A Kirchhoff-like theory for the mechanics of magnetic rods

Magneto-rheological elastomers (MREs) are functional materials that can undergo deformations when subject to external magnetic fields. MREs consist of hard magnetic particles dispersed into a nonmagnetic elastomeric (soft) matrix. There have been recent advances in the theoretical description of MREs using the framework of (3D) continuum mechanics. Reduced-order structural theories have also been developed for magnetic linear beams and elastica, based on the planar (2D) deformation of the centerline. In this talk, we derive an effective theory for rods made of MRE undergoing 3D geometrically nonlinear deformations. Our theory is based on the procedure of dimensional reduction of the 3D magneto-elastic energy functional of the MRE into a 1D (centerline and Kirchhoff-like) description, which encompasses the previous 2D theories under appropriate limits. We demonstrate the accuracy of our theory by performing precision-model experiments to explore a set of specific problems involving the buckling behavior of MRE rods. These experiments are also used to test the range of validity of our theory.