the waveguide leading to reversible control of signal transmission. Specifically, when cooled, the lowest-frequency transmission band associated with the primary acoustic mode vanishes. Experiments show the merging of the lower and upper band gaps, such that signals remain localized at the excitation boundary. Numerical simulations show that the temperature-induced destruction of the pass band is a result of inhomogeneous elastic buckling, which disturbs the waveguide's periodicity and suppresses the wave propagation. Mechanical phase transitions in waveguides open opportunities for drastic phononic band reconfiguration in on-chip circuitry and computing.

Pump it up Carbon nanotube yarns can be used as electrochemical actuators because infiltration with ions causes a contraction in length and an expansion in diameter. Either positive or negative ions can cause this effect. Chu et al. constructed an all-solid-state muscle that eliminated the need for an electrolyte bath, which may expand the potential for its use in applications. By infiltrating the yarns with charged polymers, the fibers start partially swollen, so the length can increase through the loss of ions. It is thus possible to increase the overall stroke of the muscle. Further, these composite materials show a surprising increase in stroke with scan rate. Science , this issue p. 494

Industrial production of graphene by chemical vapor deposition (CVD) requires more than the ability to synthesize large domain, high quality graphene in a lab reactor. The integration of graphene i...

This talk presents the benefit of buckling in strongly tuning nonlinear MEMS resonators. In particular, the talk shows experimental buckling achieving more than 230% tuning in the natural frequency of drumhead MEMS resonators. Moreover, the experiments demonstrate that buckling switches the frequency response between purely stiffening, purely softening, and stiffening-to-softening nonlinearities. We tune the buckling state in these experiments by controlling the electric voltage and the temperature of the resonators. Therefore, these resonators undergo electrostatically-mediated thermoelastic buckling where specific combinations of temperature and voltage are required to access the distinct vibrational responses. We explain the observed linear and nonlinear responses by a reduced-order model (ROM) that lumps the resonator into a 1-degree-of-freedom mass connected to springs reflecting bending, stretching, electrostatic forces, thermal expansions, and residual stresses. The ROM mimics von Mises trusses to model the buckling in the membrane resonators without the need for exact geometry or structure to model the resonators. This developed ROM and the electro-thermoelastic buckling tunability present useful applications for on-chip acoustic devices in different fields such as signal manipulation, filtering, and MEMS waveguides.

Additive manufacturing (AM) enables the fabrication of complex lattice structures, for which a single part may have hundreds or thousands of individual geometric features. Conventional methods for measuring part geometry and performing quality control, which typically use a small number of low-dimensional measurements, are not well suited for lattice structures. This paper describes a method for scanning and automatically extracting individual features of the lattice and applies this method to characterize AM lattice structures in both two-dimensional and three-dimensional lattices. The research measured 94 lattice parts fabricated from 3 materials in 9 different designs using either a high-resolution document scanner or X-ray computed tomography (CT). A statistical analysis considered manufacturing variances as a function of material type and part design on a subset of the data, comprising the size and location of over 15,000 individual features. We studied the geometric variations of these struts in uniform, hierarchical and gradated parts. For a single design and material, the standard deviation of lattice feature size is quite small. For example, a lattice strut with thickness 0.5 mm has a standard deviation of 30 μm. However, when the same process is used to manufacture multiple parts having different designs and from different materials, the standard deviation of feature size can be larger by 2X or more. This type of automated measurement and analysis may allow for rigorous monitoring, qualification and control of AM lattice parts in production.

