Multiphysics topology optimization of magnetic materials with continuous magnetization orientations

In recent years, magnetic-responsive soft materials with high remanent magnetization have received significant attention due to their capacity for untethered and rapid actuation under magnetic fields, with diverse applications spanning robotics, biomedicine, and vibration mitigation. Most designs of the magnetic soft materials rely on discrete remanent magnetization orientations, which could limit the actuation performance because of the restricted selection of magnetization orientations and potentially cause fabrication challenges due to the sharp changes in magnetization orientations at the interfaces that may induce strong repelling forces. To expand the programmability and improve the fabricability of the magnetic soft materials, we enable design capability with optimal continuous magnetization orientations. This paper proposes a multiphysics topology optimization framework that concurrently optimizes topologies and continuous remanent magnetization distributions in the magnetic soft materials and structures. Employing the proposed approach, we design and investigate problems of letter programming, actuators, and metamaterials with magnetic actuation under large deformations. We demonstrate that the proposed strategy enhances design flexibility, improves performance, eliminates sharp changes in magnetization orientations, and is capable of creating non-intuitive designs that can achieve multiple functionalities. Finally, we prototype our optimized design to highlight its potential to bridge design optimization and direct-ink-writing fabrication of magnetic materials with continuously varying magnetization orientations.