Dynamical modeling of magneto-hyperelastic plates based on ANCF and its application to magnetic-driven jellyfish robots

Magnetic-driven soft robots have attracted widespread attention in engineering applications due to their advantages of wireless control, high precision, and miniaturization. Accurate numerical simulation serves as an indispensable tool for the optimal design and performance prediction in robotics. In this work, an accurate dynamic model of the incompressible magneto-hyperelastic plate made of a hyperelastic elastomer matrix embedded with hard-magnetic particles is developed. To calculate the dynamics, a versatile C1-continuous ANCF triangular element is introduced to discretize the plate model, which is suitable for meshing complex geometries due to its flexibility in conforming to arbitrary boundaries. Moreover, to alleviate the volumetric locking problem, an enhanced incompressibility condition is incorporated, resulting in a correction of the elastic energy via a coupling term of the in-plane strains and out-of-plane curvatures. Several benchmarks are adopted to validate the plate model, confirming its effectiveness in describing both large displacements and large deformations under the magnetic field. To show its capability of dealing with complex geometric plates, the present model is further applied to analysis of the magnetic-driven jellyfish-inspired soft robot. The proposed magneto-hyperelastic plate model offers a reliable technique for rapid prototyping and performance optimization of magnetic-driven soft robots in soft mechatronics and bio-inspired engineering.