Magnetic chains: From self-buckling to self-assembly

TL;DR

This paper explores the mechanical behavior of magnetic chains made of neodymium magnets, introducing an effective magnetic bending stiffness to predict buckling, vibrations, and self-assembly dynamics.

Contribution

It introduces a novel effective magnetic bending stiffness for magnetic chains, enabling accurate modeling of their buckling, vibrations, and self-assembly behaviors.

Findings

Magnetic chains behave like elastic rods with an effective magnetic bending stiffness.

The model accurately predicts buckling and vibration dynamics of magnetic chains.

Magnetic chains can self-assemble into cylindrical structures based on the proposed model.

Abstract

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.