  Spherical neodymium-iron-boron magnets are perman-ent magnets that can be
assembled into a variety of structures due to their high magnetic strength. A
one-dimensional chain of these magnets responds to mechanical loadings in a
manner reminiscent of an elastic rod. We investigate the macroscopic mechanical
properties of assemblies of ferromagnetic spheres by considering chains, rings,
and chiral cylinders of magnets. Based on energy estimates and simple
experiments, we introduce an effective magnetic bending stiffness for a chain
of magnets and show that, used in conjunction with classic results for elastic
rods, it provides excellent estimates for the buckling and vibration dynamics
of magnetic chains. We then use this estimate to understand the dynamic
self-assembly of a cylinder from an initially straight chain of magnets.
