An elasto-mechanical unfeelability cloak made of pentamode metamaterials

Inherent Temporal Metamaterials with Unique Time-Varying Stiffness and Damping

Time-varying metamaterials offer new degrees of freedom for wave manipulation and enable applications unattainable with conventional materials. In these metamaterials, the pattern of temporal inhomogeneity is crucial for effective wave control. However, existing studies have only demonstrated abrupt changes in properties within a limited range or time modulation following simple patterns. This study presents the design, construction, and characterization of a novel temporal elastic metamaterial with complex time-varying constitutive parameters induced by self-reconfigurable virtual resonators (VRs). These VRs, achieved by simulating the resonating behavior of mechanical resonators in digital space, function as virtualized meta-atoms. The autonomously time-varying VRs cause significant temporal variations in both the stiffness and loss factor of the metamaterial. By programming the time-domain behavior of the VRs, the metamaterial's constitutive parameters can be modulated according to desired periodic or aperiodic patterns. The proposed time-varying metamaterial has demonstrated capabilities in shaping the amplitudes and frequency spectra of waves in the time domain. This work not only facilitates the development of materials with sophisticated time-varying properties but also opens new avenues for low-frequency signal processing in future communication systems.

Fully Polarized Topological Isostatic Metamaterials in Three Dimensions

Topological surface states are unique to topological materials and are immune to disturbances. In isostatic lattices, mechanical topological floppy modes exhibit softness depending on the polarization relative to the terminating surface. However, in three dimensions, the polarization of topological floppy modes is disrupted by the ubiquitous mechanical Weyl lines. Here, we demonstrate, both theoretically and experimentally, the fully polarized topological mechanical phases free of Weyl lines. Floppy modes emerge exclusively on a particular surface of the three-dimensional isostatic structure, leading to the strongly asymmetric stiffness between opposing boundaries. Additionally, uniform soft strains can reversibly shift the lattice configuration to Weyl phases, switching the stiffness contrast to a trivially comparable level. Our work demonstrates the fully polarized topological mechanical phases in three dimensions, and paves the way towards engineering soft and adaptive metamaterials.

Analytical realization of complex thermal meta-devices

Fourier's law dictates that heat flows from warm to cold. Nevertheless, devices can be tailored to cloak obstacles or even reverse the heat flow. Mathematical transformation yields closed-form equations for graded, highly anisotropic thermal metamaterial distributions needed for obtaining such functionalities. For simple geometries, devices can be realized by regular conductor distributions; however, for complex geometries, physical realizations have so far been challenging, and sub-optimal solutions have been obtained by expensive numerical approaches. Here we suggest a straightforward and highly efficient analytical de-homogenization approach that uses optimal multi-rank laminates to provide closed-form solutions for any imaginable thermal manipulation device. We create thermal cloaks, rotators, and concentrators in complex domains with close-to-optimal performance and esthetic elegance. The devices are fabricated using metal 3D printing, and their omnidirectional thermal functionalities are investigated numerically and validated experimentally. The analytical approach enables next-generation free-form thermal meta-devices with efficient synthesis, near-optimal performance, and concise patterns.

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.

Unravelling Size-Dependent and Coupled Properties in Mechanical Metamaterials: A Couple-Stress Theory Perspective

The lack of material characteristic length scale prevents classical continuum theory (CCT) from recognizing size effect. Additionally, the even-order material property tensors associated with CCT only characterize the materials' centrosymmetric behavior and overlook their intrinsic chirality and polarity. Moreover, CCT is not reducible to 2D and 1D space without adding couples and higher-order deformation gradients. Despite several generalized continuum theories proposed over the past century to overcome the limitations of CCT, the broad application of these theories in the field of mechanical metamaterials has encountered significant challenges. These obstacles primarily arise from a limited understanding of the material coefficients associated with these theories, impeding their widespread adoption. Implementing a bottom-up approach based on augmented asymptotic homogenization, a consistent and self-sufficient effective couple-stress theory for materials with microstructures in 3D, 2D, and 1D spaces is presented. Utilizing the developed models, material properties associated with axial-twist, shear-bending, bending-twist, and double curvature bending couplings in mechanical metamaterials are characterized. The accuracy of these homogenized models is investigated by comparing them with the detailed finite element models and experiments performed on 3D-printed samples. The proposed models provide a benchmark for the rational design, classification, and manufacturing of mechanical metamaterials with programmable coupled deformation modes.

Design Criteria for Architected Materials with Programmable Mechanical Properties Within Theoretical Limit Ranges

Architected materials comprising periodic arrangements of cells have attracted considerable interest in various fields because of their unconventional properties and versatile functionality. Although some better properties may be exhibited when this homogeneous layout is broken, most such studies rely on a fixed material geometry, which limits the design space for material properties. Here, combining heterogeneous and homogeneous assembly of cells to generate tunable geometries, a hierarchically architected material (HAM) capable of significantly enhancing mechanical properties is proposed. Guided by the theoretical model and 745 752 simulation cases, generic design criteria are introduced, including dual screening for unique mechanical properties and careful assembly of specific spatial layouts, to identify the geometry of materials with extreme properties. Such criteria facilitate the potential for unprecedented properties such as Young's modulus at the theoretical limit and tunable positive and negative Poisson's ratios in an ultra-large range. Therefore, this study opens a new paradigm for materials with extreme mechanical properties.

Mirrored transformation optics

A mirrored transformation optics (MTO) approach is presented to overcome the material mismatch in transformation optics. It makes good use of the reflection behavior and introduces a mirrored medium to offset the phase discontinuities. Using this approach, a high-performance planar focusing lens of transmission type is designed, which has a larger concentration ratio than the other focusing lens obtained by the generalized Snell's law. The MTO will not change any functionality of the original lens and has promising potential applications in imaging and light energy harvesting.