We use aligned carbon nanotube (CNT) forests as scaffolds to deposit hafnium diboride (HfB2) and fabricate millimeter-thick ultrahigh-temperature composite coating. HfB2 has a melting temperature of 3250 °C, which makes it an attractive candidate for applications requiring operation in extreme environments. Compared to typical refractory HfB2 processing, which requires temperatures exceeding 1500 °C, we use conformal HfB2 chemical vapor deposition (CVD) to coat CNT forests at a low temperature of 200 °C. During this process, nanometer-thin HfB2 films grow on the CNT surface and uniformly fill tall CNT forests, thus transforming nanometer film deposition to a scalable HfB2 coating technology. The conformal HfB2 coating process uses static (S-) CVD, where the precursor is fed into a closed system, enabling highly conformal coating and economically efficient utilization of the HfB2 precursor reaching 85%. The modulus and compressive strength of the composites are measured using flat-punch indentation of micropillars having various coating thickness. Filling the CNTs with HfB2 strengthens their node morphology and effectively enhances the mechanical properties. We study the nonlinear behavior of the material to extract a unique modulus value that describes the stress-strain response at any applied compression. At the highest HfB2 coating thickness of 45 nm, the solid fraction is increased from 2% for the bare CNTs to 36% for the composite; the modulus and strength reach 107 and 1.5 GPa, respectively. An analytical model is used to explain the mechanism of the measured structure-mechanical property scaling. Finally, the process is used to fabricate CNT-HfB2 films having 1.7 mm height, a centimeter square area, and only 5.8 × 10-6 nm/nm thickness gradient to demonstrate the potential for scalability.

The diverse chemical and physical reactions encountered during cooking connect us to science every day. Here, we theoretically and experimentally investigate the swelling and softening of pasta due to liquid imbibition as well as the elastic deformation and adhesion of pasta due to capillary force. As water diffuses into the pasta during cooking, it softens gradually from the outside inward as starch swells and relaxes. The softening follows three sequential regimes: regime I, the hard-glassy region, shows a slow decrease in modulus with cooking time; regime II, the glassy to rubbery transition region, or leathery region, is characterized by a very fast, several orders of magnitude drop in elastic modulus and regime III, the rubbery region, has an asymptotic modulus about four orders of magnitude lower than the raw pasta. We present experiments and theory to capture these regimes and relate them to the heterogeneous microstructure changes associated with swelling. Interestingly, we observe a modulus drop of two orders of magnitude within the range of “al dente” cooking duration, and we find the modulus to be extremely sensitive to the amount of salt added to the boiling water. While most chefs can gauge the pasta by tasting its texture, our proposed experiment, which only requires a measurement with a ruler, can precisely provide an optimal cooking time finely tuned for various kinds of pasta shapes.

In this work, we propose a new, simple, and highly effective passive phononic waveguide with controllable global non-reciprocity by means of local nonlinear and asymmetric elements. The nonlinearity and asymmetry in the waveguide are realized by means of a local nonlinear gate with a cubic stiffness nonlinearity that couples two detuned, dissipative gate oscillators. A wave transmits across the nonlinear gate by applying a harmonic excitation. The transmitted wave is either monochromatic or strongly modulated (SMR) and triggers the global non-reciprocity. The objectives of this work are to study the effect of local nonlinearity and asymmetry on the global non-reciprocal acoustics and to optimize the non-reciprocal performance of the waveguide. We employ the complexification averaging method (CX-A) in the acoustics to predict the bifurcations that govern the non-reciprocal acoustics. However, a limitation of the single-frequency CX-A method is its failure to predict the SMRs. Alternatively, we train machine learning simulators in order to optimize the two performance measures, i.e., energy transmissibility and non-reciprocity. The trained machine learning model drastically saves the simulation time and allows the optimization of performances. Our results show how powerful machine learning approaches can be employed for designing and optimizing practical waveguides with tailored non-reciprocity features.

We report polymorphic self-assembly of hair arranged in hollow bundles driven by capillarity, hydrodynamics, and elasticity. Bundles emerging from a liquid bath shrink but remain hollow at slow drainage due to the negative pressure of the menisci trapped between the hairs. The timescale allows the collective stiffening of the fibers to resist closure. At fast drainage, the bundles fully close before the liquid can drain through the hair. A liquid column trapped in the hole closes the bundle while the lubricated hairs still behave softly. Scaling laws predict this reversible hair polymorphism.

