Abstract

Spherical neodymium-iron-boron magnets are marketed as toys as they can be assembled into different shapes due to their high magnetic strength. In particular, we consider two simple structures, chains and cylinders of magnets. By manipulating these structures, it quickly appears that they exhibit an elastic response to small deformations. Indeed, chains buckle on their own weight, rings oscillate, and cylinders resist bending but recover their shape after poking. A natural question is then to understand the response of these structures based on the individual physical properties of the magnets and to understand to what extent they behave elastically. In this talk, I will show through illustrative experiments and simple model calculations that the idea of an effective magnetic bending stiffness is, in fact, an excellent macroscopic characterisation for the mechanical response of magnetic chains. I will then propose a more rigorous approach of the problem by considering discrete-to-continuum asymptotic analysis to derive a continuum model for the energy of a deformed chain of magnets based on the magnetostatic interactions between individual spheres.