Anisotropic Effects on the Nonlinear Dynamics of the Hard-Magnetic Soft Actuators

In recent years, there has been considerable research interest in hard-magnetic soft active materials due to their benefits, such as untethered, rapid, and reversible actuation, coupled with substantial shape change. Typically, these materials are formed by incorporating hard-magnetic particles into a soft matrix. The actuation process relies on the magnetic particles induced by the applied magnetic field on the soft matrix. Consequently, the efficiency of actuation is significantly influenced by the anisotropy of the soft matrix. This article presents a theoretical framework for modelling the dynamic behaviour of hard-magnetic soft materials and delves into an examination of how the transverse anisotropy impacts the actuation efficiency in dynamic mode. The analysis uncovers the pivotal role of transverse anisotropy in determining actuation efficiency. A physics-based Polignone material model is utilized to consider the transverse anisotropy of the HMSM. The governing equation for dynamic motion is derived using Euler-Lagrange’s principle for nonconservative systems, enabling the characterization of nonlinear oscillations under constant and periodic magnetic fluxes. The dynamic stability, resonance properties, dynamic response, and periodicity are examined through frequency response spectra, time history graphs, phase-plane diagrams, and Poincaré maps. The investigation aims to understand the effect of the anisotropy on the nonlinear oscillations and capture the dynamic behaviour of the actuators.