Perfect circular polarization of elastic waves in solid media

Elastic waves involving mechanical particle motions of solid media can couple volumetric and shear deformations, making their manipulation more difficult than electromagnetic waves. Thereby, circularly polarized waves in the elastic regime have been little explored, unlike their counterparts in the electromagnetic regime, where their practical usage has been evidenced in various applications. Here, we explore generating perfect circular polarization of elastic waves in an isotropic solid medium. We devise a novel strategy for converting a linearly polarized wave into a circularly polarized wave by employing an anisotropic medium, which induces a so-far-unexplored coupled resonance phenomenon; it describes the simultaneous occurrence of the Fabry-Pérot resonance in one diagonal plane and the quarter-wave resonance in another diagonal plane orthogonal to the former with an exact 90° out-of-phase relation. We establish a theory explaining the involved physics and validate it numerically and experimentally. As a potential application of elastic circular polarization, we present simulation results demonstrating that a circularly polarized elastic wave can detect an arbitrarily oriented crack undetectable by a linearly polarized elastic wave.

Duality and Sheared Analytic Response in Mechanism-Based Metamaterials

Mechanical metamaterials designed around a zero-energy pathway of deformation known as a mechanism, challenge the conventional picture of elasticity and generate complex spatial response that remains largely uncharted. Here, we present a unified theoretical framework to showing that the presence of a unimode in a 2D structure generates a space of anomalous zero-energy sheared analytic modes. The spatial profiles of these stress-free strain patterns is dual to equilibrium stress configurations. We show a transition at an exceptional point between bulk modes in structures with conventional Poisson ratios (anauxetic) and evanescent surface modes for negative Poisson ratios (auxetic). We suggest a first application of these unusual response properties as a switchable signal amplifier and filter for use in mechanical circuitry and computation.

Dispersion Engineering by Hybridizing the Back-Folded Soft Mode of Monomode Elastic Metamaterials with Stiff Acoustic Modes

In many cases, the hybridization of two or more excitation modes in solids has led to new and useful dispersion relations of waves. Well-studied examples are phonon polaritons, plasmon polaritons, particle-plasmon polaritons, cavity polaritons, and magnetic resonances at optical frequencies. In all of these cases, the lowest propagating mode couples to a finite-frequency localized resonance. Herein, the unusual metamaterial phonon dispersion relations arising from the hybridization of an ordinary acoustical phonon mode with a back-folded soft or easy phonon mode of a monomode elastic metamaterial are discussed. Conceptually, the single easy mode can have strictly zero wave velocity. In reality, its wave velocity is very much smaller than that of all other modes. Considering polymeric three-dimensional printed elastic monomode metamaterials at ultrasound frequencies, it is shown theoretically and experimentally that the resulting pronounced avoided crossing, with a frequency splitting comparable to the mid-frequency, leads to backward-wave behavior for the lowest band over a broad frequency range, conceptually at zero loss.

Data-Driven Design for Metamaterials and Multiscale Systems: A Review

Metamaterials are artificial materials designed to exhibit effective material parameters that go beyond those found in nature. Composed of unit cells with rich designability that are assembled into multiscale systems, they hold great promise for realizing next-generation devices with exceptional, often exotic, functionalities. However, the vast design space and intricate structure-property relationships pose significant challenges in their design. A compelling paradigm that could bring the full potential of metamaterials to fruition is emerging: data-driven design. This review provides a holistic overview of this rapidly evolving field, emphasizing the general methodology instead of specific domains and deployment contexts. Existing research is organized into data-driven modules, encompassing data acquisition, machine learning-based unit cell design, and data-driven multiscale optimization. The approaches are further categorized within each module based on shared principles, analyze and compare strengths and applicability, explore connections between different modules, and identify open research questions and opportunities.

Flexible Metasurfaces for Multifunctional Interfaces

Optical metasurfaces, capable of manipulating the properties of light with a thickness at the subwavelength scale, have been the subject of extensive investigation in recent decades. This research has been mainly driven by their potential to overcome the limitations of traditional, bulky optical devices. However, most existing optical metasurfaces are confined to planar and rigid designs, functions, and technologies, which greatly impede their evolution toward practical applications that often involve complex surfaces. The disconnect between two-dimensional (2D) planar structures and three-dimensional (3D) curved surfaces is becoming increasingly pronounced. In the past two decades, the emergence of flexible electronics has ushered in an emerging era for metasurfaces. This review delves into this cutting-edge field, with a focus on both flexible and conformal design and fabrication techniques. Initially, we reflect on the milestones and trajectories in modern research of optical metasurfaces, complemented by a brief overview of their theoretical underpinnings and primary classifications. We then showcase four advanced applications of optical metasurfaces, emphasizing their promising prospects and relevance in areas such as imaging, biosensing, cloaking, and multifunctionality. Subsequently, we explore three key trends in optical metasurfaces, including mechanically reconfigurable metasurfaces, digitally controlled metasurfaces, and conformal metasurfaces. Finally, we summarize our insights on the ongoing challenges and opportunities in this field.

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.

Exploration of truss metamaterials with graph based generative modeling

Optimisation tasks in the inverse design of metamaterials with machine learning were limited due to the representations of generative models. Here the author comments a recent publication in Nature Communications which generates a latent space representation that unlocks non-linear optimisations.

Deep Learning in Mechanical Metamaterials: From Prediction and Generation to Inverse Design

Mechanical metamaterials are meticulously designed structures with exceptional mechanical properties determined by their microstructures and constituent materials. Tailoring their material and geometric distribution unlocks the potential to achieve unprecedented bulk properties and functions. However, current mechanical metamaterial design considerably relies on experienced designers' inspiration through trial and error, while investigating their mechanical properties and responses entails time-consuming mechanical testing or computationally expensive simulations. Nevertheless, recent advancements in deep learning have revolutionized the design process of mechanical metamaterials, enabling property prediction and geometry generation without prior knowledge. Furthermore, deep generative models can transform conventional forward design into inverse design. Many recent studies on the implementation of deep learning in mechanical metamaterials are highly specialized, and their pros and cons may not be immediately evident. This critical review provides a comprehensive overview of the capabilities of deep learning in property prediction, geometry generation, and inverse design of mechanical metamaterials. Additionally, this review highlights the potential of leveraging deep learning to create universally applicable datasets, intelligently designed metamaterials, and material intelligence. This article is expected to be valuable not only to researchers working on mechanical metamaterials but also those in the field of materials informatics.

