Ultrahigh Energy Absorption Multifunctional Spinodal Nanoarchitectures

Unifying the design space and optimizing linear and nonlinear truss metamaterials by generative modeling

The rise of machine learning has fueled the discovery of new materials and, especially, metamaterials-truss lattices being their most prominent class. While their tailorable properties have been explored extensively, the design of truss-based metamaterials has remained highly limited and often heuristic, due to the vast, discrete design space and the lack of a comprehensive parameterization. We here present a graph-based deep learning generative framework, which combines a variational autoencoder and a property predictor, to construct a reduced, continuous latent representation covering an enormous range of trusses. This unified latent space allows for the fast generation of new designs through simple operations (e.g., traversing the latent space or interpolating between structures). We further demonstrate an optimization framework for the inverse design of trusses with customized mechanical properties in both the linear and nonlinear regimes, including designs exhibiting exceptionally stiff, auxetic, pentamode-like, and tailored nonlinear behaviors. This generative model can predict manufacturable (and counter-intuitive) designs with extreme target properties beyond the training domain.

Dynamic diagnosis of metamaterials through laser-induced vibrational signatures

Mechanical metamaterials at the microscale exhibit exotic static properties owing to their engineered building blocks1-4, but their dynamic properties have remained substantially less explored. Their design principles can target frequency-dependent properties5-7 and resilience under high-strain-rate deformation8,9, making them versatile materials for applications in lightweight impact resistance10-12, acoustic waveguiding7,13 or vibration damping14,15. However, accessing dynamic properties at small scales has remained a challenge owing to low-throughput and destructive characterization8,16,17 or lack of existing testing protocols. Here we demonstrate a high-throughput, non-contact framework that uses MHz-wave-propagation signatures within a metamaterial to non-destructively extract dynamic linear properties, omnidirectional elastic information, damping properties and defect quantification. Using rod-like tessellations of microscopic metamaterials, we report up to 94% direction-dependent and rate-dependent dynamic stiffening at strain rates approaching 102 s-1, as well as damping properties three times higher than their constituent materials. We also show that frequency shifts in the vibrational response allow for characterization of invisible defects within the metamaterials and that selective probing allows for the construction of experimental elastic surfaces, which were previously only possible computationally. Our work provides a route for accelerated data-driven discovery of materials and microdevices for dynamic applications such as protective structures, medical ultrasound or vibration isolation.

Experiment Investigation of the Compression Behaviors of Nickel-Coated Hybrid Lattice Structure with Enhanced Mechanical Properties

The lattice metamaterial has attracted extensive attention due to its excellent specific strength, energy absorption capacity, and strong designability of the cell structure. This paper aims to explore the functional nickel plating on the basis of biomimetic-designed lattice structures, in order to achieve higher stiffness, strength, and energy absorption characteristics. Two typical structures, the body-centered cubic (BCC) lattice and the bioinspired hierarchical circular lattice (HCirC), were considered. The BCC and HCirC lattice templates were prepared based on DLP (digital light processing) 3D printing. Based on this, chemical plating, as well as the composite plating of chemical plating followed by electroplating, was carried out to prepare the corresponding nickel-plated lattice structures. The mechanical properties and deformation failure mechanisms of the resin-based lattice, chemically plated lattice, and composite electroplated lattice structures were studied by using compression experiments. The results show that the metal coating can significantly improve the mechanical properties and energy absorption capacity of microlattices. For example, for the HCirC structure with the loading direction along the x-axis, the specific strength, specific stiffness, and specific energy absorption after composite electroplating increased by 546.9%, 120.7%, and 2113.8%, respectively. The shell-core structure formed through composite electroplating is the main factor for improving the mechanical properties of the lattice metamaterial. In addition, the functional nickel plating based on biomimetic structure design can further enhance the improvement space of mechanical performance. The research in this paper provides insights for exploring lighter and stronger lattice metamaterials and their multifunctional applications.

