The magneto-elastica: from self-buckling to self-assembly

D. Vella, E. du Pontavice, C. L. Hall, A. Goriely

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)20130609
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2162
StatePublished - Dec 4 2013
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication is based in part upon work supported by award no. KUK-C1-013-04, made by the King Abdullah University of Science and Technology (KAUST). A. G. is a Wolfson/Royal Society Merit Award holder and acknowledges support from a Reintegration grant under EC Framework VII. A. G. and C. H. acknowledge support from the EPSRC through grant no. EP/I017070/1.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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