The COVID-19 pandemic disrupted the world in 2020 by spreading at unprecedented rates and causing tens of thousands of fatalities within a few months. The number of deaths dramatically increased in regions where the number of patients in need of hospital care exceeded the availability of care. Many COVID-19 patients experience Acute Respiratory Distress Syndrome (ARDS), a condition that can be treated with mechanical ventilation. In response to the need for mechanical ventilators, designed and tested an emergency ventilator (EV) that can control a patient’s peak inspiratory pressure (PIP) and breathing rate, while keeping a positive end expiratory pressure (PEEP). This article describes the rapid design, prototyping, and testing of the EV. The development process was enabled by rapid design iterations using additive manufacturing (AM). In the initial design phase, iterations between design, AM, and testing enabled a working prototype within one week. The designs of the 16 different components of the ventilator were locked by additively manufacturing and testing a total of 283 parts having parametrically varied dimensions. In the second stage, AM was used to produce 75 functional prototypes to support engineering evaluation and animal testing. The devices were tested over more than two million cycles. We also developed an electronic monitoring system and with automatic alarm to provide for safe operation, along with training materials and user guides. The final designs are available online under a free license. The designs have been transferred to more than 70 organizations in 15 countries. This project demonstrates the potential for ultra-fast product design, engineering, and testing of medical devices needed for COVID-19 emergency response.

After Chemical Vapor Deposition (CVD), faceted structures are routinely observed on a variety of metal catalyst surfaces in the graphene-covered regions. In spite of having its bare surface flattened through high diffusivity and surface pre-melting at high temperatures, the graphene-covered copper surface still presents faceted structures. Using atomistic simulations, we show the role of graphene in the preservation of the faceted surface morphology at the graphene–copper interface, manifesting as a suppressant against surface melting and surface-specific diffusion. The results of our molecular dynamics simulations are consistent with our experimental observations and demonstrate the thermo-mechanical interfacial surface stabilization role of graphene. Our study provides an understanding applicable to most metal–graphene interfaces and is especially relevant to most metallic catalysts for graphene growth by CVD. Understanding the interaction between graphene and the catalyst surface structure is critical for producing ultra-flat and defect-free graphene.

Nonlinear lattices and the nonlinear acoustics they support have a broad impact on shock and vibration mitigation, sound isolation, and acoustic logic devices. In this work, we experimentally study wave redirection, localization, and non-reciprocity in an asymmetric network of two nonlinear lattices with weak linear inter-lattice coupling. We report on the design, fabrication, and system identification of coupled lattices with essentially nonlinear next-neighbor intra-lattice coupling and on their unusual nonlinear acoustics. By weakly coupling the lattices and introducing structural disorder in one of them, we experimentally prove the realization of irreversible breather redirection between lattices governed by a macroscopic analog of the quantum Landau–Zener tunneling effect. In the experiments performed, the input energy is applied by impulse (broadband) excitation, and the resulting acoustical mechanism for wave redirection is in the form of propagating breathers, that is, localized oscillating wave packets formed by the synergy of nonlinearity and dispersion. Moreover, we study the non-reciprocal acoustics of the experimental lattice system by applying separate impulses at each of its four terminals and investigate the tunability with the energy of the resulting acoustic non-reciprocity by systematically varying the impulse intensity. The reported experimental results show that the weakly coupled, disordered, and nonlinear lattice system has wave tailoring properties that are tunable with energy. Altogether, the experimental results agree well with theoretical predictions reported in a companion work based on reduced-order numerical models and prove the efficacy of the system for applications, providing a path for applying these advanced concepts in future structures and devices.

