Micro-Scale Auxetic Hierarchical Mechanical Metamaterials for Shape Morphing

Dynamic photomask directed lithography based on electrically stimulated nematic liquid crystal architectures

Lithography technology is a powerful tool for preparing complex microstructures through projecting patterns from static templates with permanent features onto samples. To simplify fabrication and alignment processes, dynamic photomask for multiple configurations preparation becomes increasingly noteworthy. Hereby, we report a dynamic photomask by assembling the electrically stimulated nematic liquid crystal (NLC) into multifarious architectures. This results in reconfigurable and switchable diffraction patterns due to the hybrid phase arising from the NLC molecular orientations. These diffraction patterns are adopted as metamask to produce multiple microstructures with height gradients in one-step exposure and hierarchical microstructures through multiple in-situ exposures using standard photolithography. The fabricated pattern has feature size about 3.2 times smaller than the electrode pattern and can be transferred onto silicon wafer. This strategy can be extended to design diverse microstructures with great flexibility and controllability, offers a promising avenue for fabricating metamaterials via complex structures with simplified lithography processes.

3D Printing of Hierarchical Structures Made of Inorganic Silicon-Rich Glass Featuring Self-Forming Nanogratings

Hierarchical structures are abundant in nature, such as in the superhydrophobic surfaces of lotus leaves and the structural coloration of butterfly wings. They consist of ordered features across multiple size scales, and their advantageous properties have attracted enormous interest in wide-ranging fields including energy storage, nanofluidics, and nanophotonics. Femtosecond lasers, which are capable of inducing various material modifications, have shown promise for manufacturing tailored hierarchical structures. However, existing methods, such as multiphoton lithography and three-dimensional (3D) printing using nanoparticle-filled inks, typically involve polymers and suffer from high process complexity. Here, we demonstrate the 3D printing of hierarchical structures in inorganic silicon-rich glass featuring self-forming nanogratings. This approach takes advantage of our finding that femtosecond laser pulses can induce simultaneous multiphoton cross-linking and self-formation of nanogratings in hydrogen silsesquioxane. The 3D printing process combines the 3D patterning capability of multiphoton lithography and the efficient generation of periodic structures by the self-formation of nanogratings. We 3D-printed micro-supercapacitors with large surface areas and a high areal capacitance of 1 mF/cm2 at an ultrahigh scan rate of 50 V/s, thereby demonstrating the utility of our 3D printing approach for device applications in emerging fields such as energy storage.

Programmable and resilient metamaterials with anisotropic and non-linear mechanical responses composed exclusively of stiff constituents

Recently, significant progress has been made in the field of flexible bulk metamaterials composed of soft and elastic materials, unlocking the potential for achieving programmable non-linear mechanical responses, such as shape morphing, energy absorption, and information processing. However, the majority of these metamaterials utilize expensive hyperelastic materials and require complex fabrication processes. Additionally, constructing eco-friendly stiff constituents for these metamaterials remains challenging due to their limited elastic limit strains (<0.1). Here, we propose a systematic design strategy by combining curved beams with chiral metastructures to generate a family of three-dimensional programmable resilient mechanical metamaterials without relying on flexible or hyperelastic constituents. These tiled metamaterials demonstrate robust, anisotropic and non-linear resilience under large elastic compression strains (>0.75), while exhibiting a programmable effective modulus reduction of nearly 6 orders of magnitude compared to the native stiff components. Furthermore, leveraging their stable resilience under high-frequency stimuli, we successfully developed a meter-scale soft robot capable of traversing complex narrow scenarios on demand without the need for flexible materials or sophisticated pipelines. We anticipate that these mechanical metamaterials could serve as a universal platform for programmable active dampers, modular flexible robots, and medical rehabilitation equipment at various scales.

