An elasto-mechanical unfeelability cloak made of pentamode metamaterials

3D multiphoton lithography using biocompatible polymers with specific mechanical properties

The fabrication of two- and three-dimensional scaffolds mimicking the extracellular matrix and providing cell stimulation is of high importance in biology and material science. We show two new, biocompatible polymers, which can be 3D structured via multiphoton lithography, and determine their mechanical properties. Atomic force microscopy analysis of structures with sub-micron feature sizes reveals Young's modulus values in the 100 MPa range. Assessment of biocompatibility of the new resins was done by cultivating human umbilical vein endothelial cells on two-dimensionally structured substrates for four days. The cell density and presence of apoptotic cells has been quantified.

Tunable photo-responsive elastic metamaterials

The metamaterial paradigm has allowed an unprecedented space-time control of various physical fields, including elastic and acoustic waves. Despite the wide variety of metamaterial configurations proposed so far, most of the existing solutions display a frequency response that cannot be tuned, once the structures are fabricated. Few exceptions include systems controlled by electric or magnetic fields, temperature, radio waves and mechanical stimuli, which may often be unpractical for real-world implementations. To overcome this limitation, we introduce here a polymeric 3D-printed elastic metamaterial whose transmission spectrum can be deterministically tuned by a light field. We demonstrate the reversible doubling of the width of an existing frequency band gap upon selective laser illumination. This feature is exploited to provide an elastic-switch functionality with a one-minute lag time, over one hundred cycles. In perspective, light-responsive components can bring substantial improvements to active devices for elastic wave control, such as beam-splitters, switches and filters.

Viewpoint: From Responsive to Adaptive and Interactive Materials and Materials Systems: A Roadmap

Soft matter systems and materials are moving toward adaptive and interactive behavior, which holds outstanding promise to make the next generation of intelligent soft materials systems inspired from the dynamics and behavior of living systems. But what is an adaptive material? What is an interactive material? How should classical responsiveness or smart materials be delineated? At present, the literature lacks a comprehensive discussion on these topics, which is however of profound importance in order to identify landmark advances, keep a correct and noninflating terminology, and most importantly educate young scientists going into this direction. By comparing different levels of complex behavior in biological systems, this Viewpoint strives to give some definition of the various different materials systems characteristics. In particular, the importance of thinking in the direction of training and learning materials, and metabolic or behavioral materials is highlighted, as well as communication and information-processing systems. This Viewpoint aims to also serve as a switchboard to further connect the important fields of systems chemistry, synthetic biology, supramolecular chemistry and nano- and microfabrication/3D printing with advanced soft materials research. A convergence of these disciplines will be at the heart of empowering future adaptive and interactive materials systems with increasingly complex and emergent life-like behavior.

Environmental Response of 2D Thermal Cloak under Dynamic External Temperature Field

As a typical representative of transformation thermodynamics, which is the counterpart of transformation optics, the thermal cloak has been explored extensively while most current research focuses on the structural design instead of adaptability and practicability in a dynamic environment. The evaluation of energy processes involved in the thermal cloak under dynamic conditions are also lacking, which is essential to the engineering application of this functional structure. In this paper, based on the dynamic environment of a sinusoidal form with ambient amplitude, distribution density, phase, and temperature difference as variables, we evaluated the cloaking performance and environmental response of a 2D thermal cloak. Considering the heat dissipation and energy loss in the whole procedure, local entropy production rate and response entropy were introduced to analyze the different influences of each environmental parameter on the cloaking system. Moreover, we constructed a series of comprehensive schemes to obtain the fitting equation as well as an appropriate scope to apply the thermal cloak. The results are beneficial to the novel use of the concept of entropy and valuable for further improving the working efficiency and potential engineering applications of the thermal cloak.

Physical Realization of Elastic Cloaking with a Polar Material

An elastic cloak is a coating material that can be applied to an arbitrary inclusion to make it indistinguishable from the background medium. Cloaking against elastic disturbances, in particular, has been demonstrated using several designs and gauges. None, however, tolerate the coexistence of normal and shear stresses due to a shortage of physical realization of transformation-invariant elastic materials. Here, we overcome this limitation to design and fabricate a new class of polar materials with a distribution of body torque that exhibits asymmetric stresses. A static cloak for full two-dimensional elasticity is thus constructed based on the transformation method. The proposed cloak is made of a functionally graded multilayered lattice embedded in an isotropic continuum background. While one layer is tailored to produce a target elastic behavior, the other layers impose a set of kinematic constraints equivalent to a distribution of body torque that breaks the stress symmetry. Experimental testing under static compressive and shear loads demonstrates encouraging cloaking performance in good agreement with our theoretical prediction. The work sets a precedent in the field of transformation elasticity and should find applications in mechanical stress shielding and stealth technologies.

