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Thin beams made of magnetorheological elastomers embedded with hard magneticparticles (hard-MREs) are capable of large deflections under an appliedmagnetic field. We propose a comprehensive framework, comprising a beam modeland 3D finite element modeling (FEM), to describe the behavior of hard-MREbeams under both uniform and constant gradient magnetic fields. First, based onthe Helmholtz free energy of bulk (3D) hard-MREs, we perform dimensionalreduction to derive a 1D description and obtain the equilibrium equation of thebeam through variational methods. In parallel, we extend the existing 3Dcontinuum theory for hard-MREs to the general case of non-uniform fields byincorporating the magnetic body force induced by the field gradient andimplementing it in FEM. The beam model and FEM are first validated usingexperiments and then employed to predict the deflection of a cantilever beam ineither a uniform or a constant gradient field. The corresponding parametersgoverning the magneto-elastic coupling are identified. Then, a set ofcomparative numerical studies for actuation in different configurations yieldsadditional insight into the beam response. Our study builds on previous work onhard-MRE beams, while providing a more complete framework, both in terms of themethodologies used and the configurations considered, to serve as a valuablepredictive toolbox for the rational design of beam-like hard-magneticstructures.

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