Auxeticity Tuning by Nanolayer Inclusion Ordering in Hard Sphere Crystals

Designing a particular change in a system structure to achieve the desired elastic properties of materials for a given task is challenging. Recent studies of purely geometrical atomic models have shown that structural modifications on a molecular level can lead to interesting and desirable elastic properties. Still, the result of such changes is usually difficult to predict. The present work concerns the impact of nanolayer inclusion ordering in hard sphere crystals on their elastic properties, with special attention devoted to their auxetic properties. Two sets of representative models, based on cubic crystals consisting of 6×6×6 unit cells of hard spheres and containing either neighboring or separated layers of spheres of another diameter, oriented orthogonally to the [001] direction, have been studied by Monte Carlo simulations in the isothermal-isobaric (NpT) ensemble. Their elastic constants have been evaluated using the Parinello-Rahman approach. The Monte Carlo simulations showed that introducing the layer inclusions into a pure face-centered cubic (FCC) structure leads to the system's symmetry changes from cubic symmetry to tetragonal in both cases. Essential changes in the elastic properties of the systems due to layer ordering were found both for neighboring and separated inclusions. It has been found that the choice of a set of layer inclusions allows one to tune the auxetic properties in two crystallographic directions ([110][11¯0] and [101][1¯01]). In particular, this study revealed that the change in layer ordering (from six separated layers to six neighboring ones) allows for, respectively: (i) enhancing auxeticity of the system in the [101][1¯01] direction with almost loss of auxetic properties in the [110][11¯0] direction in the case of six separated layers, while (ii) in the case of six neighboring layers, keeping the auxetic properties in both auxetic directions independently of the size of spheres constituting inclusions.

Assembled mechanical metamaterials with integrated functionalities of programmable multistability and multitransition behaviors

Mechanical metamaterials with integrated functionalities can simultaneously fulfill multiple design requirements through design consolidation, which is highly desirable for weight-sensitive and space-constrained applications. Despite the extensive research on multistable metamaterials, their integration with other functionalities, such as vibration isolation, sensing, and hierarchical energy absorption, remains largely untapped. Here, we report a novel class of mechanical metamaterial featuring programmable multistability and function-oriented multitransition behaviors. This integration is realized through a novel assembly-based design concept that incorporates interchangeable contact block (CB) units into a classical bistable structure. By varying the position, number, and shape of CB units, we can obtain a spectrum of function-oriented transition behaviors, offering reconfigurability through unit replacement. To ensure the rational design of CB, we employ a comprehensive approach that combines theoretical analysis, numerical simulations, and experimental validation to investigate the nonlinear behaviors of these assembled metamaterials, including snap-through instability and contact behaviors. Additionally, we explore design strategies such as 2D arraying and 3D extension to achieve programmable multistability. Furthermore, we demonstrate the versatility of these assembled mechanical metamaterials by constructing digital materials with scalability, reconfigurability, and multidirectionality. The proposed assembly-based design concept breaks new ground in engineering multistable structures with integrated functionalities for deployable structures, robotics, and beyond.

Hybrid-Microstructure-Based Soft Network Materials with Independent Tunability of Mechanical Properties over Large Deformations

Introducing auxetic metamaterials into stretchable electronics shows promising prospects for enhancing the performance and innovating the functionalities of various devices, such as stretchable strain sensors. Nevertheless, most existing auxetics fail to meet the requirement of stretchable electronics, which typically include high mechanical flexibility and stable Poisson's ratio over large deformations. Moreover, despite being highly advantageous for application in diverse load-bearing conditions, achieving tunability of J-shaped stress-strain response independent of negative Poisson's ratio remains a significant challenge. This paper introduces a class of hybrid-microstructure-based soft network materials (HMSNMs) consisting of different types of microstructures along the loading and transverse directions. The J-shaped stress-strain curve and nonlinear Poisson's ratio for HMSNMs can be tuned independently of each other. The HMSNM provides much higher strength than the corresponding existing metamaterial while offering a nearly stable negative Poisson's ratio over large strains. Both mechanical properties under infinitesimal and large deformations can be well-tuned by geometric parameters. Fascinating functionalities such as shape programming and stress regulation are achieved by integrating a set of HMSNMs in series/parallel configurations. A stretchable LED-integrated display capable of displaying dynamic images without distortion under uniaxial stretching serves as a demonstrative application.

