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Abstract 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. 

Abstract Liquid crystal elastomer (LCE) is a type of soft active material that generates large and reversible spontaneous deformations upon temperature changes, facilitating various environmentally responsive smart applications. Despite their success, most existing LCE metamaterials are designed in a forward fashion based on intuition and feature regular material patterns, which may hinder the reach of LCE’s full potential in producing complex and desired functionalities. Here, we develop a computational inverse design framework for discovering diverse sophisticated temperature-activated and -interactive nonlinear behaviors for LCE metamaterials in a fully controllable fashion. We generate intelligent LCE metamaterials with a wide range of switchable functionalities upon temperature changes. By sensing the environment, these metamaterials can realize maximized spontaneous area expansion/contraction, precisely programmable enclosed opening size change, and temperature-switchable nonlinear stress–strain relations and deformation modes. The optimized unit cells feature irregular LCE patterns and form complex and highly nonlinear mechanisms. The inverse design computational framework, optimized material patterns, and revealed underlying mechanisms fundamentally advance the design capacity of LCE metamaterials, benefiting environment-aware and -adaptive smart materials. 

Abstract Topology optimization has emerged as a versatile design tool embraced across diverse domains. This popularity has led to great efforts in the development of education-centric topology optimization codes with various focuses, such as targeting beginners seeking user-friendliness and catering to experienced users emphasizing computational efficiency. In this study, we introduce , a novel 2D and 3D topology optimization software developed in Python and built upon the open-source library, designed to harmonize usability with computational efficiency and post-processing for fabrication. employs a modular architecture, offering a unified input script for defining topology optimization problems and six replaceable modules to streamline subsequent optimization tasks. By enabling users to express problems in the weak form, eliminates the need for matrix manipulations, thereby simplifying the modeling process. The software also integrates automatic differentiation to mitigate the intricacies associated with chain rules in finite element analysis and sensitivity analysis. Furthermore, provides access to a comprehensive array of readily available solvers and preconditioners, bolstering flexibility in problem-solving. is designed for scalability, furnishing robust support for parallel computing that seamlessly adapts to diverse computing platforms, spanning from laptops to distributed computing clusters. It also facilitates effortless transitions for various spatial dimensions, mesh geometries, element types and orders, and quadrature degrees. Apart from the computational benefits, facilitates the automated exportation of optimized designs, compatible with open-source software for post-processing. This functionality allows for visualizing optimized designs across diverse mesh geometries and element shapes, automatically smoothing 3D designs, and converting smoothed designs into STereoLithography (STL) files for 3D printing. To illustrate the capabilities of , we present five representative examples showcasing topology optimization across 2D and 3D geometries, structured and unstructured meshes, solver switching, and complex boundary conditions. We also assess the parallel computational efficiency of by examining its performance across diverse computing platforms, process counts, problem sizes, and solver configurations. Finally, we demonstrate a physical 3D-printed model utilizing the STL file derived from the design optimized by . These examples showcase not only ’s rich functionality but also its parallel computing performance. The open-source is given in Appendix B and will be available to download athttps://github.com/missionlab/fenitop. 

Biological materials such as seashell nacre exhibit extreme mechanical properties due to their multilayered microstructures. Collaborative interaction among these layers achieves performance beyond the capacity of a single layer. Inspired by these multilayer biological systems, we architect materials with free-form layered microstructures to program multistage snap-buckling and plateau responses—accomplishments challenging with single-layer materials. The developed inverse design paradigm simultaneously optimizes local microstructures within layers and their interconnections, enabling intricate layer interactions. Each layer plays a synergistic role in collectively achieving high-precision control over the desired extreme nonlinear responses. Through high-fidelity simulations, hybrid fabrication, and tailored experiments, we demonstrate complex responses fundamental to various functionalities, including energy dissipation and wearable devices. We orchestrate multisnapping phenomena from complex interactions between heterogeneous local architectures to encode and store information within architected materials, unlocking data encryption possibilities. These layered architected materials offer transformative advancements across diverse fields, including vibration control, wearables, and information encryption. 

We envision programmable matters that can alter their physical properties in desirable manners based on user input or autonomous sensing. This vision motivates the pursuit of mechanical metamaterials that interact with the environment in a programmable fashion. However, this has not been systematically achieved for soft metamaterials because of the highly nonlinear deformation and underdevelopment of rational design strategies. Here, we use computational morphogenesis and multimaterial polymer 3D printing to systematically create soft metamaterials with arbitrarily programmable temperature-switchable nonlinear mechanical responses under large deformations. This is made possible by harnessing the distinct glass transition temperatures of different polymers, which, when optimally synthesized, produce local and giant stiffness changes in a controllable manner. Featuring complex geometries, the generated structures and metamaterials exhibit fundamentally different yet programmable nonlinear force-displacement relations and deformation patterns as temperature varies. The rational design and fabrication establish an objective-oriented synthesis of metamaterials with freely tunable thermally adaptive behaviors. This imbues structures and materials with environment-aware intelligence.