Modular reprogrammable 3D mechanical metamaterials with unusual hygroscopic deformation modes

The majority of polymer-based materials demonstrate expansion upon absorbing water from the air. Mechanical metamaterials provide an interesting way to achieve unusual hygroscopic deformation. However, previous studies have only accommodated the limited tunability of negative hygroscopic expansion by theoretical analysis but have never involved other deformation modes. This work proposes modular reprogrammable 3D moisture-sensitive mechanical metamaterials with switchable hygroscopic deformation modes, which are built up of multi-material 3D-printed bi-material curved strips and cubic nodes. Depending on the geometrical parameters and spatial layouts of the curved strips, the metamaterials exhibit tunable coefficient of hygroscopic expansion from negative to positive. In addition to homogeneous deformation, complex 3D hygroscopic deformation modes can be achieved including shear and twist. More interestingly, the metamaterials are reprogrammable since all the deformation modes can be switched by modular disassembling and reassembling of the curved strips, just like LEGO building blocks. This work demonstrates a feasible approach to achieve customized 3D hygroscopic deformation through easy block building for specific engineering applications including eliminating hygroscopic stress, shape morphing structures, and smart actuators.

Active metamaterials for realizing odd mass density

Solids built out of active components have exhibited odd elastic stiffness tensors whose active moduli appear in the antisymmetric part and which give rise to non-Hermitian static and dynamic phenomena. Here, we present a class of active metamaterial featured with an odd mass density tensor whose asymmetric part arises from active and nonconservative forces. The odd mass density is realized using metamaterials with inner resonators connected by asymmetric and programmable feed-forward control on acceleration and active forces along the two perpendicular directions. The active forces produce unbalanced off-diagonal mass density coupling terms, leading to non-Hermiticity. The odd mass is then experimentally validated through a one-dimensional nonsymmetric wave coupling where propagating transverse waves are coupled with longitudinal ones whereas the reverse is forbidden. We reveal that the two-dimensional active metamaterials with the odd mass can perform in either energy-unbroken or energy-broken phases separated by exceptional points along principal directions of the mass density. The odd mass density contributes to the wave anisotropy in the energy-unbroken phase and directional wave energy gain in the energy-broken phase. We also numerically illustrate and experimentally demonstrate the two-dimensional wave propagation phenomena that arise from the odd mass in active solids. Finally, the existence of non-Hermitian skin effect is discussed in which boundaries host an extensive number of localized modes. It is our hope that the emergent concept of the odd mass can open up a new research platform for mechanical non-Hermitian system and pave the ways for developing next-generation wave steering devices.

3D Printed Graphene-Based Metamaterials: Guesting Multi-Functionality in One Gain

Advanced functional materials with fascinating properties and extended structural design have greatly broadened their applications. Metamaterials, exhibiting unprecedented physical properties (mechanical, electromagnetic, acoustic, etc.), are considered frontiers of physics, material science, and engineering. With the emerging 3D printing technology, the manufacturing of metamaterials becomes much more convenient. Graphene, due to its superior properties such as large surface area, superior electrical/thermal conductivity, and outstanding mechanical properties, shows promising applications to add multi-functionality into existing metamaterials for various applications. In this review, the aim is to outline the latest developments and applications of 3D printed graphene-based metamaterials. The structure design of different types of metamaterials and the fabrication strategies for 3D printed graphene-based materials are first reviewed. Then the representative explorations of 3D printed graphene-based metamaterials and multi-functionality that can be introduced with such a combination are further discussed. Subsequently, challenges and opportunities are provided, seeking to point out future directions of 3D printed graphene-based metamaterials.

Tetramode Metamaterials as Phonon Polarizers

In classical Cauchy elasticity, 3D materials exhibit six eigenmodes of deformation. Following the 1995 work of Milton and Cherkaev, extremal elastic materials can be classified by the number of eigenmodes, N, out of these six that are "easy". Using Greek number words, this leads to hexamode (N = 6), pentamode (N = 5), tetramode (N = 4), trimode (N = 3), dimode (N = 2), and monomode (N = 1) materials. While hexamode materials are unstable in all regards, the possibility of pentamode metamaterials ("meta-fluids") has attracted considerable attention throughout the last decade. Here, inspired by the 2021 theoretical work of Wei, Liu, and Hu, microstructured 3D polymer-based tetramode metamaterials are designed and characterized by numerical band-structure calculations, fabricated by laser printing, characterized by ultrasound experiments, and compared to the theoretical ideal. An application in terms of a compact and broadband polarizer for acoustical phonons at ultrasound frequencies is demonstrated.

A flexible design framework to design graded porous bone scaffolds with adjustable anisotropic properties

Since the success of bone regenerative medicine depends on scaffold morphological and mechanical properties, numerous scaffolds designs have been proposed in the last decade, including graded structures that are suited to enhance tissue ingrowth. Most of these structures are based either on foams with a random pore definition, or on the periodic repetition of a unit cell (UC). These approaches are limited by the range of target porosities and obtained effective mechanical properties, and do not permit to easily generate a pore size gradient from the core to the periphery of the scaffold. In opposition, the objective of the present contribution is to propose a flexible design framework to generate various three-dimensional (3D) scaffolds structures including cylindrical graded scaffolds from the definition of a UC by making use of a non-periodic mapping. Conformal mappings are firstly used to generate graded circular cross-sections, while 3D structures are then obtained by stacking the cross-sections with or without a twist between different scaffold layers. The effective mechanical properties of different scaffold configurations are presented and compared using an energy-based efficient numerical method, pointing out the versatility of the design procedure to separately govern longitudinal and transverse anisotropic scaffold properties. Among these configurations, a helical structure exhibiting couplings between transverse and longitudinal properties is proposed and permits to extend the adaptability of the proposed framework. In order to investigate the capacity of common additive manufacturing techniques to fabricate the proposed structures, a subset of these configurations is elaborated using a standard SLA setup, and subjected to experimental mechanical testing. Despite observed geometric differences between the initial design and the actual obtained structures, the effective properties are satisfyingly predicted by the proposed computational method. Promising perspectives are offered concerning the design of self-fitting scaffolds with on-demand properties depending on the clinical application.

