Bonded-particle model for magneto-elastic rods

TL;DR

This paper introduces a discrete-element bonded-particle model for magneto-elastic rods that captures large deformations, magnetic interactions, and fluid coupling within a unified framework, validated against multiple benchmarks.

Contribution

The authors develop a novel particle-based model that integrates mechanical and magnetic behaviors of rods, implemented in LAMMPS for efficiency and multiphysics simulations.

Findings

Model accurately predicts writhing and large deflections of magnetized rods.

Coupled with fluid dynamics, the model simulates magnetically actuated filaments in flow.

Good agreement with experimental, analytical, and numerical results across benchmarks.

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, bending, and twisting 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 framework against three benchmark problems: writhing instabilities of straight and curved rods under extreme twisting, large deflections of magnetized beams in uniform and constant-gradient fields, and mechanical hysteresis of helical rods with dipole--dipole interactions. 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.