Bonded-particle model for magneto-elastic rods

Abstract

We develop a bonded-particle model for magneto-elastic rods that unifies large deformations, contact, and long-range magnetic interactions within a single discrete-element framework. The rod is discretized into orientable particles connected by co-rotational bonds that capture stretching, shearing, twisting, and bending through a symmetric decomposition of relative displacement and rotation. Magnetic coupling is introduced at the particle level: each particle carries a dipole moment that rotates with it, enabling both external-field actuation and long-range dipole--dipole interactions without modifying the structural formulation. We implement the model in LAMMPS to take advantage of its parallel efficiency, long-range electrostatic solvers, and multiphysics capabilities. We validate the model on three problems spanning writhing instabilities, non-uniform magnetic actuation, and dipole-induced mechanical hysteresis. To demonstrate multiphysics capability, we couple the model with a lattice Boltzmann fluid solver via the immersed boundary method and simulate filaments in oscillatory channel flow and fluid pumping by magnetically actuated cilia arrays. Across all examples, the model shows good agreement with experimental, analytical, and numerical reference results.