A discrete model for the geometrically nonlinear mechanics of hard-magnetic slender structures

Abstract

Hard-magnetic soft (HMS) materials and structures, which can undergo rapid configurational transformation under non-contact magnetic stimuli, have attracted extensive attentions in a wide range of engineering applications, such as soft robotics, biomedical devices and stretchable electronics, etc. In order to realize the full potentials of HMS structures, it is crucial to be able to predict their mechanical (both static and dynamic) responses. In this work, we propose a discrete magneto-elastic rod model with the aim to analyse the mechanical behaviours of slender structures made of HMS materials under magnetic loading. The configuration of a slender object is described by multiply connected nodes and edges, from which the force vector and the associated Hessian matrix are derived by taking the variation of Kirchhoff-like magneto-elastic potentials. The nonlinear dynamical equations of motion are next evaluated through Newton-type optimization, and the static analysis can be obtained using dynamical relaxation method. For verification, we quantitatively compare our numerical results with either analytical solutions or experimental data for several representative cases. Good agreements in all these cases indicate the correctness and accuracy of our discrete model. We further extend the model to take the dipole–dipole interaction and viscous effect into consideration. Finally, as a demonstration, we perform simulations to reproduce the locomotion of a magnetic crawling robot. The developed discrete magneto-elastic model significantly improves the computational efficiency, enabling the practicability of simulating the mechanical, especially dynamic, behaviours of the hard-magnetic slender structures.