Extreme damping in composite materials with negative-stiffness inclusions

Hyperbranched Vitrimer for Ultrahigh Energy Dissipation

Polymers are ideally utilized as damping materials due to the high internal friction of molecular chains, enabling effective suppression of vibrations and noises in various fields. Current strategies rely on broadening the glass transition region or introducing additional relaxation components to enhance the energy dissipation capacity of polymeric damping materials. However, it remains a significant challenge to achieve high damping efficiency through structural control while maintaining dynamic characteristics. In this work, we propose a new strategy to develop hyperbranched vitrimers (HBVs) containing dense pendant chains and loose dynamic crosslinked networks. A novel yet weak dynamic transesterification between the carboxyl and boronic acid ester was confirmed and used to prepare HBVs based on poly (hexyl methacrylate-2-(4-ethenylphenyl)-5,5-dimethyl-1,3,2-dioxaborinane) P(HMA-co-ViCL) copolymers. TheA B n ${{AB}_{n}}$ -type of macromonomers, the crosslinking points formed by the dynamic covalent connection via the associative exchange, and the weak yet dynamic exchange reaction are the three keys to developing high-performance HBV damping materials. We found that P(HMA-co-ViCL) 20k-40-60 HBV exhibited ultrahigh energy-dissipation performance over a broad frequency and temperature range, attributed to the synergistic effect of dense pendant chains and weak dynamic covalent crosslinks. This unique design concept will provide a general approach to developing advanced damping materials.

Buckling Metamaterials for Extreme Vibration Damping

Damping mechanical resonances is a formidable challenge in an increasing number of applications. Many passive damping methods rely on using low stiffness, complex mechanical structures or electrical systems, which render them unfeasible in many of these applications. Herein, a new method for passive vibration damping, by allowing buckling of the primary load path in mechanical metamaterials and lattice structures, is introduced, which sets an upper limit for vibration transmission: the transmitted acceleration saturates at a maximum value in both tension and compression, no matter what the input acceleration is. This nonlinear mechanism leads to an extreme damping coefficient tanδ ≈ 0.23 in a metal metamaterial-orders of magnitude larger than the linear damping coefficient of traditional lightweight structural materials. This principle is demonstrated experimentally and numerically in free-standing rubber and metal mechanical metamaterials over a range of accelerations. It is also shown that damping nonlinearities even allow buckling-based vibration damping to work in tension, and that bidirectional buckling can further improve its performance. Buckling metamaterials pave the way toward extreme vibration damping without mass or stiffness penalty, and, as such, could be applicable in a multitude of high-tech applications, including aerospace, vehicles, and sensitive instruments.

Self-bridging metamaterials surpassing the theoretical limit of Poisson's ratios

A hallmark of mechanical metamaterials has been the realization of negative Poisson's ratios, associated with auxeticity. However, natural and engineered Poisson's ratios obey fundamental bounds determined by stability, linearity and thermodynamics. Overcoming these limits may substantially extend the range of Poisson's ratios realizable in mechanical systems, of great interest for medical stents and soft robots. Here, we demonstrate freeform self-bridging metamaterials that synthesize multi-mode microscale levers, realizing Poisson's ratios surpassing the values allowed by thermodynamics in linear materials. Bridging slits between microstructures via self-contacts yields multiple rotation behaviors of microscale levers, which break the symmetry and invariance of the constitutive tensors under different load scenarios, enabling inaccessible deformation patterns. Based on these features, we unveil a bulk mode that breaks static reciprocity, providing an explicit and programmable way to manipulate the non-reciprocal transmission of displacement fields in static mechanics. Besides non-reciprocal Poisson's ratios, we also realize ultra-large and step-like values, which make metamaterials exhibit orthogonally bidirectional displacement amplification, and expansion under both tension and compression, respectively.

Ultrathin ferroic HfO2-ZrO2 superlattice gate stack for advanced transistors

With the scaling of lateral dimensions in advanced transistors, an increased gate capacitance is desirable both to retain the control of the gate electrode over the channel and to reduce the operating voltage¹. This led to a fundamental change in the gate stack in 2008, the incorporation of high-dielectric-constant HfO₂ (ref. ²), which remains the material of choice to date. Here we report HfO₂-ZrO₂ superlattice heterostructures as a gate stack, stabilized with mixed ferroelectric-antiferroelectric order, directly integrated onto Si transistors, and scaled down to approximately 20 ångströms, the same gate oxide thickness required for high-performance transistors. The overall equivalent oxide thickness in metal-oxide-semiconductor capacitors is equivalent to an effective SiO₂ thickness of approximately 6.5 ångströms. Such a low effective oxide thickness and the resulting large capacitance cannot be achieved in conventional HfO₂-based high-dielectric-constant gate stacks without scavenging the interfacial SiO₂, which has adverse effects on the electron transport and gate leakage current³. Accordingly, our gate stacks, which do not require such scavenging, provide substantially lower leakage current and no mobility degradation. This work demonstrates that ultrathin ferroic HfO₂-ZrO₂ multilayers, stabilized with competing ferroelectric-antiferroelectric order in the two-nanometre-thickness regime, provide a path towards advanced gate oxide stacks in electronic devices beyond conventional HfO₂-based high-dielectric-constant materials.

Giant Viscoelasticity near Mott Criticality in PbCrO_{3} with Large Lattice Anomalies

Coupling of charge and lattice degrees of freedom in materials can produce intriguing electronic phenomena, such as conventional superconductivity where the electrons are mediated by lattice for creating supercurrent. The Mott transition, which is a source for many fascinating emergent behaviors, is originally thought to be driven solely by correlated electrons with an Ising criticality. Recent studies on the known Mott systems have shown that the lattice degree of freedom is also at play, giving rise to either Landau or unconventional criticality. However, the underlying coupling mechanism of charge and lattice degrees of freedom around the Mott critical end point remains elusive, leading to difficulties in understanding the associated Mott physics. Here, we report a study of Mott transition in cubic PbCrO_{3} by measuring the lattice parameter, using high-pressure x-ray diffraction techniques. The Mott criticality in this material is revealed with large lattice anomalies, which is governed by giant viscoelasticity that presumably results from a combination of lattice elasticity and electron viscosity. Because of the viscoelastic effect, the lattice of this material behaves peculiarly near the critical end point, inconsistent with any existing university classes. We argue that the viscoelasticity may play as a hidden degree of freedom behind the Mott criticality.

