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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.