Magnetically Driven Modular Mechanical Metamaterials with High Programmability, Reconfigurability, and Multiple Applications

Shape transformation and motion guidance are emerging research hotspots of mechanical metamaterials. In this case, the key issue is how to improve the programmability and reconfigurability of metamaterials. The magnetically driven method enables materials to accomplish remote, fast, and reversible deformation, so it is desired for improving the programmability and reconfigurability of metamaterials. However, conventional magnetically driven materials are often pure elastomer materials. Their magnetic programming method is single, and their overall shape is unchangeable after fabrication, which limits their programmability and reconfigurability. Herein, this article proposes a kind of magnetically driven, programmable, and reconfigurable modular mechanical metamaterial based on origami and kirigami design mechanisms. The motion and deformation were designed to follow the predefined creases and incisions that could be transformed into each other. This metamaterial enabled more discrete motion and force transmission and integrated the fold of origami, the rotation of kirigami, and the fold guided by cuts. Such designs laid the foundation for complex, three-dimensional structures which could be quickly reassembled and constructed to deal with complex situations. This paper also demonstrated applications of this metamaterial in information storage and manifestation, mechanical logic computing, reconfigurable robotics, deployable mechanisms, and so on. The results indicated that the high programmability and reconfigurability expanded the application potential of the metamaterial for broader needs.

An acoustic cloaking design based on topology optimization

In this work, we explain how to utilize the topology optimization method for the design of acoustic cloaks based on the principle of scattering cancellation. To take account of the challenging fabrication restriction, we impose boundary control inside the optimization objective function and enforce hyperbolic tangent projection to minimize the gray transition regions of the optimized design. In addition, a filter based on the Helmholtz differential equation is used to remove any tiny structures due to the effect of discretized grids. Then, we fabricate the designed cloaks and conduct the experiments in a couple of representative set-ups to validate the proposed design approach. The experiments are conducted inside both air and water. We found that the current cloaking design performs much better in air than in water and reveal the associated reason. Overall, this work paves the way for the acoustic cloaking design, fabrication, and experiments for future practical applications.

Flexible Metamaterial Electronics

Over the last decade, extensive efforts have been made on utilizing advanced materials and structures to improve the properties and functionalities of flexible electronics. While the conventional ways are approaching their natural limits, a revolutionary strategy, namely metamaterials, is emerging toward engineering structural materials to break the existing fetters. Metamaterials exhibit supernatural physical behaviors, in aspects of mechanical, optical, thermal, acoustic, and electronic properties that are inaccessible in natural materials, such as tunable stiffness or Poisson's ratio, manipulating electromagnetic or elastic waves, and topological and programmable morphability. These salient merits motivate metamaterials as a brand-new research direction and have inspired extensive innovative applications in flexible electronics. Here, such a groundbreaking interdisciplinary field is first coined as "flexible metamaterial electronics," focusing on enhancing and innovating functionalities of flexible electronics via the design of metamaterials. Herein, the latest progress and trends in this infant field are reviewed while highlighting their potential value. First, a brief overview starts with introducing the combination of metamaterials and flexible electronics. Then, the developed applications are discussed, such as self-adaptive deformability, ultrahigh sensitivity, and multidisciplinary functionality, followed by the discussion of potential prospects. Finally, the challenges and opportunities facing flexible metamaterial electronics to advance this cutting-edge field are summarized.

Buckling versus unilateral constraint for a multistable metamaterial element

A structural element is designed and investigated, forming the basis for the development of an elastic multistable metamaterial. The leitmotif of the structural design is the implementation of a strut characterized by a bifurcation occurring at either vanishing tensile or compressive load. It is shown that buckling at null load leads to a mechanical equivalence with a unilateral constraint formulation, introducing shocks in dynamics. Towards a future analysis of the latter, the nonlinear quasi-static response is investigated, showing the multistable character of the structure, which may appear as bistable or tetrastable. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

Programmable gear-based mechanical metamaterials

Elastic properties of classical bulk materials can hardly be changed or adjusted in operando, while such tunable elasticity is highly desired for robots and smart machinery. Although possible in reconfigurable metamaterials, continuous tunability in existing designs is plagued by issues such as structural instability, weak robustness, plastic failure and slow response. Here we report a metamaterial design paradigm using gears with encoded stiffness gradients as the constituent elements and organizing gear clusters for versatile functionalities. The design enables continuously tunable elastic properties while preserving stability and robust manoeuvrability, even under a heavy load. Such gear-based metamaterials enable excellent properties such as continuous modulation of Young's modulus by two orders of magnitude, shape morphing between ultrasoft and solid states, and fast response. This allows for metamaterial customization and brings fully programmable materials and adaptive robots within reach.

Photo-responsive hydrogel-based re-programmable metamaterials

This paper explores a novel programmable metamaterial using stimuli-responsive hydrogels with a demonstration of bandgap formation and tuning. Specifically, a photo-responsive hydrogel beam that can achieve re-programmable periodicity in geometric and material properties through patterned light irradiation is designed. Hydrogels consist of polymeric networks and water molecules. Many unique properties of hydrogels, including bio-compatibility, stimuli-responsiveness, and low dissipation make them ideal for enabling re-programmable metamaterials for manipulating structural dynamic response and wave propagation characteristics. Bandgap generation and tunability in photo-responsive hydrogel-based metamaterial (in the form of a diatomic phononic chain) as well as the effects of system parameters such as light exposure pattern and photo-sensitive group concentration on the bandgap width and center frequency are systematically studied. In agreement with finite-element model simulations, it is observed that an increase in light exposure region size reduces both the bandgap width and center frequency, while an increase in the concentration of photo-sensitive group increases bandgap width, attenuation and reduces its center frequency. This work unveils the potential of stimuli-response hydrogels as a new class of low-loss soft metamaterials, unlike most other soft materials that are too lossy to sustain and exploit wave phenomena.

