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Abstract The properties of materials and structures typically remain fixed after being designed and manufactured. There is a growing interest in systems with the capability of altering their behaviors without changing geometries or material constitutions, because such reprogrammable behaviors could unlock multiple functionalities within a single design. We introduce an optimization-driven approach, based on multi-objective magneto-mechanical topology optimization, to design magneto-active metamaterials and structures whose properties can be seamlessly reprogrammed by switching on and off the external stimuli fields. This optimized material system exhibits one response under pure mechanical loading, and switches to a distinct response under joint mechanical and magnetic stimuli. We discover and experimentally demonstrate magneto-mechanical metamaterials and metastructures that realize a wide range of reprogrammable responses, including multi-functional actuation responses, adaptable snap-buckling behaviors, switchable deformation modes, and tunable bistability. The proposed approach paves the way for promising applications such as magnetic actuators, soft robots, and energy harvesters.

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.

Abstract Practical engineering designs typically involve many load cases. For topology optimization with many deterministic load cases, a large number of linear systems of equations must be solved at each optimization step, leading to an enormous computational cost. To address this challenge, we propose a mirror descent stochastic approximation (MD-SA) framework with various step size strategies to solve topology optimization problems with many load cases. We reformulate the deterministic objective function and gradient into stochastic ones through randomization, derive the MD-SA update, and develop algorithmic strategies. The proposed MD-SA algorithm requires only low accuracy in the stochastic gradient and thus uses only a single sample per optimization step (i.e., the sample size is always one). As a result, we reduce the number of linear systems to solve per step from hundreds to one, which drastically reduces the total computational cost, while maintaining a similar design quality. For example, for one of the design problems, the total number of linear systems to solve and wall clock time are reduced by factors of 223 and 22, respectively.