A comprehensive framework for hard-magnetic beams: Reduced-order theory, 3D simulations, and experiments

Thin beams made of magnetorheological elastomers embedded with hard-magnetic particles (hard-MREs) are capable large deflections under an applied magnetic field. We propose a comprehensive framework, comprising beam model and 3D finite element modeling (FEM), to describe the behavior hard-MRE both uniform constant gradient fields. First, based on Helmholtz free energy bulk (3D) hard-MREs, we perform dimensional reduction derive 1D description obtain equilibrium equation through variational methods. In parallel, extend existing continuum theory for hard-MREs general case non-uniform fields by incorporating body force induced field implementing it in FEM. Then, validate FEM using experiments cantilever either or field, identify dimensionless parameters governing magneto-elastic coupling. Further, set comparative numerical studies different configurations magnetization profiles yields additional insight into response. Our study builds previous work beams, while providing more complete terms methodologies used broader range considered, serving as valuable predictive toolbox rational design beam-like structures.