Direct laser writing-enabled 3D printing strategies for microfluidic applications

Over the past decade, additive manufacturing-or "three-dimensional (3D) printing"-has attracted increasing attention in the Lab on a Chip community as a pathway to achieve sophisticated system architectures that are difficult or infeasible to fabricate via conventional means. One particularly promising 3D manufacturing technology is "direct laser writing (DLW)", which leverages two-photon (or multi-photon) polymerization (2PP) phenomena to enable high geometric versatility, print speeds, and precision at length scales down to the 100 nm range. Although researchers have demonstrated the potential of using DLW for microfluidic applications ranging from organ on a chip and drug delivery to micro/nanoparticle processing and soft microrobotics, such scenarios present unique challenges for DLW. Specifically, microfluidic systems typically require macro-to-micro fluidic interfaces (e.g., inlet and outlet ports) to facilitate fluidic loading, control, and retrieval operations; however, DLW-based 3D printing relies on a micron-to-submicron-sized 2PP volume element (i.e., "voxel") that is poorly suited for manufacturing these larger-scale fluidic interfaces. In this Tutorial Review, we highlight and discuss the four most prominent strategies that researchers have developed to circumvent this trade-off and realize macro-to-micro interfaces for DLW-enabled microfluidic components and systems. In addition, we consider the possibility that-with the advent of next-generation commercial DLW printers equipped with new dynamic voxel tuning, print field, and laser power capabilities-the overall utility of DLW strategies for Lab on a Chip fields may soon expand dramatically.

3D Tiled Auxetic Metamaterial: A New Family of Mechanical Metamaterial with High Resilience and Mechanical Hysteresis

For artificial materials, desired properties often conflict. For example, engineering materials often achieve high energy dissipation by sacrificing resilience and vice versa, or desired auxeticity by losing their isotropy, which limits their performance and applications. To solve these conflicts, a strategy is proposed to create novel mechanical metamaterial via 3D space filling tiles with engaging key-channel pairs, exemplified via auxetic 3D keyed-octahedron-cuboctahedron metamaterials. This metamaterial shows high resilience while achieving large mechanical hysteresis synergistically under large compressive strain. Especially, this metamaterial exhibits ideal isotropy approaching the theoretical limit of isotropic Poisson's ratio, -1, as rarely seen in existing 3D mechanical metamaterials. In addition, the new class of metamaterials provides wide tunability on mechanical properties and behaviors, including an unusual coupled auxeticity and twisting behavior under normal compression. The designing methodology is illustrated by the integral of numerical modeling, theoretical analysis, and experimental characterization. The new mechanical metamaterials have broad applications in actuators and dampers, soft robotics, biomedical materials, and engineering materials/systems for energy dissipation.

Bone cell response to additively manufactured 3D micro-architectures with controlled Poisson's ratio: Auxetic vs. non-auxetic meta-biomaterials

The Poisson's ratio and elastic modulus are two parameters determining the elastic behavior of biomaterials. While the effects of elastic modulus on the cell response is widely studied, very little is known regarding the effects of the Poisson's ratio. The micro-architecture of meta-biomaterials determines not only the Poisson's ratio but also several other parameters that also influence cell response, such as porosity, pore size, and effective elastic modulus. It is, therefore, very challenging to isolate the effects of the Poisson's ratio from those of other micro-architectural parameters. Here, we computationally design meta-biomaterials with controlled Poisson's ratios, ranging between -0.74 and +0.74, while maintaining consistent porosity, pore size, and effective elastic modulus. The 3D meta-biomaterials were additively manufactured at the micro-scale using two-photon polymerization (2PP), and were mechanically evaluated at the meso‑scale. The response of murine preosteoblasts to these meta-biomaterials was then studied using in vitro cell culture models. Meta-biomaterials with positive Poisson's ratios resulted in higher metabolic activity than those with negative values. The cells could attach and infiltrate all meta-biomaterials from the bottom to the top, fully covering the scaffolds after 17 days of culture. Interestingly, the meta-biomaterials exhibited different cell-induced deformations (e.g., shrinkage or local bending) as observed via scanning electron microscopy. The outcomes of osteogenic differentiation (i.e., Runx2 immunofluorescent staining) and matrix mineralization (i.e., Alizarin red staining) assays indicated the significant potential impact of these meta-biomaterials in the field of bone tissue engineering, paving the way for the development of advanced bone meta-implants. STATEMENT OF SIGNIFICANCE: We studied the influence of Poisson's ratio on bone cell response in meta-biomaterials. While elastic modulus effects are well-studied, the impact of Poisson's ratio, especially negative values found in architected biomaterials, remains largely unexplored. The complexity arises from intertwined micro-architectural parameters, such as porosity and elastic modulus, making it challenging to isolate the Poisson's ratio. To overcome this limitation, this study employed rational computational design to create meta-biomaterials with controlled Poisson's ratios, alongside consistent effective elastic modulus, porosity, and pore size. The study reveals that two-photon polymerized 3D meta-biomaterials with positive Poisson's ratios displayed higher metabolic activity, while all the developed meta-biomaterials supported osteogenic differentiation of preosteoblasts as well as matrix mineralization. The outcomes pave the way for the development of advanced 3D bone tissue models and meta-implants.

