Mechanical cloak via data-driven aperiodic metamaterial design

Thermal Metamaterials with Configurable Mechanical Properties

Thermal metamaterials are typically achieved by mixing different natural materials to realize effective thermal conductivities (ETCs) that conventional materials do not possess. However, the necessity for multifunctional design of metamaterials, encompassing both thermal and mechanical functionalities, is somewhat overlooked, resulting in the fixation of mechanical properties in thermal metamaterials designed within current research endeavors. Thus far, conventional methods have faced challenges in designing thermal metamaterials with configurable mechanical properties because of intricate inherent relationships among the structural configuration, thermal and mechanical properties in metamaterials. Here, a data-driven approach is proposed to design a thermal metamaterial capable of seamlessly achieving thermal functionalities and harnessing the advantages of microstructural diversity to configure its mechanical properties. The designed metamaterial possesses thermal cloaking functionality while exhibiting exceptional mechanical properties, such as load-bearing capacity, shearing strength, and tensile resistance, thereby affording mechanical protection for the thermal metadevice. The proposed approach can generate numerous distinct inverse design candidate topological functional cells (TFCs), designing thermal metamaterials with dramatic improvements in mechanical properties compared to traditional ones, which sets up a novel paradigm for discovering thermal metamaterials with extraordinary mechanical structures. Furthermore, this approach also paves the way for investigating thermal metamaterials with additional physical properties.

Active mechanical cloaking for unsupervised damage resilience in programmable elastic metamaterials

Owing to the architected void-filled low-density configurations, metamaterials are prone to defects during the complex manufacturing process, or damages under operational conditions. Recently mechanical cloaking has been proposed to shield the effect of such disorders in terms of homogenized mechanical responses. The major drawback in these studies are that the damage location should be known a priori, and the cloak is designed around that damaged zone before manufacturing. Such postulation does not allow unsupervised damage resilience during the manufacturing and service life of metamaterials by active reconfiguration of the stress field depending on the random and unpredictable evolution of damage. Here, we propose a radically different approach by introducing piezoelectric lattices where the effect of random appearance of any single or multiple disorders and damages with complex shapes, sizes and distributions can be shielded through active multi-physically controlled cloaks by voltage-dependent modulation of the stress fields within the cloaking region. Notably, this can be achieved without breaking periodicity and any additional material in the cloaking region unlike earlier studies concerning mechanical cloaks. The proposed active class of elastic metamaterials will bring a step-change in the on-demand mechanical performance of critically important structural components and unsupervised damage resilience for enhanced durability and sustainability.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

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.

Modulate stress distribution with bio-inspired irregular architected materials towards optimal tissue support

Natural materials typically exhibit irregular and non-periodic architectures, endowing them with compelling functionalities such as body protection, camouflage, and mechanical stress modulation. Among these functionalities, mechanical stress modulation is crucial for homeostasis regulation and tissue remodeling. Here, we uncover the relationship between stress modulation functionality and the irregularity of bio-inspired architected materials by a generative computational framework. This framework optimizes the spatial distribution of a limited set of basic building blocks and uses these blocks to assemble irregular materials with heterogeneous, disordered microstructures. Despite being irregular and non-periodic, the assembled materials display spatially varying properties that precisely modulate stress distribution towards target values in various control regions and load cases, echoing the robust stress modulation capability of natural materials. The performance of the generated irregular architected materials is experimentally validated with 3D printed physical samples - a good agreement with target stress distribution is observed. Owing to its capability to redirect loads while keeping a proper amount of stress to stimulate bone repair, we demonstrate the potential application of the stress-programmable architected materials as support in orthopedic femur restoration.