Polar Metamaterials: A New Outlook on Resonance for Cloaking Applications

Rotationally resonant metamaterials are leveraged to answer a longstanding question regarding the existence of transformation-invariant elastic materials and the ad hoc possibility of transformation-based passive cloaking in full plane elastodynamics. Combined with tailored lattice geometries, rotational resonance is found to induce a polar and chiral behavior, that is, a behavior lacking stress and mirror symmetries, respectively. The central, and simple, idea is that a population of rotating resonators can exert a density of body torques strong enough to modify the balance of angular momentum on which hang these symmetries. The obtained polar metamaterials are used as building blocks of a cloaking device. Numerical tests show satisfactory cloaking performance under pressure and shear probing waves, further coupled through a free boundary. The work sheds new light on the phenomenon of resonance in metamaterials and should help put transformation elastodynamics on equal footing with transformation acoustics and optics.

2D Mechanical Metamaterials with Widely Tunable Unusual Modes of Thermal Expansion

Most natural materials expand uniformly in all directions upon heating. Artificial, engineered systems offer opportunities to tune thermal expansion properties in interesting ways. Previous reports exploit diverse design principles and fabrication techniques to achieve a negative or ultralow coefficient of thermal expansion, but very few demonstrate tunability over different behaviors. This work presents a collection of 2D material structures that exploit bimaterial serpentine lattices with micrometer feature sizes as the basis of a mechanical metamaterials system capable of supporting positive/negative, isotropic/anisotropic, and homogeneous/heterogeneous thermal expansion properties, with additional features in unusual shearing, bending, and gradient modes of thermal expansion. Control over the thermal expansion tensor achieved in this way provides a continuum-mechanics platform for advanced strain-field engineering, including examples of 2D metamaterials that transform into 3D surfaces upon heating. Integrated electrical and optical sources of thermal actuation provide capabilities for reversible shape reconfiguration with response times of less than 1 s, as the basis of dynamically responsive metamaterials.

Stiffer, Stronger and Centrosymmetrical Class of Pentamodal Mechanical Metamaterials

Pentamode metamaterials have been used as a crucial element to achieve elastical unfeelability cloaking devices. They are seen as potentially fragile and not simple for integration in anisotropic structures due to a non-centrosymmetric crystalline structure. Here, we introduce a new class of pentamode metamaterial with centrosymmetry, which shows better performances regarding stiffness, toughness, stability and size dependence. The phonon band structure is calculated based on the finite element method, and the pentamodal properties are evaluated by analyzing the single band gap and the ratio of bulk and shear modulus. The Poisson’s ratio becomes isotropic and close to 0.5 in the limit of small double-cone connections. Stability and scalability analysis results show that the critical load factor of this structure is obviously higher than the classical pentamode structure under the same static elastic properties, and the Young’s modulus gradually converges to a stable value (the infinite case) with an increasing number of unit cells.

Omnidirectional flexural invisibility of multiple interacting voids in vibrating elastic plates

In elasticity, the design of a cloaking for an inclusion or a void to leave a vibrational field unperturbed by its presence, so to achieve its invisibility, is a thoroughly analysed, but still unchallenged, mechanical problem. The 'cloaking transformation' concept, originally developed in electromagnetism and optics, is not directly applicable to elastic waves, displaying a complex vectorial nature. Consequently, all examples of elastic cloaking presented so far involve complex design and thick coating skins. These cloakings often work only for problems of unidirectional propagation, within narrow ranges of frequency, and considering only one cloaked object. Here, a new method based on the concept of reinforcement, achieved via elastic stiffening and mass redistribution, is introduced to cloak multiple voids in an elastic plate. This simple technique produces invisibility of the voids to flexural waves within an extremely broad range of frequencies and thus surpassing in many aspects all existing cloaking techniques. The proposed design principle is applicable in mechanical problems ranging from the micro-scale to the scale of civil engineering. For instance, our results show how to design a perforated load-bearing building wall, vibrating during an earthquake exactly as the same wall, but unperforated, a new finding for seismic protection.