An Amorphous Peri-Implant Ligament with Combined Osteointegration and Energy-Dissipation

Progress toward developing metal implants as permanent hard-tissue substitutes requires both osteointegration to achieve load-bearing support, and energy-dissipation to prevent overload-induced bone resorption. However, in existing implants these two properties can only be achieved separately. Optimized by natural evolution, tooth-periodontal-ligaments with fiber-bundle structures can efficiently orchestrate load-bearing and energy dissipation, which make tooth-bone complexes survive extremely high occlusion loads (>300 N) for prolonged lifetimes. Here, a bioinspired peri-implant ligament with simultaneously enhanced osteointegration and energy-dissipation is presented, which is based on the periodontium-mimetic architecture of a polymer-infiltrated, amorphous, titania nanotube array. The artificial ligament not only provides exceptional osteoinductivity owing to its nanotopography and beneficial ingredients, but also produces periodontium-similar energy dissipation due to the complexity of the force transmission modes and interface sliding. The ligament increases bone-implant contact by more than 18% and simultaneously reduces the effective stress transfer from implant to peri-implant bone by ≈30% as compared to titanium implants, which as far as is known has not previously been achieved. It is anticipated that the concept of an artificial ligament will open new possibilities for developing high-performance implanted materials with increased lifespans.

Curvature Induced by Deflection in Thick Meta-Plates

The design of advanced functional devices often requires the use of intrinsically curved geometries that belong to the realm of non-Euclidean geometry and remain a challenge for traditional engineering approaches. Here, it is shown how the simple deflection of thick meta-plates based on hexagonal cellular mesostructures can be used to achieve a wide range of intrinsic (i.e., Gaussian) curvatures, including dome-like and saddle-like shapes. Depending on the unit cell structure, non-auxetic (i.e., positive Poisson ratio) or auxetic (i.e., negative Poisson ratio) plates can be obtained, leading to a negative or positive value of the Gaussian curvature upon bending, respectively. It is found that bending such meta-plates along their longitudinal direction induces a curvature along their transverse direction. Experimentally and numerically, it is shown how the amplitude of this induced curvature is related to the longitudinal bending and the geometry of the meta-plate. The approach proposed here constitutes a general route for the rational design of advanced functional devices with intrinsically curved geometries. To demonstrate the merits of this approach, a scaling relationship is presented, and its validity is demonstrated by applying it to 3D-printed microscale meta-plates. Several applications for adaptive optical devices with adjustable focal length and soft wearable robotics are presented.

Asymptotic freedom and noninteger dimensionality

This paper shows that below a critical value of dimensionality that lies between two and three, the potential between objects begins to fall as the energy levels increase. For dimensionality below two, the potential becomes constant irrespective of separation and the force between them disappears, which represents a new paradigm of asymptotic freedom. Since asymptotic freedom is at the basis of many applications such as those associated with strange metals, unconventional superconductors, and fractional quantum Hall states, the new paradigm can have novel applications. It also is of relevance to the study of anomalous mechanical effects that are important in metamaterials.

Periodic training of creeping solids

We consider disordered solids in which the microscopic elements can deform plastically in response to stresses on them. We show that by driving the system periodically, this plasticity can be exploited to train in desired elastic properties, both in the global moduli and in local "allosteric" interactions. Periodic driving can couple an applied "source" strain to a "target" strain over a path in the energy landscape. This coupling allows control of the system's response, even at large strains well into the nonlinear regime, where it can be difficult to achieve control simply by design.

Anomalous mechanical materials squeezing three-dimensional volume compressibility into one dimension

Anomalous mechanical materials, with counterintuitive stress-strain responding behaviors, have emerged as novel type of functional materials with highly enhanced performances. Here we demonstrate that the materials with coexisting negative, zero and positive linear compressibilities can squeeze three-dimensional volume compressibility into one dimension, and provide a general and effective way to precisely stabilize the transmission processes under high pressure. We propose a "corrugated-graphite-like" structural model and discover lithium metaborate (LiBO2) to be the first material with such a mechanical behavior. The capability to keep the flux density stability under pressure in LiBO2 is at least two orders higher than that in conventional materials. Our study opens a way to the design and search of ultrastable transmission materials under extreme conditions.

Foundations for Soft, Smart Matter by Active Mechanical Metamaterials

Emerging interest to synthesize active, engineered matter suggests a future where smart material systems and structures operate autonomously around people, serving diverse roles in engineering, medical, and scientific applications. Similar to biological organisms, a realization of active, engineered matter necessitates functionality culminating from a combination of sensory and control mechanisms in a versatile material frame. Recently, metamaterial platforms with integrated sensing and control have been exploited, so that outstanding non-natural material behaviors are empowered by synergistic microstructures and controlled by smart materials and systems. This emerging body of science around active mechanical metamaterials offers a first glimpse at future foundations for autonomous engineered systems referred to here as soft, smart matter. Using natural inspirations, synergy across disciplines, and exploiting multiple length scales as well as multiple physics, researchers are devising compelling exemplars of actively controlled metamaterials, inspiring concepts for autonomous engineered matter. While scientific breakthroughs multiply in these fields, future technical challenges remain to be overcome to fulfill the vision of soft, smart matter. This Review surveys the intrinsically multidisciplinary body of science targeted to realize soft, smart matter via innovations in active mechanical metamaterials and proposes ongoing research targets that may deliver the promise of autonomous, engineered matter to full fruition.