Learning Stiffness Tensors in Self-Activated Solids via a Local Rule

Mechanical metamaterials are often designed with particular properties for specific load-bearing functions. Alternatively, this study aims to create a class of active lattice metamaterials, dubbed self-activated solids, that can learn desired stiffness tensors from the elastic deformations they experienced, a crucial feature to improve the performance, efficiency, and functionality of materials. Artificial adaptive matters that combine sensory, control, and actuation elements can offer appealing solutions. However, challenges still remain: The designs will rely on accurate off-line and global computations, as well as intricate coordination among individual elements. Here, a simple online and local learning strategy is initiated based on contrastive Hebbian learning to gradually guide self-activated solids to possess sought-after stiffness tensors autonomously and reversibly. During learning, the bond stiffness of the active lattice varies depending only on its local strain. The numerical tests show that the self-activated solid can not only achieve the desired bulk, shear, and coupling moduli but also manifest uni-mode and bi-mode extremal materials by itself after experiencing the corresponding elastic deformations. Further, the self-activated solid can also achieve the desired time-varying moduli when exposed to temporally different loads. The design is applicable to any lattice geometries and is resistant to damage and instabilities. The material design approach and the physical learning strategy suggested can benefit the design of autonomous materials, physical learning machines, and adaptive robots.

Ultrastiff metamaterials generated through a multilayer strategy and topology optimization

Metamaterials composed of different geometrical primitives have different properties. Corresponding to the fundamental geometrical forms of line, plane, and surface, beam-, plate-, and shell-based lattice metamaterials enjoy many advantages in many aspects, respectively. To fully exploit the advantages of each structural archetype, we propose a multilayer strategy and topology optimization technique to design lattice metamaterial in this study. Under the frame of the multilayer strategy, the design space is enlarged and diversified, and the design freedom is increased. Topology optimization is applied to explore better designs in the larger and diverse design space. Beam-plate-shell-combined metamaterials automatically emerge from the optimization to achieve ultrahigh stiffness. Benefiting from high stiffness, energy absorption performances of optimized results also demonstrate substantial improvements under large geometrical deformation. The multilayer strategy and topology optimization can also bring a series of tunable dimensions for lattice design, which helps achieve desired mechanical properties, such as isotropic elasticity and functionally grading material property, and superior performances in acoustic tuning, electrostatic shielding, and fluid field tuning. We envision that a broad array of synthetic and composite metamaterials with unprecedented performance can be designed with the multilayer strategy and topology optimization.

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.

Anomalous Transport of Small Polarons Arises from Transient Lattice Relaxation or Immovable Boundaries

Elucidating transport mechanisms is crucial for advancing material design, yet state-of-the-art theory is restricted to exact simulations of small lattices with severe finite-size effects or approximate ones that assume the nature of transport. We leverage algorithmic advances to tame finite-size effects and exactly simulate small polaron formation and transport in the Holstein model. We further analyze the applicability of the ubiquitously used equilibrium-based Green-Kubo relations and nonequilibrium methods to predict charge mobility. We find that these methods can converge to different values and track this disparity to finite-size dependence and the sensitivity of Green-Kubo relations to the system's topology. Contrary to standard perturbative calculations, our results demonstrate that small polarons exhibit anomalous transport that manifests transiently due to nonequilibrium lattice relaxation or permanently as a signature of immovable boundaries. These findings can offer new interpretations of transport experiments on polymers and transition metal oxides.

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.

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.

Photoinduced Mechanical Cloaking of Diarylethene-Crosslinked Microgels

The serial connection of multiple stimuli-responses in polymer architectures enables the logically conjunctive gating of functional material processes on demand. Here, a photoswitchable diarylethene (DAE) acts as a crosslinker in poly(N-vinylcaprolactam) microgels and allows the light-induced shift of the volume phase-transition temperature (VPTT). While swollen microgels below the VPTT are susceptible to force and undergo breakage-aggregation processes, collapsed microgels above the VPTT stay intact in mechanical fields induced by ultrasonication. Within a VPTT shift regime, photoswitching of the DAE transfers microgels from the swollen to the collapsed state and thereby gates their response to force as demonstrated by the light-gated activation of an embedded fluorogenic mechanophore. This photoinduced mechanical cloaking system operates on the polymer topology level and is thereby principally universally applicable.