Manipulating cell: flexibly manipulating thermal and DC fields in arbitrary domain

To extend the metamaterial applications on simultaneously regulating multiple fields with transformation optics, we propose a class of manipulative cell here to manipulate thermal and DC fields simultaneously in non-conformal angular schemes. Significant behaviors of thermal cloaking, electrical concentration, and related switched functions are numerically demonstrated with appropriate media. The findings not only present an efficient method for simultaneously manipulating various energy, but also break the limitation of structural profiles in the designs of bi-functional meta-device. Moreover, it may also provide references for efficient energy manipulation and management in conventional energy techniques.

Tacticity in chiral phononic crystals

The study of vibrational properties in engineered periodic structures relies on the early intuitions of Haüy and Boscovich, who regarded crystals as ensembles of periodically arranged point masses interacting via attractive and repulsive forces. Contrary to electromagnetism, where mechanical properties do not couple to the wave propagation mechanism, in elasticity this paradigm inevitably leads to low stiffness and high-density materials. Recent works transcend the Haüy-Boscovich perception, proposing shaped atoms with finite size, which relaxes the link between their mass and inertia, to achieve unusual dynamic behavior at lower frequencies, leaving the stiffness unaltered. Here, we introduce the concept of tacticity in spin-spin-coupled chiral phononic crystals. This additional layer of architecture has a remarkable effect on their dispersive behavior and allows to successfully realize material variants with equal mass density and stiffness but radically different dynamic properties.

Here, the authors study the influence of tacticity on the dynamic behaviour of chiral structured periodic media comprising rotational inertia elements. This opens the way towards new mechanisms for wave control by exploiting spin-spin coupling mechanism.

Toward Imperfection-Insensitive Soft Network Materials for Applications in Stretchable Electronics

Development of stretchable devices with mechanical responses that mimic those of biological tissues/organs is of particular importance for the long-term biointegration, as the discomfort induced by the mechanical mismatch can be minimized. Recent works have established the bioinspired designs of soft network materials that can precisely reproduce the unconventional J-shaped stress-strain curves of human skin at different regions. Existing studies mostly focused on the design, fabrication, and modeling of perfect soft network materials. When utilized as the substrates of biointegrated electronics, the soft network designs, however, often need to incorporate deterministic holes, a type of imperfection, to accommodate hard, inorganic electronic components. Understanding of the effect of hole imperfections on the mechanical properties of soft network materials is thereby essential in practical applications. This paper presents a combined experimental and computational study of the stretchability and elastic modulus of imperfect soft network materials consisting of circular holes with a variety of diameters. Both the size and location of the circular-hole imperfections are shown to have profound influences on the stretchability. Based on these results, design guidelines of imperfection-insensitive network materials are introduced. For the imperfections that result in an evident reduction of stretchability, an effective reinforcement approach is presented by enlarging the width of horseshoe microstructures at strategic locations, which can enhance the stretchability considerably. A stretchable and imperfection-insensitive integrated device with a light-emitting diode embedded in the network material serves a demonstrative application.

Designing 3D Digital Metamaterial for Elastic Waves: From Elastic Wave Polarizer to Vibration Control

Elastic wave polarizers, which can filter out linearly polarized elastic waves from hybrid elastic waves, remain a challenge since elastic waves contain both transverse and longitudinal natures. Here, a tunable, digital, locally resonant metamaterial inspired by abacus is proposed, which consists of 3D-printed octahedral frames and built-in electromagnets. By controlling current in the electromagnets, each unit cell exhibits three digital modes, where the elastic waves have different characteristics of propagation under each mode. A variety of waveguides can be formed by a combination of the three modes and desired polarization can be further filtered out from hybrid elastic waves in a tunable manner. The underlying mechanism of these polarizer-like characteristics is investigated through a combination of theoretical analysis, numerical simulation, and experimental testing. This study provides a means of filtering out the desired wave from hybrid elastic waves, and offers promise for vibration control of particle distribution and flexible structure.

Hydrodynamic Metamaterial Cloak for Drag-Free Flow

Metamaterials engineered based on transformation optics have facilitated inaccessible manipulation of various physical phenomena. However, such metamaterials have not been introduced for flowing viscous matter. Here we propose a hydrodynamic metamaterial cloak that can conceal an object in two-dimensional creeping flow by guiding viscous forces. Coordinate transformation of fluidic space is implemented to calculate a tensoric viscosity based on a form invariance of Navier-Stokes equations. The hydrodynamic cloak with the viscosity tensor is numerically simulated to verify a fictitious fluidic empty space created in it. The corresponding metamaterial microstructure is systemically designed and fabricated in a microfluidic device. The experimental results reveal that a solid object amid the flow can be hydrodynamically hidden without entailing a disturbance in flow fields and experiencing a drag.

