Topology optimization of hard-magnetic soft materials

Hard-magnetic soft materials, which consist of soft matrix embedded with hard-magnetic particles, have attracted tremendous interests owing to their untethered control capability, rapid response, and flexible programmability. This work introduces a powerful topology optimization framework to guide the rational design of hard-magnetic soft materials and structures with precisely programmable functionalities under large deformations. Built upon a unified design parameterization scheme, the proposed framework is capable of simultaneously optimizing topology, remnant magnetization distribution, and applied magnetic fields. Thus, guided by the analytical gradient information, our framework can effectively explore the entire design space to search for optimized structures with multiple target functionalities, such as programmable deformations and maximized actuation, under the corresponding optimized magnetic fields. Through five design examples, we showcase applications of the proposed framework in generating optimized shape-programming metastructures and robots, magnetic actuators, and unit cells with encoded and adaptable modes. We demonstrate how simultaneous optimization in topology, magnetization distribution, and applied magnetic field can greatly improve the performance of a design, and highlight the importance of accounting for finite-rotation kinematics to capture the influence of body torque-related magnetic force on the optimized remnant magnetization distribution. Various optimized magnetic-responsive designs with comparable performances yet distinct mechanisms are discovered, showing the effectiveness of the proposed framework to generate unconventional designs with highly programmable magnetic-actuated behaviors. We envision that the proposed topology optimization framework can potentially benefit the design process in a wide spectrum of magnetic-responsive applications, such as soft robots, magnetic actuators, and programmable metamaterials.