Design and Reconfiguration of Multicomponent Hydrodynamic Manipulation Devices with Arbitrary Complex Structures

Being a powerful strategy to preclude drag and achieve hydrodynamic invisibility, flow field manipulation is attracting widespread attention. In this investigation, we introduce a systematic set of arbitrary-space divide-and-conquer transformation strategies to design complex hydrodynamic cloaks. This theory removes the difficulties associated with the analytic description of complicated and irregular structures to construct hydrodynamic cloaks by adopting the divide-and-conquer algorithm and reconfiguring strategies. It also provides an approach for redistributing the flow field energy and guiding the fluid flow as desired. The proposed theory not only opens up new ideas for improving the speed and concealment of marine vehicles but also provides a new strategy for ensuring the safety of aquatic and underwater structure operations.

Elastic Metamaterials of Hexagonal Unit Cells with Double-Cone Arms from Pentamode to Band Gap at Low Frequencies

Metamaterials are artificial materials with properties that can be designed by man-made structures. Pentamode metamaterials only support compressional stresses at specific frequency ranges, and a band gap is a frequency range where no stresses are supported. In this paper, an elastic metamaterial with hexagonal unit cells is studied where pentamode bands or band gaps at low frequencies are obtained by varying the inner structures. The effects of structural and geometric parameters on the band width of pentamode bands or band gaps are analyzed. Simulations of materials composed of primitive cells with pentamode or band gap properties are conducted with harmonic stimulation based on the finite element method. The metamaterials can be applied as pentamode metamaterials or vibration isolation materials.

Mechanical cloak via data-driven aperiodic metamaterial design

An invisibility cloak to conceal objects from an outside observer has long been a subject of interest in metamaterial design. While cloaks have been manufactured for optical, thermal, and electric fields, limited progress has been made for mechanical cloaks. Most existing designs rely on mapping-based methods, which have so far been limited to special base cells and a narrow selection of voids with simple shapes. In this study, we develop a fundamentally different approach by exploiting data-driven designs to offer timely, customized solutions to mechanical cloaking that were previously difficult to obtain. Through simulations and experimental validations, we show that excellent cloaking performance can be achieved for various boundary conditions, shapes of voids, base cells, and even multiple voids.

Mechanical cloaks are materials engineered to manipulate the elastic response around objects to make them indistinguishable from their homogeneous surroundings. Typically, methods based on material-parameter transformations are used to design optical, thermal, and electric cloaks. However, they are not applicable in designing mechanical cloaks, since continuum-mechanics equations are not form invariant under general coordinate transformations. As a result, existing design methods for mechanical cloaks have so far been limited to a narrow selection of voids with simple shapes. To address this challenge, we present a systematic, data-driven design approach to create mechanical cloaks composed of aperiodic metamaterials using a large precomputed unit cell database. Our method is flexible to allow the design of cloaks with various boundary conditions, multiple loadings, different shapes and numbers of voids, and different homogeneous surroundings. It enables a concurrent optimization of both topology and properties distribution of the cloak. Compared to conventional fixed-shape solutions, this results in an overall better cloaking performance and offers unparalleled versatility. Experimental measurements on additively manufactured structures further confirm the validity of the proposed approach. Our research illustrates the benefits of data-driven approaches in quickly responding to new design scenarios and resolving the computational challenge associated with multiscale designs of functional structures. It could be generalized to accommodate other applications that require heterogeneous property distribution, such as soft robots and implants design.

Design and characterization of a three-dimensional anisotropic additively manufactured pentamode material

A metamaterial of particular interest for underwater applications is the three-dimensional (3D) anisotropic pentamode (PM), i.e., a structure designed to support a single longitudinal wave with a sound speed that depends on the propagation direction. The present work attempts to experimentally verify anisotropic sound speeds predicted by finite element simulations using additively manufactured anisotropic 3D PM samples made of titanium. The samples were suspended in front of a plane wave source emitting a broadband chirp in a water tank to measure time of flight for wavefronts with and without the PM present. The measurement utilizes a deconvolution method that extracts the band limited impulse response of data gathered by a scanning hydrophone in a plane of constant depth behind the samples. Supporting material takes the form of finite element simulations developed to model the response of a semi-infinite PM medium to an incident normal plane wave. A technique to extract the longitudinal PM wave speed for frequency domain simulations based on Fourier series expansions is given.

Responsive materials architected in space and time

Rationally designed architected materials have attained previously untapped territories in materials property space. The properties and behaviours of architected materials need not be stagnant after fabrication; they can be encoded with a temporal degree of freedom such that they evolve over time. In this Review, we describe the variety of materials architected in both space and time, and their responses to various stimuli, including mechanical actuation, changes in temperature and chemical environment, and variations in electromagnetic fields. We highlight the additive manufacturing methods that can precisely prescribe complex geometries and local inhomogeneities to make such responsiveness possible. We discuss the emergent physics phenomena observed in architected materials that are analogous to those in classical materials, such as the formation and behaviour of defects, phase transformations and topologically protected properties. Finally, we offer a perspective on the future of architected materials that have a degree of intelligence through mechanical logic and artificial neural networks.

Recent Progress in Active Mechanical Metamaterials and Construction Principles

Active mechanical metamaterials (AMMs) (or smart mechanical metamaterials) that combine the configurations of mechanical metamaterials and the active control of stimuli-responsive materials have been widely investigated in recent decades. The elaborate artificial microstructures of mechanical metamaterials and the stimulus response characteristics of smart materials both contribute to AMMs, making them achieve excellent properties beyond the conventional metamaterials. The micro and macro structures of the AMMs are designed based on structural construction principles such as, phase transition, strain mismatch, and mechanical instability. Considering the controllability and efficiency of the stimuli-responsive materials, physical fields such as, the temperature, chemicals, light, electric current, magnetic field, and pressure have been adopted as the external stimuli in practice. In this paper, the frontier works and the latest progress in AMMs from the aspects of the mechanics and materials are reviewed. The functions and engineering applications of the AMMs are also discussed. Finally, existing issues and future perspectives in this field are briefly described. This review is expected to provide the basis and inspiration for the follow-up research on AMMs.

Transformation Metamaterials

Based on the form-invariance of Maxwell's equations under coordinate transformations, mathematically smooth deformation of space can be physically equivalent to inhomogeneous and anisotropic electromagnetic (EM) medium (called a transformation medium). It provides a geometric recipe to control EM waves at will. A series of examples of achieving transformation media by artificially structured units from conventional materials is summarized here. Such concepts are firstly implemented for EM waves, and then extended to other wave dynamics, such as elastic waves, acoustic waves, surface water waves, and even stationary fields. These shall be cataloged as transformation metamaterials. In addition, it might be conceptually attractive and practically useful to control diverse waves for multi-physics designs.