Non-affinity in multi-material mechanical metamaterials

Non-affine deformations enable mechanical metamaterials to achieve their unusual properties while imposing implications for their structural integrity. The presence of multiple phases with different mechanical properties results in additional non-affinity of the deformations, a phenomenon that has never been studied before in the area of extremal mechanical metamaterials. Here, we studied the degree of non-affinity, [Formula: see text], resulting from the random substitution of a fraction of the struts,[Formula: see text], that make up a lattice structure and are printed using a soft material (elastic modulus = [Formula: see text]) by those printed using a hard material ([Formula: see text]). Depending on the unit cell angle (i.e., [Formula: see text] = 60°, 90°, or 120°), the lattice structures exhibited negative, near-zero, or positive values of the Poisson's ratio, respectively. We found that the auxetic structures exhibit the highest levels of non-affinity, followed by the structures with positive and near-zero values of the Poisson's ratio. We also observed an increase in [Formula: see text] with [Formula: see text] and [Formula: see text] until [Formula: see text] =10⁴ and [Formula: see text]= 75%-90% after which [Formula: see text] saturated. The dependency of [Formula: see text] upon [Formula: see text] was therefore found to be highly asymmetric. The positive and negative values of the Poisson's ratio were strongly correlated with [Formula: see text]. Interestingly, achieving extremely high or extremely low values of the Poisson's ratio required highly affine deformations. In conclusion, our results clearly show the importance of considering non-affinity when trying to achieve a specific set of mechanical properties and underscore the structural integrity implications in multi-material mechanical metamaterials.

Effects of chain polarity of hindered phenol on the damping properties of polymer-based hybrid materials: insights into the molecular mechanism

For hindered phenol (HP)/polymer-based hybrid damping materials, the damping properties are greatly affected by the structure variation of HPs. However, the unclear relationship between them limits the exploitation of such promising materials. Therefore, three HPs with different chain polarity were synthesized to explore the relationship in this paper. The structures of the HPs were firstly confirmed by Nuclear Magnetic Resonance Spectrum, Fourier Transform Infrared Spectroscopy (FT-IR) and X-ray Diffraction (XRD). For further prepared HP/polyurethane hybrids, FT-IR and XRD were also adopted to confirm the hydrogen bonding interactions and micromorphologies. And, Molecular dynamics simulation was further used to characterize the effects of polarity variation on the hydrogen bonding interactions and chain packing of the hybrids in a quantitative manner. Then, combined with dynamic mechanical analysis, the relationship between the chain polarity variation of the hindered phenols and the damping properties was established.

Designing complex architectured materials with generative adversarial networks

Architectured materials on length scales from nanometers to meters are desirable for diverse applications. Recent advances in additive manufacturing have made mass production of complex architectured materials technologically and economically feasible. Existing architecture design approaches such as bioinspiration, Edisonian, and optimization, however, generally rely on experienced designers' prior knowledge, limiting broad applications of architectured materials. Particularly challenging is designing architectured materials with extreme properties, such as the Hashin-Shtrikman upper bounds on isotropic elasticity in an experience-free manner without prior knowledge. Here, we present an experience-free and systematic approach for the design of complex architectured materials with generative adversarial networks. The networks are trained using simulation data from millions of randomly generated architectures categorized based on different crystallographic symmetries. We demonstrate modeling and experimental results of more than 400 two-dimensional architectures that approach the Hashin-Shtrikman upper bounds on isotropic elastic stiffness with porosities from 0.05 to 0.75.

Acoustic response for nonlinear, coupled multiscale model containing subwavelength designed microstructure instabilities

Nonperiodic arrangements of inclusions with incremental linear negative stiffness embedded within a host material offer the ability to achieve unique and useful material properties on the macroscale. In an effort to study such types of inclusions, the present paper develops a time-domain model to capture the nonlinear dynamic response of a heterogeneous medium containing a dilute concentration of subwavelength nonlinear inclusions embedded in a lossy, nearly incompressible medium. Each length scale is modeled via a modified Rayleigh-Plesset equation, which differs from the standard form used in bubble dynamics by accounting for inertial and viscoelastic effects of the oscillating spherical element and includes constitutive equations formulated with incremental deformations. The two length scales are coupled through the constitutive relations and viscoelastic loss for the effective medium, both dependent on the inclusion and matrix properties. The model is then applied to an example nonlinear inclusion with incremental negative linear stiffness stemming from microscale elastic instabilities embedded in a lossy, nearly incompressible host medium. The macroscopic damping performance is shown to be tunable via an externally applied hydrostatic pressure with the example system displaying over two orders of magnitude change in energy dissipation due to changes in prestrain. The numerical results for radial oscillations versus time, frequency spectra, and energy dissipation obtained from the coupled dynamic model captures the expected response for quasistatic and dynamic regimes for an example buckling inclusion for both constrained and unconstrained negative stiffness inclusions.

Stability dependence of local structural heterogeneities of stable amorphous solids

The universal anomalous vibrational and thermal properties of amorphous solids are believed to be related to the local variations of the elasticity. Recently it has been shown that the vibrational properties are sensitive to the glass's stability. Here we study the stability dependence of the local elastic constants of a simulated glass former over a broad range of stabilities, from a poorly annealed glass to a glass whose stability is comparable to laboratory exceptionally stable vapor deposited glasses. We show that with increasing stability the glass becomes more uniform as evidenced by a smaller variance of local elastic constants. We find that, according to the definition of local elastic moduli used in this work, the local elastic moduli are not spatially correlated.

Continuous roll-to-roll patterning of three-dimensional periodic nanostructures

In this work, we introduce a roll-to-roll system that can continuously print three-dimensional (3D) periodic nanostructures over large areas. This approach is based on Langmuir-Blodgett assembly of colloidal nanospheres, which diffract normal incident light to create a complex intensity pattern for near-field nanolithography. The geometry of the 3D nanostructure is defined by the Talbot effect and can be precisely designed by tuning the ratio of the nanosphere diameter to the exposure wavelength. Using this system, we have demonstrated patterning of 3D photonic crystals with a 500 nm period on a 50 × 200 mm² flexible substrate, with a system throughput of 3 mm/s. The patterning yield is quantitatively analyzed by an automated electron beam inspection method, demonstrating long-term repeatability of an up to 88% yield over a 4-month period. The inspection method can also be employed to examine pattern uniformity, achieving an average yield of up to 78.6% over full substrate areas. The proposed patterning method is highly versatile and scalable as a nanomanufacturing platform and can find application in nanophotonics, nanoarchitected materials, and multifunctional nanostructures.

