A theory of magneto-elastic nanorods obtained through rigorous dimension reduction

Starting from a two-dimensional theory of magneto-elasticity for fiber-reinforced magnetic elastomers we carry out rigorous dimension reduction to derive rod model that describes thin magneto-elastic strip undergoing planar deformations. The main features the are following: interaction energy manifests itself through distributed torque; penalization term prevents local interpenetration matter; regularization depends on second gradient deformation and models microstructure-induced size effects. As an application, consider problem involving magnetically-induced buckling study how intensity field at onset instability increases if length is decreased. Finally, assess accuracy deduced by performing numerical simulations where compare one-dimensional theories in some special cases, observe excellent agreement.