Machine learning unifies flexibility and efficiency of spinodal structure generation for stochastic biomaterial design

Porous biomaterials design for bone repair is still largely limited to regular structures (e.g. rod-based lattices), due to their easy parameterization and high controllability. The capability of designing stochastic structure can redefine the boundary of our explorable structure-property space for synthesizing next-generation biomaterials. We hereby propose a convolutional neural network (CNN) approach for efficient generation and design of spinodal structure-an intriguing structure with stochastic yet interconnected, smooth, and constant pore channel conducive to bio-transport. Our CNN-based approach simultaneously possesses the tremendous flexibility of physics-based model in generating various spinodal structures (e.g. periodic, anisotropic, gradient, and arbitrarily large ones) and comparable computational efficiency to mathematical approximation model. We thus successfully design spinodal bone structures with target anisotropic elasticity via high-throughput screening, and directly generate large spinodal orthopedic implants with desired gradient porosity. This work significantly advances stochastic biomaterials development by offering an optimal solution to spinodal structure generation and design.

Toughness Amplification via Controlled Nanostructure in Lightweight Nano-Bouligand Materials

The enhanced properties of nanomaterials make them attractive for advanced high-performance materials, but their role in promoting toughness has been unclear. Fabrication challenges often prevent the proper organization of nanomaterial constituents, and inadequate testing methods have led to a poor knowledge of toughness at small scales. In this work, the individual roles of nanomaterials and nanoarchitecture on toughness are quantified by creating lightweight materials made from helicoidal polymeric nanofibers (nano-Bouligand). Unidirectional ( θ $\theta $  = 0°) and nano-Bouligand beams ( θ $\theta $  = 2°-90°) are fabricated using two-photon lithography and are designed in a micro-single edge notch bend (µ-SENB) configuration with relative densities ρ ¯ $\overline \rho $ between 48% and 81%. Experiments demonstrate two unique toughening mechanisms. First, size-enhanced ductility of nanoconfined polymer fibers increases specific fracture energy by 70% in the 0° unidirectional beams. Second, nanoscale stiffness heterogeneity created via inter-layer fiber twisting impedes crack growth and improves absolute fracture energy dissipation by 48% in high-density nano-Bouligand materials. This demonstration of size-enhanced ductility and nanoscale heterogeneity as coexisting toughening mechanisms reveals the capacity for nanoengineered materials to greatly improve mechanical resilience in a new generation of advanced materials.

Bioinspired Nanonetwork Hydroxyapatite from Block Copolymer Templated Synthesis for Mechanical Metamaterials

Inspired by Mantis shrimp, this work aims to suggest a bottom-up approach for the fabrication of nanonetwork hydroxyapatite (HAp) thin film using self-assembled polystyrene-block-polydimethylsiloxane (PS-b-PDMS) block copolymer (BCP) with a diamond nanostructure as a template for templated sol-gel reaction. By introducing poly(vinylpyrrolidone) (PVP) into precursors of calcium nitrate tetrahydrate and triethyl phosphite, which limits the growth of forming HAp nanoparticles, well-ordered nanonetwork HAp thin film can be fabricated. Based on nanoindentation results, the well-ordered nanonetwork HAp shows high energy dissipation compared to the intrinsic HAp. Moreover, the uniaxial microcompression test for the nanonetwork HAp shows high energy absorption per volume and high compression strength, outperforming many cellular materials due to the topologic effect of the well-ordered network at the nanoscale. This work highlights the potential of exploiting BCP templated synthesis to fabricate ionic solid materials with a well-ordered nanonetwork monolith, giving rise to the brittle-to-ductile transition, and thus appealing mechanical properties with the character of mechanical metamaterials.