A facile multi-material direct laser writing strategy

Direct laser writing (DLW) is a three-dimensional (3D) manufacturing technology that offers vast architectural control at submicron scales, yet remains limited in cases that demand microstructures comprising more than one material. Here we present an accessible microfluidic multi-material DLW (μFMM-DLW) strategy that enables 3D nanostructured components to be printed with average material registration accuracies of 100 ± 70 nm (ΔX) and 190 ± 170 nm (ΔY) - a significant improvement versus conventional multi-material DLW methods. Results for printing 3D microstructures with up to five materials suggest that μFMM-DLW can be utilized in applications that demand geometrically complex, multi-material microsystems, such as for photonics, meta-materials, and 3D cell biology.

An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces

We consider a periodic array of resonators, formed from Euler-Bernoulli beams, attached to the surface of an elastic half-space. Earlier studies of such systems have concentrated on compressional resonators. In this paper, we consider the effect of the flexural motion of the resonators, adapting a recently established asymptotic methodology that leads to an explicit scalar hyperbolic equation governing the propagation of Rayleigh-like waves. Compared with classical approaches, the asymptotic model yields a significantly simpler dispersion relation, with closed-form solutions, shown to be accurate for surface wave-speeds close to that of the Rayleigh wave. Special attention is devoted to the effect of various junction conditions joining the beams to the elastic half-space which arise from considering flexural motion and are not present for the case of purely compressional resonators. Such effects are shown to provide significant and interesting features and, in particular, the choice of junction conditions dramatically changes the distribution and sizes of stop bands. Given that flexural vibrations in thin beams are excited more readily than compressional modes and the ability to model elastic surface waves using the scalar wave equation (i.e. waves on a membrane), the paper provides new pathways towards novel experimental set-ups for elastic metasurfaces.

Encrypted Thermal Printing with Regionalization Transformation

Artificially structured thermal metamaterials provide an unprecedented possibility of molding heat flow that is drastically distinct from the conventional heat diffusion in naturally conductive materials. The Laplacian nature of heat conduction makes the transformation thermotics, as a design principle for thermal metadevices, compatible with transformation optics. Various functional thermal devices, such as thermal cloaks, concentrators, and rotators, have been successfully demonstrated. How far can it possible go beyond just realizing a heat-distribution function in a thermal metadevice? Herein, the concept of encrypted thermal printing is proposed and experimentally validated, which could conceal encrypted information under natural light and present static or dynamic messages in an infrared image. Regionalization transformation is developed for structuring thermal metamaterial-strokes as infrared signatures, enabling letters of the alphabet to be written, paintings to be drawn, movies to be made, and information to be displayed. This strategy successfully demonstrates an extreme level of manipulation of heat flow for encryption, illusions, and messaging.

Metamaterial for elastostatic cloaking under thermal gradients

We introduce the optimization-based method for the design of thermo-mechanical metamaterials and, particularly, for the elastostatic cloaking under thermal loads. It consists of solving a large-scale, nonlinear constrained optimization problem, where the objective function is the error in the cloaking task accomplishment. The design variables define the required metamaterial distribution. In this way, the cloaking task is accomplished, if not exactly, optimally. Further, the design variables dictate how to fabricate the metamaterial, avoiding the uncertainty of simultaneously mimicking several thermal and mechanical effective properties, as required by transformation-based metamaterial design methods.

Additive Manufacturing: Applications and Directions in Photonics and Optoelectronics

The combination of materials with targeted optical properties and of complex, 3D architectures, which can be nowadays obtained by additive manufacturing, opens unprecedented opportunities for developing new integrated systems in photonics and optoelectronics. The recent progress in additive technologies for processing optical materials is here presented, with emphasis on accessible geometries, achievable spatial resolution, and requirements for printable optical materials. Relevant examples of photonic and optoelectronic devices fabricated by 3D printing are shown, which include light-emitting diodes, lasers, waveguides, optical sensors, photonic crystals and metamaterials, and micro-optical components. The potential of additive manufacturing applied to photonics and optoelectronics is enormous, and the field is still in its infancy. Future directions for research include the development of fully printable optical and architected materials, of effective and versatile platforms for multimaterial processing, and of high-throughput 3D printing technologies that can concomitantly reach high resolution and large working volumes.