Directional actuation and phase transition-like behavior in anisotropic networks of responsive microfibers

Two-dimensional shape-morphing networks are common in biological systems and have garnered attention due to their nontrivial physical properties that emanate from their cellular nature. Here, we present the fabrication and characterization of anisotropic shape-morphing networks composed of thermoresponsive polymeric microfibers. By strategically positioning fibers with varying responses, we construct networks that exhibit directional actuation. The individual segments within the network display either a linear extension or buckling upon swelling, depending on their radius and length, and the transition between these morphing behaviors resembles Landau's second-order phase transition. The microscale variations in morphing behaviors are translated into observable macroscopic effects, wherein regions undergoing linear expansion retain their shape upon swelling, whereas buckled regions demonstrate negative compressibility and shrink. Manipulating the macroscale morphing by adjusting the properties of the fibrous microsegments offers a means to modulate and program morphing with mesoscale precision and unlocks novel opportunities for developing programmable microscale soft robotics and actuators.

Folk arts-inspired twice-coagulated configuration-editable tough aerogels enabled by transformable gel precursors

Aerogels, as famous lightweight and porous nanomaterials, have attracted considerable attention in various emerging fields in recent decades, however, both low density and weak mechanical performance make their configuration-editing capability challenging. Inspired by folk arts, herein we establish a highly efficient twice-coagulated (TC) strategy to fabricate configuration-editable tough aerogels enabled by transformable gel precursors. As a proof of concept, aramid nanofibers (ANFs) and polyvinyl alcohol (PVA) are selected as the main components of aerogel, among which PVA forms a flexible configuration-editing gel network in the first coagulation process, and ANF forms a configuration-locking gel network in the second coagulation process. TC strategy guarantees the resulting aerogels with both high toughness and feasible configuration editing capability individually or simultaneously. Altogether, the resulting tough aerogels with special configuration through soft to hard modulation provide great opportunities to break through the performance limits of the aerogels and expand application areas of aerogels.

Hardening of fcc hard-sphere crystals by introducing nanochannels: Auxetic aspects

Tailoring the materials for a given task by modifying their elastic properties is attractive to material scientists. However, recent studies of purely geometrical atomic models with structural modifications showed that designing a particular change to achieve the desired elastic properties is complex. This work concerns the impact of nanochannel inclusions in fcc hard sphere crystal on its elastic properties, especially auxetic ones. The models containing six nanochannel arrays of spheres of another diameter, oriented along the [110]-direction and its symmetric equivalents, have been studied by Monte Carlo simulations in the isothermal-isobaric (NpT) ensemble using the Parinello-Rahman approach. The inclusions have been designed such that they do not affect the cubic symmetry of the crystal. The elastic properties of three different models containing inclusions of various sizes are investigated under four thermodynamic conditions. We find that six nanochannels filled with hard spheres of larger diameter increase system stiffness compared with the fcc crystal without nanoinclusions. The current finding contrasts the recently reported results [J.W. Narojczyk et al. Phys. Status Solidi B 259, 2200464 (2022)0370-197210.1002/pssb.202200464], where the fcc hard sphere crystal with four nanochannels shows reduced stiffness compared to the system without nanoinclusions. Moreover, the six nanochannel models preserve auxetic properties in contrast to the fcc hard sphere crystal with four nanochannel arrays, which loses auxeticity.