Achieving the theoretical limit of strength in shell-based carbon nanolattices

Recent developments in mechanical metamaterials exemplify a new paradigm shift called mechanomaterials, in which mechanical forces and designed geometries are proactively deployed to program material properties at multiple scales. Here, we designed shell-based micro-/nanolattices with I-WP (Schoen's I-graph-wrapped package) and Neovius minimal surface topologies. Following the designed topologies, polymeric microlattices were fabricated via projection microstereolithography or two-photon lithography, and pyrolytic carbon nanolattices were created through two-photon lithography and subsequent pyrolysis. The shell thickness of created lattice metamaterials varies over three orders of magnitude from a few hundred nanometers to a few hundred micrometers, covering a wider range of relative densities than most plate-based micro-/nanolattices. In situ compression tests showed that the measured modulus and strength of our shell-based micro-/nanolattices with I-WP topology are superior to those of the optimized plate-based lattices with cubic and octet plate unit cells and truss-based lattices. More strikingly, when the density is larger than 0.53 g cm^-3, the strength of shell-based pyrolytic carbon nanolattices with I-WP topology was found to achieve its theoretical limit. In addition, our shell-based carbon nanolattices exhibited an ultrahigh strength of 3.52 GPa, an ultralarge fracture strain of 23%, and an ultrahigh specific strength of 4.42 GPa g^-1 cm³, surpassing all previous micro-/nanolattices at comparable densities. These unprecedented properties can be attributed to the designed topologies inducing relatively uniform strain energy distributions and avoiding stress concentrations as well as the nanoscale feature size. Our study demonstrates a mechanomaterial route to design and synthesize micro-/nanoarchitected materials.

Nanoarchitected metal/ceramic interpenetrating phase composites

Architected metals and ceramics with nanoscale cellular designs, e.g., nanolattices, are currently subject of extensive investigation. By harnessing extreme material size effects, nanolattices demonstrated classically inaccessible properties at low density, with exceptional potential for superior lightweight materials. This study expands the concept of nanoarchitecture to dense metal/ceramic composites, presenting co-continuous architectures of three-dimensional printed pyrolytic carbon shell reinforcements and electrodeposited nickel matrices. We demonstrate ductile compressive deformability with elongated ultrahigh strength plateaus, resulting in an extremely high combination of compressive strength and strain energy absorption. Simultaneously, property-to-weight ratios outperform those of lightweight nanolattices. Superior to cellular nanoarchitectures, interpenetrating nanocomposites may combine multiple size-dependent characteristics, whether mechanical or functional, which are radically antagonistic in existing materials. This provides a pathway toward previously unobtainable multifunctionality, extending far beyond lightweight structure applications.

Optimally-Tailored Spinodal Architected Materials for Multiscale Design and Manufacturing

Spinodal architected materials with tunable anisotropy unify optimal design and manufacturing of multiscale structures. By locally varying the spinodal class, orientation, and porosity during topology optimization, a large portion of the anisotropic material space is exploited such that material is efficiently placed along principal stress trajectories at the microscale. Additionally, the bicontinuous, nonperiodic, unstructured, and stochastic nature of spinodal architected materials promotes mechanical and biological functions not explicitly considered during optimization (e.g., insensitivity to imperfections, fluid transport conduits). Furthermore, in contrast to laminated composites or periodic, structured architected materials (e.g., lattices), the functional representation of spinodal architected materials leads to multiscale, optimized designs with clear physical interpretation that can be manufactured directly, without special treatment at spinodal transitions. Physical models of the optimized, spinodal-embedded parts are manufactured using a scalable, voxel-based strategy to communicate with a masked stereolithography (m-SLA) 3D printer.

Inverting the structure-property map of truss metamaterials by deep learning

Inspired by crystallography, the periodic assembly of trusses into architected materials has enjoyed popularity for more than a decade and produced countless cellular structures with beneficial mechanical properties. Despite the successful and steady enrichment of the truss design space, the inverse design has remained a challenge: While predicting effective truss properties is now commonplace, efficiently identifying architectures that have homogeneous or spatially varying target properties has remained a roadblock to applications from lightweight structures to biomimetic implants. To overcome this gap, we propose a deep-learning framework, which combines neural networks with enforced physical constraints, to predict truss architectures with fully tailored anisotropic stiffness. Trained on millions of unit cells, it covers an enormous design space of topologically distinct truss lattices and accurately identifies architectures matching previously unseen stiffness responses. We demonstrate the application to patient-specific bone implants matching clinical stiffness data, and we discuss the extension to spatially graded cellular structures with locally optimal properties.