Double square rings with different dimensions produce multiple absorption bands

The quantity of absorption bands is traditionally less than the quantity of resonator subunits. Based on the absorption theory of electromagnetic resonance, three-millimeter-wave metamaterial absorbers (MWMAs) based on periodic resonators with double square rings (DSRs) are proposed, discussed, fabricated, and measured. Multiple absorption bands including two, three, and four bands can be effectively achieved by adjusting the dimensions of the DSRs. The electric field distributions at the corresponding resonance frequency can adequately explain the physical mechanism of adjustable absorption bands affected by the strong LC, dipole, and surface responses complexly. Detailed influence produced by sizes and materials is elaborated. The adjustable absorption can be easily scaled to the entire spectrum by geometrical regulation. The presented MWMAs show attractive prospects in electromagnetic devices, biological sensing, material detection, and function materials because of their size adaptation, flexible design, ultrathin thickness, strong flexibility, and convenient fabrication.

Folding 2D Structures into 3D Configurations at the Micro/Nanoscale: Principles, Techniques, and Applications

Compared to their 2D counterparts, 3D micro/nanostructures show larger degrees of freedom and richer functionalities; thus, they have attracted increasing attention in the past decades. Moreover, extensive applications of 3D micro/nanostructures are demonstrated in the fields of mechanics, biomedicine, optics, etc., with great advantages. However, the mainstream micro/nanofabrication technologies are planar ones; therefore, they cannot be used directly for the construction of 3D micro/nanostructures, making 3D fabrication at the micro/nanoscale a great challenge. A promising strategy to overcome this is to combine the state-of-the-art planar fabrication techniques with the folding method to produce 3D structures. In this strategy, 2D components can be easily produced by traditional planar techniques, and then, 3D structures are constructed by folding each 2D component to specific orientations. In this way, not only will the advantages of existing planar techniques, such as high precision, programmable patterning, and mass production, be preserved, but the fabrication capability will also be greatly expanded without complex and expensive equipment modification/development. The goal here is to highlight the recent progress of the folding method from the perspective of principles, techniques, and applications, as well as to discuss the existing challenges and future prospectives.

Field responsive mechanical metamaterials

Typically, mechanical metamaterial properties are programmed and set when the architecture is designed and constructed, and do not change in response to shifting environmental conditions or application requirements. We present a new class of architected materials called field responsive mechanical metamaterials (FRMMs) that exhibit dynamic control and on-the-fly tunability enabled by careful design and selection of both material composition and architecture. To demonstrate the FRMM concept, we print complex structures composed of polymeric tubes infilled with magnetorheological fluid suspensions. Modulating remotely applied magnetic fields results in rapid, reversible, and sizable changes of the effective stiffness of our metamaterial motifs.

Frequency domain transformation optics for diffusive photon density waves' cloaking

We make use of transformation optics technique to realize cloaking operation in the light diffusive regime, for spherical objects. The cloak requires spatially heterogeneous anisotropic diffusivity, as well as spatially varying speed of light and absorption. Analytic calculations of Photon's fluence confirm minor role of absorption in reduction of far-field scattering, and a monopole fluence field converging to a constant in the static regime in the invisibility region. The latter is in contrast to acoustic and electromagnetic cloaks, for which the field vanishes inside the core. These results are finally discussed in the context of mass diffusion, where cloaking can be achieved with a heterogeneous anisotropic diffusivity.

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

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

Towards deployable meta-implants

Meta-biomaterials exhibit unprecedented or rare combinations of properties not usually found in nature. Such unusual mechanical, mass transport, and biological properties could be used to develop novel categories of orthopedic implants with superior performance, otherwise known as meta-implants. Here, we use bi-stable elements working on the basis of snap-through instability to design deployable meta-implants. Deployable meta-implants are compact in their retracted state, allowing them to be brought to the surgical site with minimum invasiveness. Once in place, they are deployed to take their full-size load-bearing shape. We designed five types of meta-implants by arranging bi-stable elements in such a way to obtain a radially-deployable structure, three types of auxetic structures, and an axially-deployable structure. The intermediate stable conditions (i.e. multi-stability features), deployment force, and stiffness of the meta-implants were found to be strongly dependent on the geometrical parameters of the bi-stable elements as well as on their arrangement.

