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

Magneto-rheological elastomers (MREs) are functional materials that can be actuated by applying an external magnetic field. MREs comprise a composite of hard particles dispersed into nonmagnetic elastomeric matrix. By strong field, one magnetize the structure to program its deformation under subsequent application Hard MREs, whose coercivities large, have been receiving particular attention because programmed magnetization remains unchanged upon actuation. Hence, once made MRE is magnetized, it regarded as magnetized permanently. Motivated new realm applications, there significant theoretical developments in continuum description MREs. reducing 3D 1D or 2D via dimensional reduction, several theories slender structures such linear beams, elastica, and shells recently proposed. In this paper, we derive effective theory for rods geometrically nonlinear deformation. Our based on magneto-elastic energy Kirchhoff-like description. Restricting 2D, reproduce previous works planar deformations. For further validation general case deformation, perform precision experiments with both naturally straight curved either constant constant-gradient fields. predictions excellent agreement discrete simulations precision-model experiments. Finally, discuss some limitations our framework, highlighted experiments, where long-range dipole interactions, which neglected theory, play role.