Excess floppy modes and multibranched mechanisms in metamaterials with symmetries

Floppy modes-deformations that cost zero energy-are central to the mechanics of a wide class of systems. For disordered systems, such as random networks and particle packings, it is well-understood how the number of floppy modes is controlled by the topology of the connections. Here we uncover that symmetric geometries, present in, e.g., mechanical metamaterials, can feature an unlimited number of excess floppy modes that are absent in generic geometries, and in addition can support floppy modes that are multibranched. We study the number Δ of excess floppy modes by comparing generic and symmetric geometries with identical topologies, and show that Δ is extensive, peaks at intermediate connection densities, and exhibits mean-field scaling. We then develop an approximate yet accurate cluster counting algorithm that captures these findings. Finally, we leverage our insights to design metamaterials with multiple folding mechanisms.

Focusing and Mode Separation of Elastic Vector Solitons in a 2D Soft Mechanical Metamaterial

Soft mechanical metamaterials can support a rich set of dynamic responses, which, to date, have received relatively little attention. Here, we report experimental, numerical, and analytical results describing the behavior of an anisotropic two-dimensional flexible mechanical metamaterial when subjected to impact loading. We not only observe the propagation of elastic vector solitons with three components-two translational and one rotational-that are coupled together, but also very rich direction-dependent behaviors such as the formation of sound bullets and the separation of pulses into different solitary modes.

Towards a Stable and High-Performance Hindered Phenol/Polymer-Based Damping Material Through Structure Optimization and Damping Mechanism Revelation

Although hindered phenol/polymer-based hybrid damping materials, with excellent damping performance, attract more and more attention, the poor stability of hindered phenol limits the application of such promising materials. To solve this problem, a linear hindered phenol with amorphous state and low polarity was synthesized and related polyurethane-based hybrid materials were prepared in this study. The structure and state of the hindered phenol were confirmed by nuclear magnetic resonance spectrum, Fourier transform infrared spectroscopy (FT-IR) and X-ray diffraction (XRD). The existence of intermolecular hydrogen bonds (HBs) between hindered phenol and polyurethane was confirmed by FT-IR, and the amorphous state of the hybrids was confirmed by XRD. Moreover, by a combination of molecular dynamics simulation and dynamic mechanical analysis, the relationship between the structure optimization of the hindered phenol and the high damping performance of the hybrids was quantitatively revealed. By constructing the synthetic hindered phenol, the intramolecular HBs between hindered phenols were restricted, while the strength and concentration of the intermolecular HBs increased by increasing the amount of hindered phenol. Thus, intermolecular interactions were enhanced, which lead to the compact chain packing of polyurethane, extended chain packing of hindered phenol, and good dispersion of hindered phenol in polyurethane. Therefore, the stability of the hindered phenol and the damping properties of the hybrids were both improved. The experiment results are expected to provide some useful information for the design and fabrication of high-performance polymeric damping materials.

On the Frequency Up-Conversion Mechanism in Metamaterials-Inspired Vibro-Impact Structures

Conventional acoustic absorbers like foams, fiberglass or liners are used commonly in structures for industrial, infrastructural, automotive and aerospace applications to mitigate noise. However, these have limited effectiveness for low-frequencies (LF, <~500 Hz) due to impractically large mass or volume requirements. LF content being less evanescent is a major contributor to environmental noise pollution and induces undesirable structural responses causing diminished efficiency, comfort, payload integrity and mission capabilities. There is, therefore a need to develop lightweight, compact, structurally-integrated solutions to mitigate LF noise in several applications. Inspired by metamaterials, tuned mass-loaded membranes as vibro-impact attachments on a baseline structure are considered to investigate their performance as an LF acoustic barrier. LF incident waves are up-converted via impact to higher modes in the baseline structure which may then be effectively mitigated using conventional means. Such Metamaterials-Inspired Vibro-Impact Structures (MIVIS) could be tuned to match the dominant frequency content of LF acoustic sources. Prototype MIVIS unit cells were designed and tested to study energy transfer mechanism via impact-induced frequency up-conversion and sound transmission loss. Structural acoustic simulations were done to predict responses using models based on normal incidence transmission loss tests. Simulations were validated using experiments and utilized to optimize the energy up-conversion mechanism using parametric studies. Up to 36 dB of sound transmission loss increase is observed at the anti-resonance frequency (326 Hz) within a tunable LF bandwidth of about 300 Hz for the MIVS under white noise excitation. Whereas, it is found that under monotonic excitations, the impact-induced up-conversion redistributes the incident LF monotone to the back plate’s first mode in the transmitted spectrum. This up-conversion could enable further broadband transmission loss via subsequent dissipation in conventional absorbers. Moreover, this approach while minimizing parasitic mass addition retains or could conceivably augment primary functionalities of the baseline structure. Successful transition to applications could enable new mission capabilities for aerospace and military vehicles and help create quieter built environments.

Toughening stretchable fibers via serial fracturing of a metallic core

Tough, biological materials (e.g., collagen or titin) protect tissues from irreversible damage caused by external loads. Mimicking these protective properties is important in packaging and in emerging applications such as durable electronic skins and soft robotics. This paper reports the formation of tough, metamaterial-like core-shell fibers that maintain stress at the fracture strength of a metal throughout the strain of an elastomer. The shell experiences localized strain enhancements that cause the higher modulus core to fracture repeatedly, increasing the energy dissipated during extension. Normally, fractures are catastrophic. However, in this architecture, the fractures are localized to the core. In addition to dissipating energy, the metallic core provides electrical conductivity and enables repair of the fractured core for repeated use. The fibers are 2.5 times tougher than titin and hold more than 15,000 times their own weight for a period 100 times longer than a hollow elastomeric fiber.