The outstanding properties of individual carbon nanotubes (CNTs) have motivated interest in CNT fibers and yarns for composite materials, high-strength conductors and multifunctional textiles. However, despite advances in manufacturing, the strength of CNT yarns remains 10–100 fold less than individual CNTs. In light of the complex, multi-scale load transfer in CNT yarns, a hierarchical model taking into consideration the morphology-dependent mechanics is necessary to understand this limitation. We present a coupled analytical and finite element model of three-dimensional morphology and the full tensile behavior of CNT yarns. By incorporating load-induced changes in morphology, simulations of yarns in tension show different load paths such as fracture-type or stick–slip failure depending on the waviness and number density of CNTs. The strength of untwisted pristine CNT yarns is shown to be limited to

While there has been exciting progress in the emerging area of nonlinear acoustic nonreciprocity, one of the main challenges is to realize $p\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}e$ nonreciprocal acoustic waveguides with predictable, reliable broadband operation. Here the authors demonstrate an entirely passive nonreciprocal acoustic waveguide that enables transmission of acoustic waves in a preferred direction. Moreover, due to its strong nonlinearity, this nonreciprocity is passively adaptive to energy and can be predictively tuned by the intensity of the applied broadband excitation. Related applications span telecommunication, optics, and biomedical imaging.

Reciprocity is a property of linear, time-invariant systems whereby the energy transmission from a source to a receiver is unchanged after exchanging the source and receiver. Nonreciprocity violates this property and can be introduced to systems if time-reversal symmetry and/or parity symmetry is lost. While many studies have induced nonreciprocity by active means, i.e., odd-symmetric external biases or time variation of system properties, considerably less attention has been given to acoustical structures that passively break reciprocity. This study presents a lattice structure with strong stiffness nonlinearities, internal scale hierarchy, and asymmetry that breaks acoustic reciprocity. Macroscopically, the structure exhibits periodicity yet asymmetry exists in its unit cell design. A theoretical study, supported by experimental validation, of a two-scale unit cell has revealed that reciprocity is broken locally, i.e., within a single unit cell of the lattice. In this work, global breaking of reciprocity in the entire lattice structure is theoretically analyzed by studying wave propagation in the periodic arrangement of unit cells. Under both narrowband and broadband excitation, the structure exhibits highly asymmetrical wave propagation, and hence a global breaking of acoustic reciprocity. Interpreting the numerical results for varying impulse amplitude, as well as varying harmonic forcing amplitude and frequency/wavenumber, provides strong evidence that transient resonant capture is the driving force behind the global breaking of reciprocity in the periodic structure. In a companion work, some of the theoretical results presented herein are experimentally validated with a lattice composed of two-scale unit cells under impulsive excitation.

Graphene synthesis on ultra-thin catalysts can allow the use of graphene-coated metal films in electronic applications. Graphene coated thin films are expected to offer superior mechanical performance owing to the strength of graphene. However, several factors need to be considered to assure the stability of thin films at the high temperatures required for graphene synthesis. In this work, we present a systematic framework for the selection of thin films (< 1 micron thickness) to be used as catalyst for graphene synthesis. We present our progress towards the rapid synthesis of graphene at 1100°C in less than two minutes, thus avoiding solid state dewetting. The quality of the graphene is assessed by Scanning Electron Microscopy, Raman spectroscopy and indentation. It is shown that these films exhibit higher stiffness and resistance to crack propagation.

Scalable production using additive manufacturing (AM) requires quality systems that monitor and control manufacturing variability across many machines in a factory environment. AM process variability can result in geometric inaccuracies in parts that can affect their mechanical behavior; however, most research focuses on a single machine and hardware set, while part inaccuracy and AM variability across multiple printers remains poorly understood. This study establishes a framework to study the accuracy of polymer parts made on three identical printers and evaluates the role of manufacturing process parameters and their impact on part variability. We fabricate 90 polymer hexagonal lattice parts over nine builds on three identical Carbon M2 machines with interchangeable hardware tools. Each part is measured using automated metrology that extracts the size and shape of the part features and automatically measures defects. Each hexagonal part consists of 237 individual walls that were measured for 90 parts, resulting in 21,330 individual geometric measurements. Using statistical methods to analyze geometric defects as a function of machine, hardware set, and location in the build, we find that the observed variability can be correlated with process parameters. Geometric defects in the wall thickness depend upon machine and location within the build but do not depend on the hardware tool, while geometric defects in the wall length and height of the part depend upon machine and tool but not location. The uniformity within the parts, measured by standard deviations of the individual features within a part, mostly depends upon unmeasured parameters. We use a generalized linear model (GLM) to model the variability and to predict defects. The framework introduced here can be extended to analyze additional machines and process parameters and provides a practical tool to account for manufacturing variability in an AM production environment.

