Fictitious Magnetic Charge Model for Magneto-Mechanical Metamaterials

Abstract Magnetically actuated intelligent structures have shown great promise in various applications ranging from soft robotics to biomedical devices. One important type of structure involves embedding rigid magnets in polymer matrices, thanks to their simplicity in manufacturing and flexibility in structure design. However, accurately modeling their behavior remains challenging due to the strong nonlinear coupling between large deformation and spatially varying magnetic fields. To address this, we employ a fictitious magnetic charge method to transfer the magnetic forces and torques into surface traction under both uniform and nonuniform external magnetic actuation. We implement the proposed method in the commercial finite element software abaqus and validate it through a series of benchmark examples, which cover tuning the area of magneto-mechanical metamaterials, the shape changing of magnetic lattice structures, and the magnetic-field-driven buckling of cellular structures. Our approach enables accurate prediction of shape transformations in magnetically responsive structures, offering a practical tool for the design and optimization of future magneto-mechanical metamaterials and devices.