Femtosecond Laser Regulated Ultrafast Growth of Mushroom-Like Architecture for Oil Repellency and Manipulation

Natural organisms can create various microstructures via a spontaneous growth mode. In contrast, artificial protruding microstructures are constructed by subtractive methods that waste materials and time or by additive methods that require additional materials. Here, we report a facile and straightforward strategy for a laser-induced self-growing mushroom-like microstructure on a flat surface. By simply controlling the localized femtosecond laser heating and ablation on the poly(ethylene terephthalate) tape/heat-shrinkable polystyrene bilayer surface, it is discovered that a mushroom-like architecture can spontaneously and rapidly grow out from the original surface within 0.36 s. The dimension of the re-entrant micropillar array (cap diameter, pillar spacing, and height) can be accurately controlled through the intentional control of laser scanning. Followed by a fluorination and spray coating, the obtained surface can realize the repellency and manipulation of oil droplets. This work provides new opportunities in the fields of microfabrication, microfluidics, microreactor engineering, and wearable antifouling electronics.

Mechanomaterials: A Rational Deployment of Forces and Geometries in Programming Functional Materials

The knowledge of mechanics of materials has been extensively implemented in developing functional materials, giving rise to recent advances in soft actuators, flexible electronics, mechanical metamaterials, tunable mechanochromics, regenerative mechanomedicine, etc. While conventional mechanics of materials offers passive access to mechanical properties of materials in existing forms, a paradigm shift is emerging toward proactive programming of materials' functionality by leveraging the force-geometry-property relationships. Here, such a rising field is coined as "mechanomaterials". To profile the concept, the design principles in this field at four scales is first outlined, namely the atomic scale, the molecular scale, the manipulation of nanoscale materials, and the microscale design of structural materials. A variety of techniques have been recruited to deliver the multiscale programming of functional mechanomaterials, such as strain engineering, capillary assembly, topological interlocking, kirigami, origami, to name a few. Engineering optical and biological functionalities have also been achieved by implementing the fundamentals of mechanochemistry and mechanobiology. Nonetheless, the field of mechanomaterials is still in its infancy, with many open challenges and opportunities that need to be addressed. The authors hope this review can serve as a modest spur to attract more researchers to further advance this field.

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.

Additive-Free All-Carbon Composite: A Two-Photon Material System for Nanopatterning of Fluorescent Sub-Wavelength Structures

The major bottleneck in fabrication of engineered 3D nanostructures is the choice of materials. Adding functionality to these nanostructures is a daunting task. In order to mitigate these issues, we report a two-photon patternable all carbon material system which can be used to fabricate fluorescent 3D micro/nanostructures using two-photon lithography, with subwavelength resolution. The synthesized material system eliminates the need to use conventional two-photon absorbing materials such as two-photon dyes or two-photon initiators. We have used two different trifunctional acrylate monomers and carbon dots, synthesized hydrothermally from a polyphenolic precursor, to formulate a two-photon processable resin. Upon two-photon excitation, photogenerated electrons in the excited states of the carbon dots facilitate the free radical formation at the surface of the carbon dots. These radicals, upon interaction with vinyl moieties, enable cross-linking of acrylate monomers. Free-radical induced two-photon polymerization of acrylate monomers without any conventional proprietary two-photon absorbing materials was accomplished at an ultrafine subwavelength resolution of 250 nm using 800 nm laser excitation. The effect of critical parameters such as average laser power, carbon dot concentration, and radiation exposure were determined for the fabrication of one-, two-, and three-dimensional functional nanostructures, applicable in a range of domains where fluorescence and toxicity are of the utmost importance. A fabrication speed as high as 100 mm/s was achieved. The ability to fabricate functional 3D micro-/nanostructures is anticipated to instigate a paradigm shift in various areas such as metamaterials, energy storage, drug delivery, and optoelectronics to name a few.

Theoretical verification of three-dimensional manufacturable pentamode metamaterial microstructure

A special kind of pentamode metamaterial, which is composed of double-cone elements and forms simple-cubic lattice, is investigated in this paper. Based on finite-element method, the phonon band structure and the transmission spectrum of the pentamode metamaterial are calculated, and then the pentamodal behavior of this structure is theoretically verified from two aspects, i.e. the physical properties and the mathematical definition. Results show that in the phonon band structure, there is a wider single-mode band gap, corresponding to the remarkable loss in the transmission spectrum. The ratio of bulk modulusBto shear modulusGis more than 300, which is obviously larger than that of traditional materials. Except for the isotropic bulk modulusB, the other mechanical moduli are all anisotropic. Five of six eigenvalues of elastic coefficient matrix are nearly zero for the microstructure, and only one is non-zero. These results demonstrate that this metamaterial microstructure performs excellent pentamodal characteristics, and also conforms to the mathematical definition of 'pentamode'.

Optimized lattice-based metamaterials for elastostatic cloaking

An optimization-based approach is proposed to design elastostatic cloaking devices in two-dimensional (2D) lattices. Given an elastic lattice with a defect, i.e. a circular or elliptical hole, a small region (cloak) around the hole is designed to hide the effect of the hole on the elastostatic response of the lattice. Inspired by the direct lattice transformation approach to elastostatic cloaking in 2D lattices, the lattice nodal positions in the design region are obtained using a coordinate transformation of the reference (undisturbed) lattice nodes. Subsequently, additional connectivity (i.e. a ground structure) is defined in the design region and the stiffness properties of these elements are optimized to mimic the global stiffness characteristics of the reference lattice. A weighted least-squares objective function is proposed, where the weights have a physical interpretation—they are the design-dependent coefficients of the design lattice stiffness matrix. The formulation leads to a convex objective function that does not require a solution to an additional adjoint system. Optimization-based cloaks are designed considering uniaxial tension in multiple directions and are shown to exhibit approximate elastostatic cloaking, not only when subjected to the boundary conditions they were designed for but also for uniaxial tension in directions not used in design and for shear loading.