Capillary-driven binding of thin triangular prisms at fluid interfaces

We observe capillary-driven binding between thin, equilateral triangular prisms at a flat air-water interface. The edge length of the equilateral triangle face is 120 μm, and the thickness of the prism is varied between 2 and 20 μm. For thickness to length (T/L) ratios of 1/10 or less, pairs of triangles preferentially bind in either tip-to-tip or tip-to-midpoint edge configurations; for pairs of prisms of thickness T/L = 1/5, the tip of one triangle binds to any position along the other triangle's edge. The distinct binding configurations for small T/L ratios result from physical bowing of the prisms, a property that arises during their fabrication. When bowed prisms are placed at the air-water interface, two distinct polarity states arise: prisms either sit with their center of mass above or below the interface. The interface pins to the edge of the prism's concave face, resulting in an interface profile that is similar to that of a capillary hexapole, but with important deviations close to the prism that enable directed binding. We present corresponding theoretical and numerical analysis of the capillary interactions between these prisms and show how prism bowing and contact-line pinning yield a capillary hexapole-like interaction that results in the two sets of distinct, highly-directional binding events. Prisms of all T/L ratios self-assemble into space-spanning open networks; the results suggest design parameters for the fabrication of building blocks of ordered open structures such as the Kagome lattice.

Designing perturbative metamaterials from discrete models

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

Topological guiding of elastic waves in phononic metamaterials based on 2D pentamode structures

A topological state with protected propagation of elastic waves is achieved by appropriately engineering a phononic metamaterial based on 2D pentamode structures in silicon. Gapless edge states in the designed structure, which are characterized by pseudospin-dependent transport, provide backscattering-immune propagation of the elastic wave along bend paths. The role of the states responsible for forward and backward transfer can be interchanged by design.

Direct laser writing for micro-optical devices using a negative photoresist

Direct laser writing (DLW) via two-photon absorption (TPA) has attracted much attention as a new microfabrication technique because it can be applied to fabricate complex, three-dimensional (3D) microstructures. In this study, 3D microstructures and micro-optical devices of micro-lens array on the micrometer scale are fabricated using the negative photoresist SU-8 through TPA with a femtosecond laser pulse under a microscope. The effects of the irradiation conditions on linewidths, such as laser power, writing speed, and writing cycles (a number of times a line is overwritten), are investigated before the fabrication of the 3D microstructures. Various microstructures such as woodpiles, hemisphere and microstructures, 3D micro-lens and micro-lens array for micro-optical devices are fabricated. The shape of the micro-lens is evaluated using the shape analysis mode of a laser microscope to calculate the working distance of the fabricated micro-lenses. The calculated working distance corresponds well to the experimentally measured value. The focusing performance of the fabricated micro-lens is confirmed by the TPA fluorescence of an isopropyl thioxanthone (ITX) ethanol solution excited by a Ti:sapphire femtosecond laser at 800 nm. Micro-lens array (assembled 9 micro-lenses) are fabricated. Nine independent woodpile structures are simultaneously manufactured by DLW via TPA to confirm the multi-focusing ability using the fabricated micro-lens array.

Ultra-low and ultra-broad-band nonlinear acoustic metamaterials

Linear acoustic metamaterials (LAMs) are widely used to manipulate sound; however, it is challenging to obtain bandgaps with a generalized width (ratio of the bandgap width to its start frequency) >1 through linear mechanisms. Here we adopt both theoretical and experimental approaches to describe the nonlinear chaotic mechanism in both one-dimensional (1D) and two-dimensional (2D) nonlinear acoustic metamaterials (NAMs). This mechanism enables NAMs to reduce wave transmissions by as much as 20–40 dB in an ultra-low and ultra-broad band that consists of bandgaps and chaotic bands. With subwavelength cells, the generalized width reaches 21 in a 1D NAM and it goes up to 39 in a 2D NAM, which overcomes the bandwidth limit for wave suppression in current LAMs. This work enables further progress in elucidating the dynamics of NAMs and opens new avenues in double-ultra acoustic manipulation.

Linear acoustic metamaterials based on resonances are generally tunable but limited by their narrow bands. Here, Fang et al. fabricate one- and two-dimensional nonlinear acoustic metamaterials with a broadband, low-frequency, response—greatly suppressing low frequency noise.

Broadband dual-anisotropic solid metamaterials

We have proposed solid elastic metamaterials with anisotropic stiffness and inertial mass simultaneously, denoted as the dual anisotropy, for the potential use of elastic wave controlling. The dual anisotropy has been designed weakly dispersive in a broad frequency range, wherein broadband anisotropic mass is achieved by employing the sliding-interface concept in fluid-solid composites. Results have been validated through the band-structure, effective-medium, and modal-field analyses. We have further found that the proposed solid metamaterial, when its shear stiffness is diminished until neglected, would reduce to the pentamode-inertial material model. This reduced model is the general form of mediums following transformation acoustic theory, which has been proved vital for acoustic wave controlling. Our studies are expected to pave a new route toward broadband acoustic and elastic wave controlling using dual-anisotropic solid metamaterials.