On anomalous localized resonance and plasmonic cloaking beyond the quasi-static limit

In this paper, we give the mathematical construction of novel core-shell plasmonic structures that can induce anomalous localized resonance and invisibility cloaking at certain finite frequencies beyond the quasi-static limit. The crucial ingredient in our study is that the plasmon constant and the loss parameter are constructed in a delicate way that are correlated and depend on the source and the size of the plasmonic structure. As a significant by-product of this study, we also derive the complete spectrum of the Neumann–Poincáre operator associated with the Helmholtz equation with finite frequencies in the radial geometry. The spectral result is the first one in its type and is of significant mathematical interest for its own sake.

Mechanical Performance of Multidirectional Buckling-Based Negative Stiffness Metamaterials: An Analytical and Numerical Study

Unidirectional, bidirectional and tridirectional Buckling-based Negative Stiffness (BNS) lattice metamaterials are designed by adding prefabricated curved beams into multidimensional rigid frames. Finite Element Analysis models are built, and their mechanical performance is investigated and discussed. First, geometric parameters of the curved beam were systematically studied with numerical analyses and the results were validated by theoretical solutions. Next, within unidirectional designs of different layer numbers, the basic properties of multilayer BNS metamaterials were revealed via quasi-static compressions. Then, the bidirectional and tridirectional designs were loaded on orthogonal axes to research both the quasi-static and dynamic behaviors. For dynamic analysis conditions, simulation scenarios of different impact velocities were implemented and compared. The results demonstrate that the proposed numerical analysis step has accurately predicted the force-displacement relations of both the curved beam and multilayer designs and the relations can be tuned via different geometric parameters. Moreover, the macroscopic performance of the metamaterials is sensitive to the rigidity of supporting frames. The shock force during impact is reduced down below the buckling thresholds of metamaterial designs and sharp impact damage is avoided. The presented metamaterials are able to undergo multiaxial stress conditions while retaining the negative stiffness effect and energy-absorbing nature and possess abundant freedom of parametric design, which is potentially useful in shock and vibration engineering.

Magnetoactive Acoustic Metamaterials

Acoustic metamaterials with negative constitutive parameters (modulus and/or mass density) have shown great potential in diverse applications ranging from sonic cloaking, abnormal refraction and superlensing, to noise canceling. In conventional acoustic metamaterials, the negative constitutive parameters are engineered via tailored structures with fixed geometries; therefore, the relationships between constitutive parameters and acoustic frequencies are typically fixed to form a 2D phase space once the structures are fabricated. Here, by means of a model system of magnetoactive lattice structures, stimuli-responsive acoustic metamaterials are demonstrated to be able to extend the 2D phase space to 3D through rapidly and repeatedly switching signs of constitutive parameters with remote magnetic fields. It is shown for the first time that effective modulus can be reversibly switched between positive and negative within controlled frequency regimes through lattice buckling modulated by theoretically predicted magnetic fields. The magnetically triggered negative-modulus and cavity-induced negative density are integrated to achieve flexible switching between single-negative and double-negative. This strategy opens promising avenues for remote, rapid, and reversible modulation of acoustic transportation, refraction, imaging, and focusing in subwavelength regimes.

The pH-dependent elastic properties of nanoscale DNA films and the resultant bending signals for microcantilever biosensors

The diverse mechanical properties of nanoscale DNA films on solid substrates have a close correlation with complex detection signals of micro-/nano-devices. This paper is devoted to formulating several multiscale models to study the effect of pH-dependent ionic inhomogeneity on the graded elastic properties of nanoscale DNA films and the resultant bending deflections of microcantilever biosensors. First, a modified inverse Debye length is introduced to improve the classical Poisson-Boltzmann equation for the electrical potential of DNA films to consider the inhomogeneous effect of hydrogen ions. Second, the graded characteristics of the particle distribution are taken into consideration for an improvement in Parsegian's mesoscopic potential for both attraction-dominated and repulsion-dominated films. Third, by the improved interchain interaction potential and the thought experiment about the compression of a macroscopic continuum DNA bar, we investigate the diversity of the elastic properties of single-stranded DNA (ssDNA) films due to pH variations. The relevant theoretical predictions quantitatively or qualitatively agree well with the relevant DNA experiments on the electrical potential, film thickness, condensation force, elastic modulus, and microcantilever deflections. The competition between attraction and repulsion among the fixed charges and the free ions endows the DNA film with mechanical properties such as a remarkable size effect and a non-monotonic behavior, and a negative elastic modulus is first revealed in the attraction-dominated ssDNA film. There exists a transition between the pH-sensitive parameter interval and the pH-insensitive one for the bending signals of microcantilevers, which is predominated by the initial stress effect in the DNA film.

Escaping the Ashby limit for mechanical damping/stiffness trade-off using a constrained high internal friction interfacial layer

The development of new materials with reduced noise and vibration levels is an active area of research due to concerns in various aspects of environmental noise pollution and its effects on health. Excessive vibrations also reduce the service live of the structures and limit the fields of their utilization. In oscillations, the viscoelastic moduli of a material are complex and it is their loss part - the product of the stiffness part and loss tangent - that is commonly viewed as a figure of merit in noise and vibration damping applications. The stiffness modulus and loss tangent are usually mutually exclusive properties so it is a technological challenge to develop materials that simultaneously combine high stiffness and high loss. Here we achieve this rare balance of properties by filling a solid polymer matrix with rigid inorganic spheres coated by a sub-micron layer of a viscoelastic material with a high level of internal friction. We demonstrate that this combination can be experimentally realised and that the analytically predicted behaviour is closely reproduced, thereby escaping the often termed 'Ashby' limit for mechanical stiffness/damping trade-off and offering a new route for manufacturing advanced composite structures with markedly reduced noise and vibration levels.

