Robustly printable freeform thermal metamaterials

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.

Damage-programmable design of metamaterials achieving crack-resisting mechanisms seen in nature

The fracture behaviour of artificial metamaterials often leads to catastrophic failures with limited resistance to crack propagation. In contrast, natural materials such as bones and ceramics possess microstructures that give rise to spatially controllable crack path and toughened material resistance to crack advances. This study presents an approach that is inspired by nature's strengthening mechanisms to develop a systematic design method enabling damage-programmable metamaterials with engineerable microfibers in the cells that can spatially program the micro-scale crack behaviour. Machine learning is applied to provide an effective design engine that accelerate the generation of damage-programmable cells that offer advanced toughening functionality such as crack bowing, crack deflection, and shielding seen in natural materials; and are optimised for a given programming of crack path. This paper shows that such toughening features effectively enable crack-resisting mechanisms on the basis of the crack tip interactions, crack shielding, crack bridging and synergistic combinations of these mechanisms, increasing up to 1,235% absorbed fracture energy in comparison to conventional metamaterials. The proposed approach can have broad implications in the design of damage-tolerant materials, and lightweight engineering systems where significant fracture resistances or highly programmable damages for high performances are sought after.

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.

Free-form and multi-physical metamaterials with forward conformality-assisted tracing

Transformation theory, active control and inverse design have been mainstream in creating free-form metamaterials. However, existing frameworks cannot simultaneously satisfy the requirements of isotropic, passive and forward design. Here we propose a forward conformality-assisted tracing method to address the geometric and single-physical-field constraints of conformal transformation. Using a conformal mesh composed of orthogonal streamlines and isotherms (or isothermal surfaces), this method quasi-analytically produces free-form metamaterials using only isotropic media. The geometric nature of this approach allows for universal regulation of both dissipative thermal fields and non-dissipative electromagnetic fields. We experimentally demonstrate free-form thermal cloaking in both two and three dimensions. Additionally, the multi-physical functionalities of our method, including optical cloaking, bending and thermo-electric transparency, confirm its broad applicability. Our method features improvements in efficiency, accuracy and adaptability over previous approaches. This study provides an effective method for designing complex metamaterials with arbitrary shapes across various physical domains.

Accelerating the design of lattice structures using machine learning

Lattices remain an attractive class of structures due to their design versatility; however, rapidly designing lattice structures with tailored or optimal mechanical properties remains a significant challenge. With each added design variable, the design space quickly becomes intractable. To address this challenge, research efforts have sought to combine computational approaches with machine learning (ML)-based approaches to reduce the computational cost of the design process and accelerate mechanical design. While these efforts have made substantial progress, significant challenges remain in (1) building and interpreting the ML-based surrogate models and (2) iteratively and efficiently curating training datasets for optimization tasks. Here, we address the first challenge by combining ML-based surrogate modeling and Shapley additive explanation (SHAP) analysis to interpret the impact of each design variable. We find that our ML-based surrogate models achieve excellent prediction capabilities (R2 > 0.95) and SHAP values aid in uncovering design variables influencing performance. We address the second challenge by utilizing active learning-based methods, such as Bayesian optimization, to explore the design space and report a 5 × reduction in simulations relative to grid-based search. Collectively, these results underscore the value of building intelligent design systems that leverage ML-based methods for uncovering key design variables and accelerating design.

Observation of parity-time symmetry in diffusive systems

Phase modulation has scarcely been mentioned in diffusive physical systems because the diffusion process does not carry the momentum like waves. Recently, non-Hermitian physics provides a unique perspective for understanding diffusion and shows prospects in thermal phase regulation, exemplified by the discovery of anti-parity-time (APT) symmetry in diffusive systems. However, precise control of thermal phase remains elusive hitherto and can hardly be realized, due to the phase oscillations. Here we construct the PT-symmetric diffusive systems to achieve the complete suppression of thermal phase oscillation. The real coupling of diffusive fields is readily established through a strong convective background, and the decay-rate detuning is enabled by thermal metamaterial design. We observe the phase transition of PT symmetry breaking with the symmetry-determined amplitude and phase regulation of coupled temperature fields. Our work shows the existence of PT symmetry in dissipative energy exchanges and provides unique approaches for harnessing the mass transfer of particles, wave dynamics in strongly scattering systems, and thermal conduction.

