Reduced theory for hard magnetic rods with dipole-dipole interactions

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2 Citations (Scopus)


Hard magnetic elastomers are composites of soft elastic foundations and magnetic particles with high coercivity. We formulate a theoretical framework to predict the large deformation of a hard magnetic elastomeric rod. In the previous work, the magnetic Kirchhoff rod equations, which constitute a framework for analyzing instabilities for hard magnetic rods, have been developed and validated experimentally for negligible dipole-dipole interactions. Building on previous studies, we derive the magnetic Kirchhoff rod equations with dipole-dipole interactions. The derived equations are integro-differential equations, representing the force and moment balance along the rod centerline that include long-ranged dipole-magnetic force and torque. On the basis of its discrete numerical simulation, we systematically study the effect of the the dipole-dipole interactions strength on the large deformation of hard magnetic rods. In addition, we find that our theory can predict previous experimental results without any adjustable parameters.

Original languageEnglish
Article number104002
JournalJournal of Physics A: Mathematical and Theoretical
Issue number10
Publication statusPublished - 2022 Mar 11


  • dimensional reduction
  • geometry
  • instability in nonlinear systems
  • magneto-rheological elastomer
  • mechanics
  • slender structures

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)


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