title: Themagneto-elastica: from self-buckling to self-assembly.
abstract: Spherical neodymium-iron-boron magnets are permanent magnets that can be assembled into a variety of structures owing 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.
authors: Mathematical Institute , University of Oxford , Oxford OX2 6GG, UK.
authors: Dominic
authors: D
authors: Vella
authors: Mathematical Institute , University of Oxford , Oxford OX2 6GG, UK.
authors: Emmanuel
authors: E
authors: du Pontavice
authors: Mathematical Institute , University of Oxford , Oxford OX2 6GG, UK.
authors: Cameron L
authors: CL
authors: Hall
authors: Mathematical Institute , University of Oxford , Oxford OX2 6GG, UK.
authors: Alain
authors: A
authors: Goriely
keywords: discrete-to-continuum asymptotics; elasticity; self-assembly