High-Performance Nanocomposites Inspired by Nature

Natural materials, including nacre, bone, and the lobster cuticle, exhibit excellent mechanical properties, combining high strength and toughness. Such materials have the added benefit of being light in weight. These advantageous features are due to such natural materials' orderly hierarchical architectures and abundant interface interactions. How to utilize these design principles created by nature to fabricate high-performance bioinspired nanocomposites remains a great research challenge. A logical roadmap for developing these nanocomposites can be described as "discovery, invention, and creation." Here, the discovery of the relationship between natural materials' design principles and such materials' extraordinary mechanical properties is discussed. Then, the invention of bioinspired strategies for mimicking natural materials is considered and representative strategies addressed. Next, the creation of multifunctional nanocomposites is discussed and bioinspired nanocomposites, including fiber nanocomposites, 2D film nanocomposites, and 3D bulk nanocomposites reviewed. Finally, a perspective and outlook for future directions in making bioinspired nanocomposites is provided to offer inspiration to the community and a clear vision for future research.

Harnessing mechanical instabilities at the nanoscale to achieve ultra-low stiffness metals

Alloy and microstructure optimization have led to impressive improvements in the strength of engineering metals, while the range of Young's moduli achievable has remained essentially unchanged. This is because stiffness is insensitive to microstructure and bounded by individual components in composites. Here we design ultra-low stiffness in fully dense, nanostructured metals via the stabilization of a mechanically unstable, negative stiffness state of a martensitic alloy by its coherent integration with a compatible, stable second component. Explicit large-scale molecular dynamics simulations of the metamaterials with state of the art potentials confirm the expected ultra-low stiffness while maintaining full strength. We find moduli as low as 2 GPa, a value typical of soft materials and over one order of magnitude lower than either constituent, defying long-standing composite bounds. Such properties are attractive for flexible electronics and implantable devices. Our concept is generally applicable and could significantly enhance materials science design space.

Drop-on-coilable-fibre systems exhibit negative stiffness events and transitions in coiling morphology

We investigate the mechanics of elastic fibres carrying liquid droplets. In such systems, buckling may localize inside the drop cavity if the fibre is thin enough. This so-called drop-on-coilable-fibre system exhibits a surprising liquid-like response under compression and a solid-like response under tension. Here we analyze this unconventional behavior in further detail and find theoretical, numerical and experimental evidence of negative stiffness events. We find that the first and main negative stiffness regime owes its existence to the transfer of capillary-stored energy into mechanical curvature energy. The following negative stiffness events are associated with changes in the coiling morphology of the fibre. Eventually coiling becomes tightly locked into an ordered phase where liquid and solid deformations coexist.

Abiotic tooth enamel

Tooth enamel comprises parallel microscale and nanoscale ceramic columns or prisms interlaced with a soft protein matrix. This structural motif is unusually consistent across all species from all geological eras. Such invariability-especially when juxtaposed with the diversity of other tissues-suggests the existence of a functional basis. Here we performed ex vivo replication of enamel-inspired columnar nanocomposites by sequential growth of zinc oxide nanowire carpets followed by layer-by-layer deposition of a polymeric matrix around these. We show that the mechanical properties of these nanocomposites, including hardness, are comparable to those of enamel despite the nanocomposites having a smaller hard-phase content. Our abiotic enamels have viscoelastic figures of merit (VFOM) and weight-adjusted VFOM that are similar to, or higher than, those of natural tooth enamels-we achieve values that exceed the traditional materials limits of 0.6 and 0.8, respectively. VFOM values describe resistance to vibrational damage, and our columnar composites demonstrate that light-weight materials of unusually high resistance to structural damage from shocks, environmental vibrations and oscillatory stress can be made using biomimetic design. The previously inaccessible combinations of high stiffness, damping and light weight that we achieve in these layer-by-layer composites are attributed to efficient energy dissipation in the interfacial portion of the organic phase. The in vivo contribution of this interfacial portion to macroscale deformations along the tooth's normal is maximized when the architecture is columnar, suggesting an evolutionary advantage of the columnar motif in the enamel of living species. We expect our findings to apply to all columnar composites and to lead to the development of high-performance load-bearing materials.

Double-Negative Mechanical Metamaterials Displaying Simultaneous Negative Stiffness and Negative Poisson's Ratio Properties

A scalable mechanical metamaterial simultaneously displaying negative stiffness and negative Poisson's ratio responses is presented. Interlocking hexagonal subunit assemblies containing 3 alternative embedded negative stiffness (NS) element types display Poisson's ratio values of -1 and NS values over two orders of magnitude (-1.4 N mm^-1 to -160 N mm^-1 ), in good agreement with model predictions.

Programmable mechanical metamaterials: the role of geometry

We experimentally and numerically study the role of geometry for the mechanics of biholar metamaterials, which are quasi-2D slabs of rubber patterned by circular holes of two alternating sizes. We recently showed how the response to uniaxial compression of these metamaterials can be programmed by lateral confinement. In particular, there is a range of confining strains ε_x for which the resistance to compression becomes non-trivial-non-monotonic or hysteretic-in a range of compressive strains ε_y. Here we show how the dimensionless geometrical parameters t and χ, which characterize the wall thickness and size ratio of the holes that pattern these metamaterials, can significantly tune these ranges over a wide range. We study the behavior for the limiting cases where the wall thickness t and the size ratio χ become large, and discuss the new physics that arises there. Away from these extreme limits, the variation of the strain ranges of interest is smooth with porosity, but the variation with size ratio evidences a cross-over at low χ from biholar to monoholar (equal sized holes) behavior, related to the elastic instabilities in purely monoholar metamaterials. Our study provides precise guidelines for the rational design of programmable biholar metamaterials, tailored to specific applications, and indicates that the widest range of programmability arises for moderate values of both t and χ.