Nanolattices: An Emerging Class of Mechanical Metamaterials

In 1903, Alexander Graham Bell developed a design principle to generate lightweight, mechanically robust lattice structures based on triangular cells; this has since found broad application in lightweight design. Over one hundred years later, the same principle is being used in the fabrication of nanolattice materials, namely lattice structures composed of nanoscale constituents. Taking advantage of the size-dependent properties typical of nanoparticles, nanowires, and thin films, nanolattices redefine the limits of the accessible material-property space throughout different disciplines. Herein, the exceptional mechanical performance of nanolattices, including their ultrahigh strength, damage tolerance, and stiffness, are reviewed, and their potential for multifunctional applications beyond mechanics is examined. The efficient integration of architecture and size-affected properties is key to further develop nanolattices. The introduction of a hierarchical architecture is an effective tool in enhancing mechanical properties, and the eventual goal of nanolattice design may be to replicate the intricate hierarchies and functionalities observed in biological materials. Additive manufacturing and self-assembly techniques enable lattice design at the nanoscale; the scaling-up of nanolattice fabrication is currently the major challenge to their widespread use in technological applications.

Longitudinal elastic wave control by pre-deforming semi-linear materials

An incremental wave superimposed on a pre-deformed hyper-elastic material perceives an elastic media with the instantaneous modulus of the current material. This offers a new route with a broadband feature to control elastic waves by purposely creating finite deformation field. This study proves that the governing equation of a semi-linear material under a symmetric pre-deformation condition maintains the form invariance for longitudinal wave, so the longitudinal wave control can be made by transformation method without the constraint condition on principle stretches; however, this is not the case for shear waves. Therefore, pre-deforming a semi-linear material provides a potential method for treating longitudinal and shear waves differently. Examples with elastic wave control and band structure shift through pre-deforming a semi-linear material are provided to illustrate this finding. Finally, a one-dimensional spring lattice is proposed to mimic a semi-linear material, and the dispersion relation for longitudinal waves in a sandwich structure with such spring lattice is shown to be invariant during elongation, confirming the result found based on a homogeneous semi-linear material. These results may stimulate researches on designing new hyper-elastic microstructures as well as designing new devices based on pre-deformed hyper-elastic materials.

Control and design heat flux bending in thermal devices with transformation optics

We propose a fundamental latent function of control heat transfer and heat flux density vectors at random positions on thermal materials by applying transformation optics. The expressions for heat flux bending are obtained, and the factors influencing them are investigated in both 2D and 3D cloaking schemes. Under certain conditions, more than one degree of freedom of heat flux bending exists corresponding to the temperature gradients of the 3D domain. The heat flux path can be controlled in random space based on the geometrical azimuths, radial positions, and thermal conductivity ratios of the selected materials.

Cleaving Direct-Laser-Written Microstructures on Demand

Using an advanced functional photoresist we introduce direct-laser-written (DLW) 3D microstructures capable of complete degradation on demand. The networks consist exclusively of reversible bonds, formed by irradiation of a phenacyl sulfide linker, giving disulfide bonds in a radical-free step-growth polymerization via a reactive thioaldehyde. The bond formation was verified in solution by ESI-MS. To induce cleavage, dithiothreitol causes a thiol-disulfide exchange, erasing the written structure. The mild cleavage of the disulfide network is highly orthogonal to other, for example, acrylate-based DLW structures. To emphasize this aspect, DLW structures were prepared incorporating reversible structural elements into a non-reversible acrylate-based standard scaffold, confirming subsequent selective cleavage. The high lateral resolution achievable was verified by the preparation of well-defined line gratings with line separations of down to 300 nm.

A simple technique to overcome self-focusing, filamentation, supercontinuum generation, aberrations, depth dependence and waveguide interface roughness using fs laser processing

Several detrimental effects limit the use of ultrafast lasers in multi-photon processing and the direct manufacture of integrated photonics devices, not least, dispersion, aberrations, depth dependence, undesirable ablation at a surface, limited depth of writing, nonlinear optical effects such as supercontinuum generation and filamentation due to Kerr self-focusing. We show that all these effects can be significantly reduced if not eliminated using two coherent, ultrafast laser-beams through a single lens - which we call the Dual-Beam technique. Simulations and experimental measurements at the focus are used to understand how the Dual-Beam technique can mitigate these problems. The high peak laser intensity is only formed at the aberration-free tightly localised focal spot, simultaneously, suppressing unwanted nonlinear side effects for any intensity or processing depth. Therefore, we believe this simple and innovative technique makes the fs laser capable of much more at even higher intensities than previously possible, allowing applications in multi-photon processing, bio-medical imaging, laser surgery of cells, tissue and in ophthalmology, along with laser writing of waveguides.

