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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 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. 

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. 

Programming structures to realize any prescribed mechanical response under large deformation is highly desired for various functionalities, such as actuation and energy trapping. Yet, the use of a single material phase and heuristically developed structural patterns leads to restricted design space and potential failure to achieve specific target behaviors. Here, through a free-form inverse design approach, multiple hyperelastic materials with distinct properties are optimally synthesized into composite structures to precisely achieve arbitrary and extreme prescribed responses under large deformations. The digitally synthesized structures exhibit organic shapes and motions with irregular distributions of material phases. Within the structures, different materials play distinct roles yet seamlessly collaborate through sophisticated deformation mechanisms to produce the target behaviors, some of which are unachievable by a single material. While complex in geometry and material heterogeneity, the discovered structures are effectively manufactured via multimaterial fabrication with different polydimethylsiloxane (PDMS) elastomers with distinct behaviors and their highly nonlinear responses are physically and accurately realized in experiments. To enhance programmability, the synthesized structures are heteroassembled into architectures that exhibit highly complex yet navigable responses. The proposed synthesis, multimaterial fabrication, and heteroassembly strategy can be utilized to design function-oriented and situation-specific mechanical devices for a wide range of applications. 

We present a simple, effective, and scalable approach for significantly accelerating the convergence in Topology Optimization simulations. Specifically, treating the design process as a fixed-point iteration, we propose employing a recently developed acceleration technique in which Anderson extrapolation is applied periodically, with simple weighted relaxation used for the remaining steps. Through selected examples in compliance minimization, we show that the proposed approach is able to accelerate the overall simulation several fold, while maintaining the quality of the solution.