Systematic comparison of model polymer nanocomposite mechanics

Polymer nanocomposites render a range of outstanding materials from natural products such as silk, sea shells and bones, to synthesized nanoclay or carbon nanotube reinforced polymer systems. In contrast to the fast expanding interest in this type of material, the fundamental mechanisms of their mixing, phase behavior and reinforcement, especially for higher nanoparticle content as relevant for bio-inorganic composites, are still not fully understood. Although polymer nanocomposites exhibit diverse morphologies, qualitatively their mechanical properties are believed to be governed by a few parameters, namely their internal polymer network topology, nanoparticle volume fraction, particle surface properties and so on. Relating material mechanics to such elementary parameters is the purpose of this work. By taking a coarse-grained molecular modeling approach, we study an range of different polymer nanocomposites. We vary polymer nanoparticle connectivity, surface geometry and volume fraction to systematically study rheological/mechanical properties. Our models cover different materials, and reproduce key characteristics of real nanocomposites, such as phase separation, mechanical reinforcement. The results shed light on establishing elementary structure, property and function relationship of polymer nanocomposites.

Tailored Buckling Microlattices as Reusable Light-Weight Shock Absorbers

Structures and materials absorbing mechanical (shock) energy commonly exploit either viscoelasticity or destructive modifications. Based on a class of uniaxial light-weight geometrically nonlinear mechanical microlattices and using buckling of inner elements, either a sequence of snap-ins followed by irreversible hysteretic - yet repeatable - self-recovery or multistability is achieved, enabling programmable behavior. Proof-of-principle experiments on three-dimensional polymer microstructures are presented.

Two-dimensional locally resonant elastic metamaterials with chiral comb-like interlayers: Bandgap and simultaneously double negative properties

In this paper, bandgap and dynamic effective properties of two-dimensional elastic metamaterials with a chiral comb-like interlayer are studied by using the finite element method. The effects of the geometrical parameters of the chiral comb-like interlayer on the band edges are investigated and discussed. Combined with the analysis of the vibration modes at the band edges, equivalent spring-mass/pendulum models are developed to investigate the mechanisms of the bandgap generation. The analytically predicted results of the band edges, including the frequency where the double negative properties appear, and the numerical ones are generally in good agreement. The research findings in this paper have relevant engineering applications of the elastic metamaterials in the low frequency range.

3D printed cellular solid outperforms traditional stochastic foam in long-term mechanical response

3D printing of polymeric foams by direct-ink-write is a recent technological breakthrough that enables the creation of versatile compressible solids with programmable microstructure, customizable shapes, and tunable mechanical response including negative elastic modulus. However, in many applications the success of these 3D printed materials as a viable replacement for traditional stochastic foams critically depends on their mechanical performance and micro-architectural stability while deployed under long-term mechanical strain. To predict the long-term performance of the two types of foams we employed multi-year-long accelerated aging studies under compressive strain followed by a time-temperature-superposition analysis using a minimum-arc-length-based algorithm. The resulting master curves predict superior long-term performance of the 3D printed foam in terms of two different metrics, i.e., compression set and load retention. To gain deeper understanding, we imaged the microstructure of both foams using X-ray computed tomography, and performed finite-element analysis of the mechanical response within these microstructures. This indicates a wider stress variation in the stochastic foam with points of more extreme local stress as compared to the 3D printed material, which might explain the latter’s improved long-term stability and mechanical performance.

Dynamically variable negative stiffness structures

Variable stiffness structures that enable a wide range of efficient load-bearing and dexterous activity are ubiquitous in mammalian musculoskeletal systems but are rare in engineered systems because of their complexity, power, and cost. We present a new negative stiffness-based load-bearing structure with dynamically tunable stiffness. Negative stiffness, traditionally used to achieve novel response from passive structures, is a powerful tool to achieve dynamic stiffness changes when configured with an active component. Using relatively simple hardware and low-power, low-frequency actuation, we show an assembly capable of fast (<10 ms) and useful (>100×) dynamic stiffness control. This approach mitigates limitations of conventional tunable stiffness structures that exhibit either small (<30%) stiffness change, high friction, poor load/torque transmission at low stiffness, or high power active control at the frequencies of interest. We experimentally demonstrate actively tunable vibration isolation and stiffness tuning independent of supported loads, enhancing applications such as humanoid robotic limbs and lightweight adaptive vibration isolators.

Viscometry of single nanoliter-volume droplets using dynamic force spectroscopy

We present an atomic force microscope-based platform for viscometry of ‘nanoliter' volume fluids.

Mechanisms for impulsive energy dissipation and small-scale effects in microgranular media

We study impulse response in one-dimensional homogeneous microgranular chains on a linear elastic substrate. Microgranular interactions are analytically described by the Schwarz contact model which includes nonlinear compressive as well as snap-to and from-contact adhesive effects forming a hysteretic loop in the force deformation relationship. We observe complex transient dynamics, including disintegration of solitary pulses, local clustering, and low-to-high-frequency energy transfers resulting in enhanced energy dissipation. We study in detail the underlying dynamics of cluster formation in the impulsively loaded medium and relate enhanced energy dissipation to the rate of cluster formation. These unusual and interesting dynamical phenomena are shown to be robust over a range of physically feasible conditions and are solely scale effects since they are attributed to surface forces, which have no effect at the macroscale. We establish a universal relation between the reclustering rate and the effective damping in these systems. Our findings demonstrate that scale effects generating new nonlinear features can drastically affect the dynamics and acoustics of microgranular materials.

Viscous-to-viscoelastic transition in phononic crystal and metamaterial band structures

The dispersive behavior of phononic crystals and locally resonant metamaterials is influenced by the type and degree of damping in the unit cell. Dissipation arising from viscoelastic damping is influenced by the past history of motion because the elastic component of the damping mechanism adds a storage capacity. Following a state-space framework, a Bloch eigenvalue problem incorporating general viscoelastic damping based on the Zener model is constructed. In this approach, the conventional Kelvin-Voigt viscous-damping model is recovered as a special case. In a continuous fashion, the influence of the elastic component of the damping mechanism on the band structure of both a phononic crystal and a metamaterial is examined. While viscous damping generally narrows a band gap, the hereditary nature of the viscoelastic conditions reverses this behavior. In the limit of vanishing heredity, the transition between the two regimes is analyzed. The presented theory also allows increases in modal dissipation enhancement (metadamping) to be quantified as the type of damping transitions from viscoelastic to viscous. In conclusion, it is shown that engineering the dissipation allows one to control the dispersion (large versus small band gaps) and, conversely, engineering the dispersion affects the degree of dissipation (high or low metadamping).