Method of image charges for describing deformation of bounded two-dimensional solids with circular inclusions

We present a method for predicting the linear response deformation of finite and semi-infinite 2D solid structures with circular holes and inclusions by employing the analogies with image charges and induction in electrostatics. Charges in electrostatics induce image charges near conductive boundaries and an external electric field induces polarization (dipoles, quadrupoles, and other multipoles) of conductive and dielectric objects. Similarly, charges in elasticity induce image charges near boundaries and external stress induces polarization (quadrupoles and other multipoles) inside holes and inclusions. Stresses generated by these induced elastic multipoles as well as stresses generated by their images near boundaries then lead to interactions between holes and inclusions and with their images, which induce additional polarization and thus additional deformation of holes and inclusions. We present a method that expands induced polarization in a series of elastic multipoles, which systematically takes into account the interactions of inclusions and holes with the external field, between them, and with their images. The results of our method for linear deformation of circular holes and inclusions near straight and curved boundaries show good agreement with both linear finite element simulations and experiments.

Elastic multipole method for describing deformation of infinite two-dimensional solids with circular inclusions

Elastic materials with holes and inclusions are important in a large variety of contexts ranging from construction material to biological membranes. More recently, they have also been exploited in mechanical metamaterials, where the geometry of highly deformable structures is responsible for their unusual properties, such as negative Poisson's ratio, mechanical cloaking, and tunable phononic band gaps. Understanding how such structures deform in response to applied external loads is thus crucial for designing novel mechanical metamaterials. Here we present a method for predicting the linear response of infinite 2D solid structures with circular holes and inclusions by employing analogies with electrostatics. Just like an external electric field induces polarization (dipoles, quadrupoles, and other multipoles) of conductive and dielectric objects, external stress induces elastic multipoles inside holes and inclusions. Stresses generated by these induced elastic multipoles then lead to interactions between holes and inclusions, which induce additional polarization and thus additional deformation of holes and inclusions. We present a method that expands the induced polarization in a series of elastic multipoles, which systematically takes into account the interactions of inclusions and holes with the external stress field and also between them. The results of our method show good agreement with both linear finite element simulations and experiments.

Wave generator as an alternative for classic and innovative wave transmission path vibration mitigation techniques

In this paper the author proposes an approach in the form of an active wave generator for ground surface vibration reduction. The idea is compared to classic and innovative vibration mitigation techniques. The solution is mainly addressed to prevent people and structures against the destructive effects of anthropogenic vibrations. The efficiency of the presented idea is verified in the paper for two types of excitation–harmonic and impact loads, for points located on the ground surface and below it. The vibration reduction effect for structures is presented in the paper in the case of a three-story building. The advantages and disadvantages of the presented solutions are summarized. Moreover, this paper presents a wide and up-to-date literature review on the vibration control of the ground surface. Classical well-known technologies in the form of ground obstacles are compared with innovative ideas such as metamaterials.

Active cloaking and illusion of electric potentials in electrostatics

Cloaking and illusion has been demonstrated theoretically and experimentally in several research fields. Here we present for the first time an active exterior cloaking device in electrostatics operating in a two-horizontally-layered electroconductive domain, and use the superposition principle to cloak electric potentials. The device uses an additional current source pattern introduced on the interface between two layers to cancel the total electric potential to be measured. Also, we present an active exterior illusion device allowing for detection of a signal pattern corresponding to any arbitrarily chosen current source instead of the existing current source. The performance of the cloaking/illusion devices is demonstrated by three-dimensional models and numerical experiments using synthetic measurements of the electric potential. Sensitivities of numerical results to a noise in measured data and to a size of cloaking devices are analysed. The numerical results show quite reasonable cloaking/illusion performance, which means that a current source can be hidden electrostatically. The developed active cloaking/illusion methodology can be used in subsurface geo-exploration studies, electrical engineering, live sciences, and elsewhere.

Pentamode metamaterials with ultra-low-frequency single-mode band gap based on constituent materials

An effective method for realizing ultra-low-frequency single-mode band gap in pentamode metamaterials is proposed based on constituent materials. Results show that the decreasing ratioE/ρ(stiffness/mass density) of constituent material can significantly lower the frequency range of single-mode band gap. By merely replacing the constituent material from Al to rubber, the center frequencyf_cof single-mode band gap can be reduced nearly 600 times (from 3621 Hz to 6.5 Hz), while the normalized bandwidth Δf/f_cand the ratio of bulk modulusBto shear modulusGof pentamode structure keep substantially stable. The nonlinear fitting demonstrates that the relation betweenf_candE/ρsatisfies the logarithmic function. The two-component pentamode structure is designed to further explore the ultra-low-frequency single-mode band gap. The effects of thick-end diameterDof double-cone, diameterD₀and material type of additional sphere, on single-mode band gap of two-component system are analyzed. This work is attractive for several ∼Hz acoustic/elastic wave regulations using pentamode metamaterials.

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.

Exploring the property space of periodic cellular structures based on crystal networks

Finding genuine novelty in cellular structures is inherently difficult due to the numerous possible topological and geometrical configurations and their complex mechanical and physical interrelations. Here, we draw inspiration from the incredibly rich collection of crystallographic periodic networks that we interpret from a structural point of view to identify and design novel cellular structures with unique properties. We provide a ready-to-use catalog with more than 17,000 unique entries and show how crystallographic symmetries relate to their mechanical properties. Our work provides a foundation to support future applications in science and engineering, ranging from mechanical and optical metamaterials, over bone tissue engineering, to the design of electrochemical devices.

The properties of periodic cellular structures strongly depend on the regular spatial arrangement of their constituent base materials and can be controlled by changing the topology and geometry of the repeating unit cell. Recent advances in three-dimensional (3D) fabrication technologies more and more expand the limits of fabricable real-world architected materials and strengthen the need of novel microstructural topologies for applications across all length scales and fields in both fundamental science and engineering practice. Here, we systematically explore, interpret, and analyze publicly available crystallographic network topologies from a structural point of view and provide a ready-to-use unit cell catalog with more than 17,000 unique entries in total. We show that molecular crystal networks with atoms connected by chemical bonds can be interpreted as cellular structures with nodes connected by mechanical bars. By this, we identify new structures with extremal properties as well as known structures such as the octet-truss or the Kelvin cell and show how crystallographic symmetries are related to the mechanical properties of the structures. Our work provides inspiration for the discovery of novel cellular structures and paves the way for computational methods to explore and design microstructures with unprecedented properties, bridging the gap between microscopic crystal chemistry and macroscopic structural engineering.

