Mechanics of hard-magnetic soft materials: A review

Hard-magnetic soft materials are a class of magnetically responsive composites obtained by embedding hard-magnetic particles into a soft polymeric matrix. They have found widespread applications in shape-morphing systems, soft robotics, biomedical devices, and active metamaterials due to their ability to feature complex, untethered, reversible, and rapid deformations in response to magnetic loads. To guide the rational design of these functional applications, extensive efforts have been devoted to studying the mechanical behavior of hard-magnetic soft materials. In this paper, we review the recent progress in the mechanics of hard-magnetic soft materials. First, we introduce existing constitutive models capable of describing the coupled magneto-elastic deformations of hard-magnetic soft materials. Then, we discuss the mechanical response of structures made of hard-magnetic soft materials, including rods, beams, plates, and shells, under mechanical and magnetic loading. Subsequently, we introduce the design and behavior of magneto-mechanical metamaterials with tunable properties enabled by hard-magnetic soft materials. In addition, optimization-guided inverse design strategies for hard-magnetic soft materials to achieve predefined properties or deformations are also briefly reviewed. Finally, we provide our views on the potential future directions in the field of mechanics of hard-magnetic soft materials. We expect the current review to guide researchers to better understand different theoretical and computational frameworks of mechanics of hard-magnetic soft materials and thus aid with designing functional systems using these materials for various applications.