A solid-shell model of hard-magnetic soft materials

Abstract

Hard-magnetic soft materials (HMSMs) consisting of an elastomer matrix filled with high remnant magnetic particles can exhibit flexible programmability and rapid shape changing under non-contact activation, showing promising potential applications in soft robotics, biomedical devices and flexible electronics. Precise predictions of large deformations of hard-magnetic soft materials would be a key for relevant applications. Here, we develop a magneto-mechanical theoretical framework to model large deformations of magneto-active elastomers by applying solid-shell formulations based on the variational principle. Within the 3D geometric description, the complete Green–Lagrange strain tensors are considered and thus 3D nonlinear material laws can be employed straightforwardly, without presupposing Kirchhoff–Love hypothesis and plane stress constraints. In addition, the solid-shell model avoids introducing rotational degrees of freedom in computation and thus does not require complex finite-rotation update, which also works well for thick shells at large strains. We adopt the enhanced assumed strain (EAS) and assumed natural strain (ANS) methods to overcome locking effects. Several representative examples with various deformed configurations are explored, showing precise predictions of morphological transformations of HMSMs based on our model, in good agreement with experiments. Our model provides a versatile tool to harness large deformations of magneto-elastic structures, and could be used for rational designs of active flexible devices and robots.