Non-reciprocal and non-Newtonian mechanical metamaterials

Non-Newtonian liquids are characterized by stress and velocity-dependent dynamical response. In elasticity, and in particular, in the field of phononics, reciprocity in the equations acts against obtaining a directional response for passive media. Active stimuli-responsive materials have been conceived to overcome it. Significantly, Milton and Willis have shown theoretically in 2007 that quasi-rigid bodies containing masses at resonance can display a very rich dynamical behavior, hence opening a route toward the design of non-reciprocal and non-Newtonian metamaterials. In this paper, we design a solid structure that displays unidirectional shock resistance, thus going beyond Newton's second law in analogy to non-Newtonian fluids. We design the mechanical metamaterial with finite element analysis and fabricate it using three-dimensional printing at the centimetric scale (with fused deposition modeling) and at the micrometric scale (with two-photon lithography). The non-Newtonian elastic response is measured via dynamical velocity-dependent experiments. Reversing the direction of the impact, we further highlight the intrinsic non-reciprocal response.

Micro-Scale Mechanical Metamaterial with a Controllable Transition in the Poisson's Ratio and Band Gap Formation

The ability to significantly change the mechanical and wave propagation properties of a structure without rebuilding it is currently one of the main challenges in the field of mechanical metamaterials. This stems from the enormous appeal that such tunable behavior may offer from the perspective of applications ranging from biomedical to protective devices, particularly in the case of micro-scale systems. In this work, a novel micro-scale mechanical metamaterial is proposed that can undergo a transition from one type of configuration to another, with one configuration having a very negative Poisson's ratio, corresponding to strong auxeticity, and the other having a highly positive Poisson's ratio. The formation of phononic band gaps can also be controlled concurrently which can be very useful for the design of vibration dampers and sensors. Finally, it is experimentally shown that the reconfiguration process can be induced and controlled remotely through application of a magnetic field by using appropriately distributed magnetic inclusions.

3D Auxetic Metamaterials with Elastically-Stable Continuous Phase Transition

In solid state physics, phase transitions can influence material functionality and alter their properties. In mechanical metamaterials, structural-phase transitions can be achieved through instability or buckling of certain structural elements. However, these fast transitions in one mechanical parameter typically affect significantly the remaining parameters, hence, limiting their applications. Here, this limitation is addressed by designing a novel 3D mechanical metamaterial that is capable of undergoing a phase transition from positive to negative Poisson's ratio under compression, without significant degradation of Young's modulus (i.e. the phase transition is elastically-stable). The metamaterial is fabricated by two-photon lithography at the micro-scale and its mechanical behavior is assessed experimentally. For another choice of structural parameters, it is then shown that the auxetic behavior of the considered 3D metamaterial class can be maintained over a wide range of applied compressive strain.

Additively Manufactured Hierarchical Auxetic Mechanical Metamaterials

Due to the ability to create structures with complex geometry at micro- and nanoscales, modern additive technologies make it possible to produce artificial materials (metamaterials) with properties different from those of conventional materials found in nature. One of the classes with special properties is auxetic materials-materials with a negative Poisson's ratio. In the review, we collect research results on the properties of auxetics, based on analytical, experimental and numerical methods. Special attention of this review is paid to the consideration of the results obtained in studies of hierarchical auxetic materials. The wide interest in the hierarchical subclass of auxetics is explained by the additional advantages of structures, such as more flexible adjustment of the desired mechanical characteristics (the porosity, stiffness, specific energy absorption, degree of material release, etc.). Possibilities of biomedical applications of hierarchical auxetic materials, such as coronary stents, filtration and drug delivery systems, implants and many others, where the ability for high-precision tuning is required, are underlined.

Brillouin Light Scattering Characterisation of Gray Tone 3D Printed Isotropic Materials

Three-dimensional direct laser writing technology enables one to print polymer microstructures whose size varies from a few hundred nanometers to a few millimeters. It has been shown that, by tuning the laser power during writing, one can adjust continuously the optical and elastic properties with the same base material. This process is referred to as gray-tone lithography. In this paper, we characterize by Brillouin light scattering the complex elastic constant C11 of different reticulated isotropic polymers, at longitudinal phonon frequencies of the order of 16 GHz. We estimate the real part of the C11 constant to vary from 7 to 11 GPa as a function of laser power, whereas its imaginary part varies between 0.25 and 0.6 GPa. The linear elastic properties are further measured at a fixed laser power as a function of temperature, from 20∘C to 80∘C. Overall, we show that our 3D printed samples have a good elastic quality with high Q factors only ten times smaller than fused silica at hypersonic frequencies.