Machine Learning Aided Design and Optimization of Thermal Metamaterials

Artificial Intelligence (AI) has advanced material research that were previously intractable, for example, the machine learning (ML) has been able to predict some unprecedented thermal properties. In this review, we first elucidate the methodologies underpinning discriminative and generative models, as well as the paradigm of optimization approaches. Then, we present a series of case studies showcasing the application of machine learning in thermal metamaterial design. Finally, we give a brief discussion on the challenges and opportunities in this fast developing field. In particular, this review provides: (1) Optimization of thermal metamaterials using optimization algorithms to achieve specific target properties. (2) Integration of discriminative models with optimization algorithms to enhance computational efficiency. (3) Generative models for the structural design and optimization of thermal metamaterials.

Deep Learning-Assisted Active Metamaterials with Heat-Enhanced Thermal Transport

Heat management is crucial for state-of-the-art applications such as passive radiative cooling, thermally adjustable wearables, and camouflage systems. Their adaptive versions, to cater to varied requirements, lean on the potential of adaptive metamaterials. Existing efforts, however, feature with highly anisotropic parameters, narrow working-temperature ranges, and the need for manual intervention, which remain long-term and tricky obstacles for the most advanced self-adaptive metamaterials. To surmount these barriers, heat-enhanced thermal diffusion metamaterials powered by deep learning is introduced. Such active metamaterials can automatically sense ambient temperatures and swiftly, as well as continuously, adjust their thermal functions with a high degree of tunability. They maintain robust thermal performance even when external thermal fields change direction, and both simulations and experiments demonstrate exceptional results. Furthermore, two metadevices with on-demand adaptability, performing distinctive features with isotropic materials, wide working temperatures, and spontaneous response are designed. This work offers a framework for the design of intelligent thermal diffusion metamaterials and can be expanded to other diffusion fields, adapting to increasingly complex and dynamic environments.

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.

Self-bridging metamaterials surpassing the theoretical limit of Poisson's ratios

A hallmark of mechanical metamaterials has been the realization of negative Poisson's ratios, associated with auxeticity. However, natural and engineered Poisson's ratios obey fundamental bounds determined by stability, linearity and thermodynamics. Overcoming these limits may substantially extend the range of Poisson's ratios realizable in mechanical systems, of great interest for medical stents and soft robots. Here, we demonstrate freeform self-bridging metamaterials that synthesize multi-mode microscale levers, realizing Poisson's ratios surpassing the values allowed by thermodynamics in linear materials. Bridging slits between microstructures via self-contacts yields multiple rotation behaviors of microscale levers, which break the symmetry and invariance of the constitutive tensors under different load scenarios, enabling inaccessible deformation patterns. Based on these features, we unveil a bulk mode that breaks static reciprocity, providing an explicit and programmable way to manipulate the non-reciprocal transmission of displacement fields in static mechanics. Besides non-reciprocal Poisson's ratios, we also realize ultra-large and step-like values, which make metamaterials exhibit orthogonally bidirectional displacement amplification, and expansion under both tension and compression, respectively.

Homogeneous Zero-Index Thermal Metadevice for Thermal Camouflaging and Super-Expanding

The infinite effective thermal conductivity (IETC) can be considered to be an equivalence of the effective zero index in photonics. A recent highly rotating metadevice has been discovered to approach near IETC, subsequently demonstrating a cloaking effect. However, this near IETC, related to a rotating radius, is quite inhomogeneous, and the high-speed rotating motor also needs a high energy input, limiting its further applications. Herein, we propose and realize an evolution of this homogeneous zero-index thermal metadevice for robust camouflaging and super-expanding through out-of-plane modulations rather than high-speed rotation. Both the theoretical simulations and experiments verify a homogeneous IETC and the corresponding thermal functionalities beyond cloaking. The recipe for our homogeneous zero-index thermal metadevice involves an external thermostat, which can be easily adjusted for various thermal applications. Our study may provide meaningful insights into the design of powerful thermal metadevices with IETCs in a more flexible way.