Top-down, decoupled control of constitutive parameters in electromagnetic metamaterials with dielectric resonators of internal anisotropy

A meta-atom platform providing decoupled tuning for the constitutive wave parameters remains as a challenging problem, since the proposition of Pendry. Here we propose an electromagnetic meta-atom design of internal anisotropy (ε_r ≠ ε_θ), as a pathway for decoupling of the effective- permittivity ε_eff and permeability μ_eff. Deriving effective parameters for anisotropic meta-atom from the first principles, and then subsequent inverse-solving the obtained decoupled solution for a target set of ε_eff and μ_eff, we also achieve an analytic, top-down determination for the internal structure of a meta-atom. To realize the anisotropy from isotropic materials, a particle of spatial permittivity modulation in r or θ direction is proposed. As an application example, a matched zero index dielectric meta-atom is demonstrated, to enable the super-funneling of a 50λ-wide flux through a sub-λ slit; unharnessing the flux collection limit dictated by the λ-zone.

Multi-Component Microscaffold With 3D Spatially Defined Proteinaceous Environment

In this paper, we present a multicomponent microenvironment consisting of proteinaceous networks with submicron-sized features optionally embedded into a photoresist microscaffold. By two-photon direct laser writing, free-standing 3D proteinaceous microstructures were fabricated for cell culture application, demonstrated with NIH/3T3 fibroblast cells. A Young's modulus of megapascal-order contributes to the challenge of structural sustainability of the proteinaceous microstructures for experiments as well as sequential fabrication steps. We propose to embed proteinaceous networks into a mechanically robust photoresist microscaffold. We investigate the limits of this 3D microfabrication of embedded proteinaceous networks and demonstrate the embedment of two different proteinaceous networks within one microscaffold. Performing cell culture of PC12 cells, we observe cell adhesion and cell motility on embedded proteinaceous networks of collagen type-IV mixed with bovine serum albumin into a photoresist microscaffold. The ability to structure proteinaceous elements for 3D spatial control of microenvironment might be a key feature in cell culture to decouple environmental cues to control cellular behavior.

Polarization bandgaps and fluid-like elasticity in fully solid elastic metamaterials

Elastic waves exhibit rich polarization characteristics absent in acoustic and electromagnetic waves. By designing a solid elastic metamaterial based on three-dimensional anisotropic locally resonant units, here we experimentally demonstrate polarization bandgaps together with exotic properties such as 'fluid-like' elasticity. We construct elastic rods with unusual vibrational properties, which we denote as 'meta-rods'. By measuring the vibrational responses under flexural, longitudinal and torsional excitations, we find that each vibration mode can be selectively suppressed. In particular, we observe in a finite frequency regime that all flexural vibrations are forbidden, whereas longitudinal vibration is allowed-a unique property of fluids. In another case, the torsional vibration can be suppressed significantly. The experimental results are well interpreted by band structure analysis, as well as effective media with indefinite mass density and negative moment of inertia. Our work opens an approach to efficiently separate and control elastic waves of different polarizations in fully solid structures.

Analytic materials

The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integerp. Ifptakes its maximum value, then we have a complete analytic material. Otherwise, it is incomplete analytic material of rankp. For two-dimensional materials, further progress can be made in the identification of analytic materials by using the well-known fact that a 90°rotation applied to a divergence-free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.

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.

Negative Poisson's Ratio in Modern Functional Materials

Materials with negative Poisson's ratio attract considerable attention due to their underlying intriguing physical properties and numerous promising applications, particularly in stringent environments such as aerospace and defense areas, because of their unconventional mechanical enhancements. Recent progress in materials with a negative Poisson's ratio are reviewed here, with the current state of research regarding both theory and experiment. The inter-relationship between the underlying structure and a negative Poisson's ratio is discussed in functional materials, including macroscopic bulk, low-dimensional nanoscale particles, films, sheets, or tubes. The coexistence and correlations with other negative indexes (such as negative compressibility and negative thermal expansion) are also addressed. Finally, open questions and future research opportunities are proposed for functional materials with negative Poisson's ratios.