A 3D hard-magnetic rod model based on co-rotational formulations

Hard-magnetic soft materials have attracted broad interests because of their flexible programmability, non-contact activation and rapid response in various applications such as soft robotics, biomedical devices and flexible electronics. Such multifunctional materials consist of a soft matrix embedded with hard-magnetic particles, and can exhibit large deformations under external magnetic stimuli. Here, we develop a three-dimensional (3D) rod model to predict spatial deformations (extension, bending and twist) of slender hard-magnetic elastica. The model follows Kirchhoff hypothesis and thus reduces the 3D magneto-elastic energy function to a one-dimensional (1D) form. Besides, the co-rotational formulation is applied to describe rigid body motion, and explicit time integration is adopted for the nonlinear resolution. Moreover, we explore finite bending, post-buckling and twisting of hard-magnetic elastica under external magnetic fields with different directions and amplitudes. Representative examples with various configurations show superior efficiency and accuracy of the model (the difference less than 1% with only a small number of elements) compared to conventional solid element. Our model could be used to guide rational designs on programmable shape morphing of ferromagnetic slender structures.

Acta Mechanica Sinica, 38, 222085, 2022. https://doi.org/10.1007/s10409-022-22085-x