Biphysical undetectable concentrators manipulating both heat flux and direct current via topology optimization

Recent remarkable developments in metamaterials and metadevices manipulating diffusive processes, such as thermal and electrical conduction, have enabled the control of multiple phenomena and the development of multifunctional devices. However, only either multiphysics operations or multiple functionalities are usually implemented on single metadevices. In this paper, we describe a method for the optimal design of metadevices that achieves both cloaking and focusing in the control of both heat flux and direct current by a single device, i.e., biphysical-bifunctional metadevices having four capabilities. Our design scheme performs well in terms of providing cloaking and focusing bifunctionality. Additionally, it assumes bulk natural materials without the use of metamaterials, which improves the manufacturability of the designed metadevices. Moreover, multidirectional metad evices are optimally designed for thermal-electrical conductions transmitted from multiple directions or from heat and voltage sources at various locations.

Nonlinear thermal responses in geometrically anisotropic metamaterials

Nonlinear metamaterials have great potential in heat management, which has aroused intensive research interest in both theory and application, especially for their response to surroundings. However, most existing works focus on geometrically isotropic (circular) structures, limiting the potential versatile functionalities. On the other hand, anisotropy in architecture promisingly offers an additional degree of freedom in modulating directional heat transfer. Here, we investigate nonlinear composition effects in geometrically anisotropic (confocal elliptical) thermal medium under the framework of effective medium approximation, and deduce a series of general formulas for quantitatively predicting nonlinearity enhancement. Enhancement coefficients are analytically derived by the Taylor expansion method in different nonlinearity cases. In particular, we find that some coupling conditions can greatly promote the nonlinear modulation coefficients, introducing stronger enhancement beyond isotropic construction. Our theoretical predictions are verified by finite-element simulation, and feasible experimental suggestions are also given. For extending these results to practical scenes, two intelligent thermal metadevices are designed in proof of concept and demonstrated by numerical simulation. Our works provide a unified theory for anisotropic nonlinear thermal metamaterial design and may benefit flexible applications in self-adaptive thermal management, such as switchable cloaks, concentrators, or macroscopic thermal diodes.

Mass Diffusion Metamaterials with "Plug and Switch" Modules for Ion Cloaking, Concentrating, and Selection: Design and Experiments

The outstanding abilities of metamaterials to manipulate physical fields are extensively studied in both wave-based and diffusion-based fields. However, mass diffusion metamaterials, with the ability to manipulate diffusion with practical applications associated with chemical and biochemical engineering, have not yet been experimentally demonstrated. In this work, ion cloaking, concentrating, and selection in liquid solvents are verified by both simulations and experiments, and the concept of a "plug and switch" metamaterial is proposed based on scattering cancellation (SC) to achieve switchable functions by plugging modularized functional units into a functional motherboard. Plugging in any module barely affects the environmental diffusion field, but the module choice impacts different diffusion behaviors in the central region. Cloaking strictly hinds ion diffusion, and concentrating increase diffusion flux, while cytomembrane-like ion selection permits the entrance of some ions but blocks others. In addition, these functions are demonstrated in special applications like the catalytic enhancement by the concentrator and the protein protection by the ion selector. This work not only experimentally demonstrates the effective manipulation of mass diffusion by metamaterials, but also shows that the "plug and switch" design is extensible and reconfigurable. It facilitates novel applications including sustained drug release, catalytic enhancement, bioinspired cytomembranes, etc.

Novel connections and physical implications of thermal metamaterials with imperfect interfaces

Thermal metamaterials are of great importance in advanced energy control and management. Previous studies mainly focused on interfaces with perfect bonding conditions. In principle, imperfectness always exists across interface and the effect is intriguingly important with small-length scales. This work reports the imperfect interface effect in thermal metamaterials thoroughly. Low conductivity- and high conductivity-type interfaces are considered. We show that an object can always be made thermally invisible, with the effect of imperfect interface, as that of a homogeneous background material. This unprecedented condition is derived in an exact and analytic form, systematically structured, with much versatile and physical implications. Conditions for thermal shielding and enhancements are analytically found and numerically exemplified, highlighting the specific role of material and geometric parameters. We find that both types of interfaces are complementing with each other which, all together, will constitute a full spectrum to achieve the thermal invisibility. The analytic finding offers a general perception that adds to the understanding of heat transport mechanism across interfaces in thermal metamaterials, in ways that drastically distinct from that of ideal interfaces. This finding opens up new possibilities for the control and management of thermal metamaterials with imperfect bonding interfaces.