Folding at the Microscale: Enabling Multifunctional 3D Origami-Architected Metamaterials

Mechanical metamaterials inspired by the Japanese art of paper folding have gained considerable attention because of their potential to yield deployable and highly tunable assemblies. The inherent foldability of origami structures enlarges the material design space with remarkable properties such as auxeticity and high deformation recoverability and deployability, the latter being key in applications where spatial constraints are pivotal. This work integrates the results of the design, 3D direct laser writing fabrication, and in situ scanning electron microscopic mechanical characterization of microscale origami metamaterials, based on the multimodal assembly of Miura-Ori tubes. The origami-architected metamaterials, achieved by means of microfabrication, display remarkable mechanical properties: stiffness and Poisson's ratio tunable anisotropy, large degree of shape recoverability, multistability, and even reversible auxeticity whereby the metamaterial switches Poisson's ratio sign during deformation. The findings here reported underscore the scalable and multifunctional nature of origami designs, and pave the way toward harnessing the power of origami engineering at small scales.

Engineering micromechanics of soft porous crystals for negative gas adsorption

Framework materials at the molecular level, such as metal-organic frameworks (MOF), were recently found to exhibit exotic and counterintuitive micromechanical properties. Stimulated by host-guest interactions, these so-called soft porous crystals can display counterintuitive adsorption phenomena such as negative gas adsorption (NGA). NGA materials are bistable frameworks where the occurrence of a metastable overloaded state leads to pressure amplification upon a sudden framework contraction. How can we control activation barriers and energetics via functionalization of the molecular building blocks that dictate the frameworks' mechanical response? In this work we tune the elastic and inelastic properties of building blocks at the molecular level and analyze the mechanical response of the resulting frameworks. From a set of 11 frameworks, we demonstrate that widening of the backbone increases stiffness, while elongation of the building blocks results in a decrease in critical yield stress of buckling. We further functionalize the backbone by incorporation of sp3 hybridized carbon atoms to soften the molecular building blocks, or stiffen them with sp2 and sp carbons. Computational modeling shows how these modifications of the building blocks tune the activation barriers within the energy landscape of the guest-free bistable frameworks. Only frameworks with free energy barriers in the range of 800 to 1100 kJ mol-1 per unit cell, and moderate yield stress of 0.6 to 1.2 nN for single ligand buckling, exhibit adsorption-induced contraction and negative gas adsorption. Advanced experimental in situ methodologies give detailed insights into the structural transitions and the adsorption behavior. The new framework DUT-160 shows the highest magnitude of NGA ever observed for nitrogen adsorption at 77 K. Our computational and experimental analysis of the energetics and mechanical response functions of porous frameworks is an important step towards tuning activation barriers in dynamic framework materials and provides critical design principles for molecular building blocks leading to pressure amplifying materials.

Tailored mechanical response and mass transport characteristic of selective laser melted porous metallic biomaterials for bone scaffolds

Porous metallic biomaterials developed from pentamode metamaterials (PMs) were rationally designed to mimic the topological, mechanical, and mass transport properties of human bones. Here, a series of diamond-based PMs with different strut parameters were fabricated from a Ti-6Al-4V powder by selective laser melting (SLM) technique. The morphological features, mechanical properties and permeability of PM samples were then characterized. In terms of morphology, the as-built PMs were well consistent with the as-designed ones, although the slight surface deviations were presented in overhanging areas. The PM scaffolds showed a switchable deformation pattern controlled by the slenderness ratio of struts. The double-cone strut topology increases the tortuosity and thereby accelerates the nutrients supply, waste removal, and cell migration to the whole scaffold region and circumambient bone tissue. The measured mechanical properties (i.e., E: 0.59-2.90 GPa, σ_y: 20.59-112.63 MPa) and computational permeability values (k: 9.87-49.19 × 10^-9 m²) of PM scaffolds were all in accordance with those of trabecular bone. The experimental permeability values were linearly dependent on the results of simulations. This study showed the great potential of PMs as bone scaffolds. Moreover, we demonstrated that PM-based porous biomaterials can decouple the mass transport and mechanical properties of bone scaffolds, so as to achieve an unprecedented level of tailoring their multi-physics properties. STATEMENT OF SIGNIFICANCE: The topological diversity can significantly improve the adaptability of the implant to the primary bone tissue. Previous studies revealed that the mechanical and mass transport properties of porous biomaterials are correlated to the material types, porosities and lattice topologies but neglected effects of strut design. We show here the influence of strut morphology on the mechanical and mass transport properties which are independently tailored, that is, the mass transport properties can be markedly increased while maintaining the mechanical properties of mimicking specific bones, vice versa. This study emphasizes the importance of strut topological design in the development of AM porous biomaterials.

Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions

New connections between static elastic cloaking, low-frequency elastic wave scattering and neutral inclusions (NIs) are established in the context of two-dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in a uniform elastic matrix. Given the core and matrix properties, we answer the questions of how to select the shell material such that (i) it acts as a static elastic cloak, and (ii) it eliminates low-frequency scattering of incident elastic waves. It is shown that static cloaking (i) requires an anisotropic shell, whereas scattering reduction (ii) can be satisfied more simply with isotropic materials. Implicit solutions for the shell material are obtained by considering the core–shell composite cylinder as a neutral elastic inclusion. Two types of NI are distinguished, weak and strong with the former equivalent to low-frequency transparency and the classical Christensen and Lo generalized self-consistent result for in-plane shear from 1979. Our introduction of the strong NI is an important extension of this result in that we show that standard anisotropic shells can act as perfect static cloaks, contrasting previous work that has employed ‘unphysical’ materials. The relationships between low-frequency transparency, static cloaking and NIs provide the material designer with options for achieving elastic cloaking in the quasi-static limit.