We consider an asymmetric dissipative network of two semi-infinite nonlinear lattices with weak linear inter-lattice coupling and study its capacity for passive wave redirection and non-reciprocity. Each lattice is composed of linearly grounded oscillators with essentially nonlinear (i.e., non-linearizable) next-neighbor intra-lattice coupling, and it supports breather propagation. Irreversible breather redirection between lattices is governed by a macroscopic analog of the quantum Landau–Zener tunneling (LZT) effect, whereby impulsive energy initially induced to the “excited lattice” is passively and irreversibly redirected to the “absorbing lattice.” Moreover, this wave redirection is realized only in a specific range of impulse intensity (energy), otherwise motion localization occurs. In this work, we show that LZT breather redirection in the dissipative network occurs only when the normalized linear inter-coupling stiffness is larger than the viscous damping ratio of the individual lattice oscillators, with breather arrest and localization occurring otherwise. Then, through a reduced-order model, we provide guidance for selecting the system parameters of the lattice network for robust breather redirection despite the presence of dissipation. To this end, we study the acoustic non-reciprocity and formulate a quantitative measure for studying it based on measured time-series responses at the four free boundaries of the finite network. Then, we show the dependence of non-reciprocity in this system on the intensity (energy) of the applied impulse. These results pave the way for conceiving practical nonlinear lattice networks with inherent capacities for passive wave redirection and acoustic non-reciprocity that are tunable (self-adaptive) to the applied impulsive excitations.

Electro-active polymers (EAP) such as dielectric elastomers can reproduce biomimetic functions requiring micro-scale actuation such as color and texture change, or tunable wetting and adhesion. For these applications, large actuation strains and energy density are required. Recent studies with fiber reinforced elastomers demonstrated the ability to obtain anisotropic in- and out-of-plane actuation in macro-scale elastomer membranes. We design a new class of fiber micro-architected elastomers capable of anisotropic actuation in the two orthogonal in-plane directions under uniform electrostatic field. We reinforce the two sides of a pre-stretched VHB film with parallel arrays of stiff ultra-high molecular weight polyethylene fibers. By controlling the spacing and bias angle between the fibers, we create diamond shaped unit cells of 100–300 um size, and demonstrate a wide range of kinematics showing maximum extension of 26% at 45 ° and maximum contraction of − 6.3 % at 65 ° at maximum efficiency of 15%. We call these devices Micro-architected Electro–Elasto-Kinematic muscles (MEEKs). We use analytical modeling and finite element analysis to explain the observed actuation kinematics and the associated non-homogeneous strain distribution. We expect this principle to be suitable for micro-actuation and smart skins where anisotropy can be advantageous.

Surface textures with three-dimensional (3D) architectures demonstrate the ability to control interfacial, optical, chemical, and mechanical properties. Potential applications range from device-scale biomolecule sensing to meter-scale optical or nonwetting coatings. In recent years, capillary forming has become a versatile and scalable approach to creating complex geometries at the nano- and micron scales. Surface tension of a liquid can deform straight pillars and assemble them into 3D architectures with predetermined orientation, where short-range adhesion forces stabilize the final forms. A variety of techniques have been demonstrated for carbon nanotubes and polymer filamentary materials to fabricate useful devices and textures. We discuss these materials and processes as well as the underlying elasto-capillary physics. We indicate the need for new simulation tools to design and engineer elasto-capillary transformations and methods to increase their throughput toward scalable manufacturing.

