Magneto-rheological elastomers (MREs) are functional materials whose mechanical properties can be controlled upon the application of an external magnetic field. MREs comprise a composite of hard magnetic particles dispersed into a nonmagnetic elastomeric (soft) matrix. Recently, there have been significant theoretical developments in continuum (3D) description of MERs and its specialization to simple structural elements, including linear beams and elastica. In this talk, we derive an effective theory for MRE rods under geometrically nonlinear deformation. Our theory is based on reducing the 3D magneto-elastic energy functional for the hard magnetic soft elastomer into a 1D (centerline and Kirchhoff-like) description. We demonstrate our theory's power by studying a set of problems where the buckling behavior of MRE rods can be programmed. Our theoretical predictions are found to be in excellent agreement with both discrete simulations and precision-model experiments.

A Kirchhoff-like theory for hard magnetic rods under three-dimensional geometrically nonlinear deformation

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