Ultra-low-density digitally architected carbon with a strutted tube-in-tube structure

Porous materials with engineered stretching-dominated lattice designs, which offer attractive mechanical properties with ultra-light weight and large surface area for wide-ranging applications, have recently achieved near-ideal linear scaling between stiffness and density. Here, rather than optimizing the microlattice topology, we explore a different approach to strengthen low-density structural materials by designing tube-in-tube beam structures. We develop a process to transform fully dense, three-dimensional printed polymeric beams into graphitic carbon hollow tube-in-tube sandwich morphologies, where, similar to grass stems, the inner and outer tubes are connected through a network of struts. Compression tests and computational modelling show that this change in beam morphology dramatically slows down the decrease in stiffness with decreasing density. In situ pillar compression experiments further demonstrate large deformation recovery after 30-50% compression and high specific damping merit index. Our strutted tube-in-tube design opens up the space and realizes highly desirable high modulus-low density and high modulus-high damping material structures.

Scalable Fabrication of High-Performance Thin-Shell Oxide Nanoarchitected Materials via Proximity-Field Nanopatterning

Nanoarchitected materials are considered as a promising research field, deriving distinctive mechanical properties by combining nanomechanical size effects with conventional structural engineering. Despite the successful demonstration of the superiority and feasibility of nanoarchitected materials, scalable and facile fabrication techniques capable of macroscopically producing such materials at a low cost are required to take advantage of the nanoarchitected materials for specific applications. Unlike conventional techniques, proximity-field nanopatterning (PnP) is capable of simultaneously obtaining high spatial resolution and mass producibility in synthesizing such nanoarchitected materials in the form of an inch-scale film. Herein, we focus on the feasibility of using PnP as a scalable fabrication technique for three-dimensional nanostructures and the superiority of the resultant thin-shell oxide nanoarchitected materials for specific applications, such as lightweight structural materials, mechanically robust nanocomposites, and high-performance piezoelectric materials. This review will discuss and summarize the relevant results obtained for nanoarchitected materials synthesized by PnP and provide suggestions for future research directions for scalable manufacturing and application.

Tensegrity Metamaterials: Toward Failure-Resistant Engineering Systems through Delocalized Deformation

Failure of materials and structures is inherently linked to localized mechanisms, from shear banding in metals, to crack propagation in ceramics and collapse of space-trusses after buckling of individual struts. In lightweight structures, localized deformation causes catastrophic failure, limiting their application to small strain regimes. To ensure robustness under real-world nonlinear loading scenarios, overdesigned linear-elastic constructions are adopted. Here, the concept of delocalized deformation as a pathway to failure-resistant structures and materials is introduced. Space-tileable tensegrity metamaterials achieving delocalized deformation via the discontinuity of their compression members are presented. Unprecedented failure resistance is shown, with up to 25-fold enhancement in deformability and orders of magnitude increased energy absorption capability without failure over same-strength state-of-the-art lattice architectures. This study provides important groundwork for design of superior engineering systems, from reusable impact protection systems to adaptive load-bearing structures.

