## Abstract

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 language | English |
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Article number | 104002 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 55 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2022 Mar 11 |

## Keywords

- 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)