In this paper, the anisotropic conductivity dispersion of horizontally aligned multi-walled carbon-nanotube (HA-MWCNT) thin films on a kapton substrate are characterized at microwave range. It is well known that a single carbon nanotube (CNT) presents highly 1-D conduction. For a thin film composed of numerous aligned CNTs, the anisotropic conduction may be preserved to some extent, as this is useful for various applications. In this paper, the anisotropic conduction of HA-MWCNT thin films is investigated in a rectangular waveguide measurement setup. The anisotropic surface conductivities of the films along the nanotube axial and radial directions are extracted from the measured S-parameters. The results reveal an anisotropic conductivity ratio of about 2 for the HA-MWCNTs thin film. Furthermore, it is observed that the real part of the extracted conductivity remains constant over the frequency band while the imaginary part increases almost linearly with frequency.

This study addresses the synthesis and mechanical behavior of graphene-metal composites comprising palladium (Pd) nanoribbons wrapped with graphene. Coating Pd nanoribbons with graphene by chemical vapor deposition (CVD) considerably increases their elastic modulus. These measurements are made by suspended microbridge indentation. A refined indentation measurement approach carefully takes into consideration the uncertainty resulting from the non-ideal bridge geometry. The measured composite moduli depend on the ribbon thickness in the range of 36 - 250 nm, with the maximum modulus of 147 GPa measured for 36 nm thick nanoribbons, representing an increase of 41.6 % over uncoated Pd nanoribbons. The results clearly demonstrate that graphene, owing to its high modulus and strong interaction with Pd, can effectively reinforce Pd nanoribbons up to thickness of 250 nm, which corresponds to a volume fraction of 0.54 %. We study the modulus scaling by deriving a mathematical rule of mixture model considering 3D "bulk" metal nanoribbons reinforced by the 2D graphene "surface". This modeling approach is inspired by the framework of surface modulus, which is typically employed to explain the deviations in the moduli of nanowires and nanoribbons observed in the sub-10 nm regime. Here, the nanoribbons are much thicker, yet graphene's extremely high modulus leads to the observed increase in the measured composite moduli. Further, in these calculations, we consider the critical role of the nonlinear modulus component of graphene -its quadratic dependence on strain- which results from the lattice mismatch-induced interfacial strains between graphene and Pd. Graphene-Pd composite nanoribbons and thin films can be very useful for a wide range of application ranging from strain-engineered catalysis to damage tolerant flexible electronic devices. Beyond nanoribbons, the proposed 3D/2D rule of mixture model may be used to explain the modulus scaling in 3D/2D heterostructures and in bulk graphene-metal nanocomposites made by powder mixing routes.

A semi-infinite network of two coupled semi-infinite nonlinear lattices is studied, having the capacity for passive irreversible energy transfer (redirection) from an “excited lattice” (forced by an impulse) to an “absorbing lattice” (that is not directly forced). This is achieved by breaking the symmetry through a spatial variation of the grounding stiffnesses of the excited lattice from the second unit cell onwards, and assuming weak coupling. We show analytically that irreversible energy transfer is caused by the macroscopic analogue (in space) of the Landau–Zener tunneling (LZT) effect, which originated in quantum mechanics in the context of linear parametric oscillators (in time). By constructing a reduced-order model (ROM) of two coupled oscillators it is possible to theoretically model the LZT-induced irreversible energy redirection from the excited to the absorbing lattice. A computational study reveals that the LZT effect is realized only in a critical band of energy, while outside this band there occurs energy localization. The lower and upper energy bounds of this critical band are theoretically approximated by constructing appropriate ROMs of the coupled lattices and studying the bifurcations in their dynamics with energy. This analysis sheds physical insight on the different regimes of the acoustics, and theoretical predictions agree well with direct numerical simulations of the full lattice network. Finally, we show that the LZT effect induces strong non-reciprocity in the dynamics of the finite asymmetric lattice network, in the sense that the impulsive response of this network depends crucially on the forcing-measurement locations and energy. The implications and the possible applications of these results are discussed.

