A mechanics model of hard-magnetic soft rod with deformable cross-section under three-dimensional large deformation

Abstract

Hard-magnetic soft (HMS) materials are soft active materials prepared by embedding the hard-magnetic particles (e.g. NdFeB) into soft elastomer, which can be actuated by applied magnetic fields. With the ability to retain remnant magnetism, HMS materials have many applications in soft robotics, haptic sensors and other fields. For HMS structures used in soft robotics, mechanics models have been developed for better exploiting the potential of the HMS materials. However, for rod-like structures made of soft materials, the nonlinear stress–strain relation and the areal change of the cross-section have not been considered in previous modeling work. In the present three-dimensional HMS rod model, started with the geometrically exact beam theory, the rigid cross-section assumption is replaced with a planar areal change assumption for soft rods, incompressible neo-Hookean material model is used to model the hyperelastic behavior of elastomers, which will be more accurate than linear relation under large deformation. Consistent with the deformable cross-section assumption, the magneto-elastic energy distribution is formulated and reduced to the line of centroid of the soft rod. To verify the accuracy and efficiency of the model, some simulation examples and experiments are performed. The error between the experimental results and the simulation results calculated by using 5 elements is within 10%. Our model can accurately and efficiently predict the 3D large deformation of the HMS rod, which can reduce the design and optimization cost and shorten the design cycle of HMS structure.