Three-dimensional large-deformation model of hard-magnetic soft beams

Abstract

By embedding hard-magnetic particles in soft materials, hard-magnetic soft (HMS) materials have recently been fabricated and received great interest owing to their unique properties and help in versatile applications, e.g. soft robotics, wearable devices and biomedical implants. To fulfill the potential applications of HMS materials, it is critical to develop theoretical models for HMS structures and accurately predict their mechanical responses. In this work, we develop a novel three-dimensional (3D) large deformation model for HMS beams, which are actuated by magnetic fields. To capture the geometrically exact nonlinearities of the HMS beams, three Euler angles are taken into consideration and the couplings among stretching, bending and twisting deformations are incorporated. Despite the complexity of the problem, the obtained governing equations contain only three basic field variables and could be solved by the Galerkin method combined with the Trust-region-dogleg algorithm. The effectiveness of the proposed 3D model is demonstrated by comparing current results with those of several previous examples. It is found that the hard-magnetic particles embedded in the HMS beams tend to align regularly with the applied magnetic field direction by deforming the beams via bending, twisting, stretching and/or compression. The developed 3D theoretical model offers a powerful tool to investigate the extremely large deformations of HMS beams and the results could guide the design and optimization of HMS structures.