3D-printed cellular tips for tuning fork atomic force microscopy in shear mode

Conventional atomic force microscopy (AFM) tips have remained largely unchanged in nanomachining processes, constituent materials, and microstructural constructions for decades, which limits the measurement performance based on force-sensing feedbacks. In order to save the scanning images from distortions due to excessive mechanical interactions in the intermittent shear-mode contact between scanning tips and sample, we propose the application of controlled microstructural architectured material to construct AFM tips by exploiting material-related energy-absorbing behavior in response to the tip–sample impact, leading to visual promotions of imaging quality. Evidenced by numerical analysis of compressive responses and practical scanning tests on various samples, the essential scanning functionality and the unique contribution of the cellular buffer layer to imaging optimization are strongly proved. This approach opens new avenues towards the specific applications of cellular solids in the energy-absorption field and sheds light on novel AFM studies based on 3D-printed tips possessing exotic properties.

The authors investigate 3D-printed tips, based on controlled microstructural architectured materials, as probes for shear-mode atomic force microscopy. They demonstrate that the tailored stiffness and energy-absorbing behaviour of the material are beneficial for improving image quality.

Pushing and Pulling on Ropes: Hierarchical Woven Materials

Hierarchy in natural and synthetic materials has been shown to grant these architected materials properties unattainable independently by their constituent materials. While exceptional mechanical properties such as extreme resilience and high deformability have been realized in many human-made three-dimensional (3D) architected materials using beam-and-junction-based architectures, stress concentrations and constraints induced by the junctions limit their mechanical performance. A new hierarchical architecture in which fibers are interwoven to construct effective beams is presented. In situ tension and compression experiments of additively manufactured woven and monolithic lattices with 30 µm unit cells demonstrate the superior ability of woven architectures to achieve high tensile and compressive strains (>50%)-without failure events-via smooth reconfiguration of woven microfibers in the effective beams and junctions. Cyclic compression experiments reveal that woven lattices accrue less damage compared to lattices with monolithic beams. Numerical studies of woven beams with varying geometric parameters present new design spaces to develop architected materials with tailored compliance that is unachievable by similarly configured monolithic-beam architectures. Woven hierarchical design offers a pathway to make traditionally stiff and brittle materials more deformable and introduces a new building block for 3D architected materials with complex nonlinear mechanics.

Thermal post-curing as an efficient strategy to eliminate process parameter sensitivity in the mechanical properties of two-photon polymerized materials

Two-photon polymerization direct laser writing (TPP-DLW) is one of the most versatile technologies to additively manufacture complex parts with nanoscale resolution. However, the wide range of mechanical properties that results from the chosen combination of multiple process parameters imposes an obstacle to its widespread use. Here we introduce a thermal post-curing route as an effective and simple method to increase the mechanical properties of acrylate-based TPP-DLW-derived parts by 20-250% and to largely eliminate the characteristic coupling of processing parameters, material properties and part functionality. We identify the underlying mechanism of the property enhancement as a self-initiated thermal curing reaction, which robustly facilitates the high property reproducibility that is essential for any application of TPP-DLW.

Plate-nanolattices at the theoretical limit of stiffness and strength

Though beam-based lattices have dominated mechanical metamaterials for the past two decades, low structural efficiency limits their performance to fractions of the Hashin-Shtrikman and Suquet upper bounds, i.e. the theoretical stiffness and strength limits of any isotropic cellular topology, respectively. While plate-based designs are predicted to reach the upper bounds, experimental verification has remained elusive due to significant manufacturing challenges. Here, we present a new class of nanolattices, constructed from closed-cell plate-architectures. Carbon plate-nanolattices are fabricated via two-photon lithography and pyrolysis and shown to reach the Hashin-Shtrikman and Suquet upper bounds, via in situ mechanical compression, nano-computed tomography and micro-Raman spectroscopy. Demonstrating specific strengths surpassing those of bulk diamond and average performance improvements up to 639% over the best beam-nanolattices, this study provides detailed experimental evidence of plate architectures as a superior mechanical metamaterial topology.

Plate-lattices are predicted to reach the upper bounds of strength and stiffness compared to traditional beam-lattices, but they are difficult to manufacture. Here, the authors use two-photon polymerization 3D-printing and pyrolysis to make carbon plate-nanolattices which reach those theoretical bounds, making them up to 639% stronger than beam-nanolattices.