Deep-Learning-Enabled Intelligent Design of Thermal Metamaterials

Thermal metamaterials are mixture-based materials that are engineered to manipulate, control, and process the flow of heat, enabling numerous advanced thermal metadevices. Conventional thermal metamaterials are predominantly designed with tractable regular geometries owing to the delicate analytical solution and easy-to-implement effective structures. Nevertheless, it is challenging to achieve the design of thermal metamaterials with arbitrary geometry, letting alone intelligent (automatic, real-time, and customizable) design of thermal metamaterials. Here, an intelligent design framework of thermal metamaterials is presented via a pre-trained deep learning model, which gracefully achieves the desired functional structures of thermal metamaterials with exceptional speed and efficiency, regardless of arbitrary geometry. It possesses incomparable versatility and is of great flexibility to achieve the corresponding design of thermal metamaterials with different background materials, anisotropic geometries, and thermal functionalities. The transformation thermotics-induced, freeform, background-independent, and omnidirectional thermal cloaks, whose structural configurations are automatically designed in real-time according to shape and background, are numerically and experimentally demonstrated. This study sets up a novel paradigm for an automatic and real-time design of thermal metamaterials in a new design scenario. More generally, it may open a door to the realization of an intelligent design of metamaterials in also other physical domains.

Mere tension output from spring-linkage-based mechanical metamaterials

Metamaterials whose properties are inaccessible with conventional materials offer powerful tools for unprecedentedly manipulating physical signals. However, an effective design strategy of metamaterials still remains a challenge for changing the compression or tension characters of stress waves during forward propagation. Here, we introduce a class of spring-linkage-based metamaterials exhibiting mere tension output at the distal end, no matter that the input is an axial impact, a sudden tension, or even alternating tension-compression. The metamaterials can turn compressive waves into pure tension and filter them out from the tension-compression mixed ones while allowing tensile signal stably propagating in soliton form. This is achieved by combining nonuniform and nonlinear properties of the proposed cells. In particular, these extraordinary functions of the metamaterial can be turned on or off and adjusted by tuning a key switch cell; thus, it is anticipated to serve as a start for more complex manipulation and utilization of mechanical signals.

Inverse design of 3D reconfigurable curvilinear modular origami structures using geometric and topological reconstructions

The recent development of modular origami structures has ushered in an era for active metamaterials with multiple degrees of freedom (multi-DOF). Notably, no systematic inverse design approach for 3D curvilinear modular origami structures has been reported. Moreover, very few modular origami topologies have been studied to design active metamaterials with multi-DOF. Herein, we develop an inverse design method for constructing 3D reconfigurable architected structures - we synthesize modular origami structures whose unit cells can be volumetrically mapped into a prescribed 3D curvilinear shape followed by volumetric shrinkage to construct modules. After modification of the tubular geometry, we search through all the possible geometric and topological combinations of the modular origami structures to attain the target mobility using a topological reconstruction of modules. Our inverse design using geometric and topological reconstructions can provide an effective solution to construct 3D curvilinear reconfigurable structures with multi-DOF. Our work opens a path toward 3D reconfigurable systems based on volumetric inverse design, such as 3D active metamaterials and 3D morphing devices for automotive, aerospace, and biomedical engineering applications.

Multilayer acoustic invisibility cloak based on composite lattice

A concentric cylindrical cloak is showed here to achieve the acoustic cloaking phenomenon. The introduced structure consists of MNE layers and water in MNE substrate in the MHz frequency range. Due to avoiding the incoming acoustic waves by the shell, the object can be hidden inside the cylindrical area of any shape. In order to improve the quality of cloaking, we have optimized the desired shell by considering the manufacturing technology. We show that an optimized, acoustic cloak based on composite lattice structure can reduce the scattering of an object more than a 20-layer realization of acoustic cloak based on multilayer cylindrical structure. This design approach can substantially simplify the fabrication of cloaking shells. In this research, to study the acoustic distribution of the desired structure, finite element method (FEM) has been used to analyze the structure in two dimensions and a cloak of natural materials with isotropic properties has been designed using effective medium theory.

Growth rules for irregular architected materials with programmable properties

Biomaterials display microstructures that are geometrically irregular and functionally efficient. Understanding the role of irregularity in determining material properties offers a new path to engineer materials with superior functionalities, such as imperfection insensitivity, enhanced impact absorption, and stress redirection. We uncover fundamental, probabilistic structure-property relationships using a growth-inspired program that evokes the formation of stochastic architectures in natural systems. This virtual growth program imposes a set of local rules on a limited number of basic elements. It generates materials that exhibit a large variation in functional properties starting from very limited initial resources, which echoes the diversity of biological systems. We identify basic rules to control mechanical properties by independently varying the microstructure's topology and geometry in a general, graph-based representation of irregular materials.