Additive manufacturing (AM) is a key enabler for architectured lattice materials, because of the geometric complexity of parts that can be produced. Recent advancements in AM have enabled rapid production speeds, high spatial resolution, and a variety of engineering polymers. An open question remains whether production grade AM can accurately and repeatably produce lattice parts. This study presents design, production, and mechanical property testing of hexagonal lattice parts manufactured using continuous liquid interface production (CLIP) based AM. We printed and tested 84 parts, in three polymer materials having relative density ranging from 0.06 to 0.23. Lattice wall structures were reliably printed when truss aspect ratio was in the range 5 to 20 and wall thicknesses were 0.35 or 0.5 mm. The printed lattice parts, each comprising hundreds of slender walls, were measured using high resolution optical scanning. The images were analyzed to evaluate the difference between the printed parts and their designs, and the effect of geometric deviations on the mechanical behavior. The measured elastic moduli of the printed parts are close to the values expected from the materials specifications. The measured strength of the printed parts deviates by 7% from the behavior predicted from the scanned geometry. The failure mode of the printed structures depends upon the material and part geometry. To our knowledge, this is the largest study on the accuracy and performance of AM lattice parts, and the first study of its type for lattice parts made using CLIP.

Owing to its large electric band gap, two-dimensional (2D) hexagonal boron nitride (hBN) is a very promising candidate for making atomically thin flexible devices. Further, its high mechanical strength makes it suitable as a reinforcing material in composites. It is thus of great interest to study the strain-induced phonon shift of mechanically exfoliated hBN of various thicknesses under tension. It is found that splitting of the ${E}_{2g}$ phonon to two subpeaks due to the lifting of degeneracy under uniaxial loading occurs at low strain level with average shift rates of $\ensuremath{-}8.4\phantom{\rule{0.28em}{0ex}}(1.0)\phantom{\rule{0.28em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}/%$ and $\ensuremath{-}25.2\phantom{\rule{0.28em}{0ex}}(1.5)\phantom{\rule{0.28em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}/%$ for the ${E}_{2g}^{+}$ and ${E}_{2g}^{\ensuremath{-}}$, respectively. These large redshifts of the ${E}_{2g}$ modes with strain are close to the values obtained from graphene and confirm the high stiffness of 2D hBN. Furthermore, the measured ${E}_{2g}$ mode Gr\"uneisen parameter is about 1.88 (2), in agreement with the values obtained by classical molecular dynamics (MD) and ab initio MD simulations. The shift rates are similar for hBN with thickness of two to four layers, which is in contrast with graphene, indicating the effective load transfer between the hBN layers. The present results provide useful insights for the use of hBN in electronic devices, 2D heterostructures, and also as a reinforcing agent in composite materials.

In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales-a linear large-scale oscillator coupled to a small scale by a nonlinear spring-and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.

In linear time-invariant systems acoustic reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and it can be broken only by odd external biases, nonlinearities, or time-dependent properties. Recently it was shown that one-dimensional lattices composed of a finite number of identical nonlinear cells with internal scale hierarchy and asymmetry exhibit nonreciprocity both locally and globally. Considering a single cell composed of a large scale nonlinearly coupled to a small scale, local dynamic nonreciprocity corresponds to vibration energy transfer from the large to the small scale, but absence of energy transfer (and localization) from the small to the large scale. This has been recently proven both theoretically and experimentally. Then, considering the entire lattice, global acoustic nonreciprocity has been recently proven theoretically, corresponding to preferential energy transfer within the lattice under transient excitation applied at one of its boundaries, and absence of similar energy transfer (and localization) when the excitation is applied at its other boundary. This work provides experimental validation of the global acoustic nonreciprocity with a one-dimensional asymmetric lattice composed of three cells, with each cell incorporating nonlinearly coupled large and small scales. Due to the intentional asymmetry of the lattice, low impulsive excitations applied to one of its boundaries result in wave transmission through the lattice, whereas when the same excitations are applied to the other end, they lead in energy localization at the boundary and absence of wave transmission. This global nonreciprocity depends critically on energy (i.e., the intensity of the applied impulses), and reduced-order models recover the nonreciprocal acoustics and clarify the nonlinear mechanism generating nonreciprocity in this system.