A Finite Element Framework for Magneto-Actuated Large Deformation and Instability of Slender Magneto-Active Elastomers

Abstract

In this paper, we present an efficient finite element framework for modeling the finite deformations of slender magneto-active elastomers (MAE) under applied magnetic fields or currents. For the convenience of numerical modeling, magnetic field is defined at fixed spatial coordinates in the background space rather than in the elastic MAEs using material coordinates. The magnetic field will vary with free or localized currents while the spatial distribution of the magnetic field will evolve with the motion or deformation of the MAE materials, which is actuated by the surface or body forces induced by external magnetic fields or equivalent currents. A staggered strategy and a Riks method are introduced to solve the strongly coupled governing equations of the magnetic field and displacement field using finite element method. The mesh distortion along the interfaces between MAE domain and free-space domain is resolved by considering concurrent deformation of the mesh in these two domains. A few 2D numerical examples demonstrate the validity and efficiency of the developed model for simulating large deformation of MAE with non-uniform spatial magnetic field under different actuation sources such as free currents, magnetization or external magnetic field. This framework offers a new solution strategy for modeling mechano-magneto problems of MAEs and will help rational design and analysis of MAE-based actuators and soft robotics in the future.