Snapping mechanical metamaterials under tension

A snapping mechanical metamaterial is designed, which exhibits a sequential snap-through behavior under tension. The tensile response of this mechanical metamaterial can be altered by tuning the architecture of the snapping segments to achieve a range of nonlinear mechanical responses, including monotonic, S-shaped, plateau, and non-monotonic snap-through behavior.

Nanoscopic dynamic mechanical analysis of resin-infiltrated dentine, under in vitro chewing and bruxism events

The aim of this study was to evaluate the induced changes in mechanical behavior and bonding capability of resin-infiltrated dentine interfaces, after application of mechanical stimuli. Dentine surfaces were subjected to partial demineralization through 37% phosphoric acid etching followed by the application of an etch-and-rinse dentine adhesive, Single Bond (3M/ESPE). Bonded interfaces were stored in simulated body fluid during 24h, and then tested or submitted to the mechanical loading challenge. Different loading waveforms were applied: No cycling (I), 24h cycled in sine (II) or square (III) waves, sustained loading held for 24h (IV) or sustained loading held for 72h (V). Microtensile bond strength (MTBS) was assessed for the different groups. Debonded dentine surfaces were studied by field emission scanning electron microscopy (FESEM). At the resin-dentine interface, both the hybrid layer (HL) and the bottom of the hybrid layer (BHL), and both peritubular and intertubular were evaluated using a nanoindenter in scanning mode. The load and displacement responses were used to perform the nano-Dynamic Mechanical analysis and to estimate the complex and storage modulus. Dye assisted Confocal Microscopy Evaluation was used to assess sealing ability. Load cycling increased the percentage of adhesive failures in all groups. Specimens load cycled in held 24h attained the highest complex and storage moduli at HL and BHL. The storage modulus was maximum in specimens load cycled in held 24h at peritubular dentine, and the lowest values were attained at intertubular dentine. The storage modulus increased in all mechanical tests, at peritubular dentine. An absence of micropermeability and nanoleakage after loading in sine and square waveforms were encountered. Porosity of the resin-dentine interface was observed when specimens were load cycled in held 72h. Areas of combined sealing and permeability were discovered at the interface of specimens load cycled in held 24h. Crack-bridging images appeared in samples load cycled with sine waveform, after FESEM examination.

Spectroscopic evidence for negative electronic compressibility in a quasi-three-dimensional spin-orbit correlated metal

Negative compressibility is a sign of thermodynamic instability of open or non-equilibrium systems. In quantum materials consisting of multiple mutually coupled subsystems, the compressibility of one subsystem can be negative if it is countered by positive compressibility of the others. Manifestations of this effect have so far been limited to low-dimensional dilute electron systems. Here, we present evidence from angle-resolved photoemission spectroscopy (ARPES) for negative electronic compressibility (NEC) in the quasi-three-dimensional (3D) spin-orbit correlated metal (Sr1-xLax)3Ir2O7. Increased electron filling accompanies an anomalous decrease of the chemical potential, as indicated by the overall movement of the deep valence bands. Such anomaly, suggestive of NEC, is shown to be primarily driven by the lowering in energy of the conduction band as the correlated bandgap reduces. Our finding points to a distinct pathway towards an uncharted territory of NEC featuring bulk correlated metals with unique potential for applications in low-power nanoelectronics and novel metamaterials.

Origami multistability: from single vertices to metasheets

We show that the simplest building blocks of origami-based materials-rigid, degree-four vertices-are generically multistable. The existence of two distinct branches of folding motion emerging from the flat state suggests at least bistability, but we show how nonlinearities in the folding motions allow generic vertex geometries to have as many as five stable states. In special geometries with collinear folds and symmetry, more branches emerge leading to as many as six stable states. Tuning the fold energy parameters, we show how monostability is also possible. Finally, we show how to program the stability features of a single vertex into a periodic fold tessellation. The resulting metasheets provide a previously unanticipated functionality-tunable and switchable shape and size via multistability.

Programmable mechanical metamaterials

We create mechanical metamaterials whose response to uniaxial compression can be programmed by lateral confinement, allowing monotonic, nonmonotonic, and hysteretic behavior. These functionalities arise from a broken rotational symmetry which causes highly nonlinear coupling of deformations along the two primary axes of these metamaterials. We introduce a soft mechanism model which captures the programmable mechanics, and outline a general design strategy for confined mechanical metamaterials. Finally, we show how inhomogeneous confinement can be explored to create multistability and giant hysteresis.

Bioinspired multifunctional vanadium dioxide: improved thermochromism and hydrophobicity

Vanadium dioxide (VO2) films with moth-eye nanostructures have been fabricated to enhance the thermochromic properties with different periodicity (d) to achieve antireflection (AR). It is revealed that the films with smaller d (210 and 440 nm) could increase both the luminous transmission (Tlum) and infrared transmission (TIR) at 25 and 90 °C, as the d is smaller than the given wavelength and the gradient refractive index produces antireflection. The average Tlum and TIR of VO2 increase with decreasing d. Compared with the planar film, the AR sample with periodicity of 210 nm and thickness of 140 nm can offer approximately 10% enhancement of Tlum and 24.5% increase in solar modulation (ΔTsol). With the addition of hydrophobic overcoat on the patterned VO2, ∼120° contact angle could be achieved. The present approach can tailor the optical transmittance in different wavelengths at high and low temperature together with self-cleaning, opening new avenues for producing hydrophobic VO2 with enhanced thermochromic properties for smart window applications.

Dynamics of periodic mechanical structures containing bistable elastic elements: from elastic to solitary wave propagation

We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.