Equilibrium and stability of soft-magnetic particle assemblies: A multipole model with polymer chain elasticity
Abstract
We present a discrete model for the equilibrium and stability of soft-magnetic particle-filled elastomers. The finite-sized spherical particles are tethered to the surrounding matrix or to neighboring particles by freely-jointed polymer chains with finite extensibility. The magnetic interactions are resolved through an approximate, self-consistent, saturating local-field magnetic dipole-dipole model augmented with dipole–quadrupole corrections. The latter become significant near contact, which is enforced through a simple Signorini contact model. The coupled magneto-elastic–contact problem is solved by two complementary strategies: an implicit arc-length continuation method that traces the complete equilibrium path, including unstable branches and limit points, and an explicit overdamped integrator that follows the physically realized loading and captures snap-through instabilities and the associated hysteresis. For two- and four-particle anchored assemblies, the model reveals three elementary regimes, i.e. repulsion, attraction, and repulsion-then-attraction. In turn, when extended to periodic body-centered-cubic arrays, the framework reveals collective particle chain formation and contact avalanches whose magnitude is governed by the compliance of the polymer chains. The additional dipole–quadrupole corrections leave global magnetization and the onset of bifurcation largely unchanged but increase the contact fraction and promote thicker particle-chain clustering near contact.
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BibTeX
@article{danas2026equilibrium,
title = {{Equilibrium and stability of soft-magnetic particle assemblies: A multipole model with polymer chain elasticity}},
author = {Kostas Danas and Noy Cohen},
journal = {Journal of the Mechanics and Physics of Solids},
year = {2026},
month = sep,
doi = {10.1016/j.jmps.2026.106848},
url = {https://polytechnique.hal.science/hal-05753962v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Equilibrium and stability of soft-magnetic particle assemblies: A multipole model with polymer chain elasticity
AU - Kostas Danas
AU - Noy Cohen
PY - 2026
DA - 2026/09/17
JO - Journal of the Mechanics and Physics of Solids
DO - 10.1016/j.jmps.2026.106848
UR - https://polytechnique.hal.science/hal-05753962v1
AB - We present a discrete model for the equilibrium and stability of soft-magnetic particle-filled elastomers. The finite-sized spherical particles are tethered to the surrounding matrix or to neighboring particles by freely-jointed polymer chains with finite extensibility. The magnetic interactions are resolved through an approximate, self-consistent, saturating local-field magnetic dipole-dipole model augmented with dipole–quadrupole corrections. The latter become significant near contact, which is enforced through a simple Signorini contact model. The coupled magneto-elastic–contact problem is solved by two complementary strategies: an implicit arc-length continuation method that traces the complete equilibrium path, including unstable branches and limit points, and an explicit overdamped integrator that follows the physically realized loading and captures snap-through instabilities and the associated hysteresis. For two- and four-particle anchored assemblies, the model reveals three elementary regimes, i.e. repulsion, attraction, and repulsion-then-attraction. In turn, when extended to periodic body-centered-cubic arrays, the framework reveals collective particle chain formation and contact avalanches whose magnitude is governed by the compliance of the polymer chains. The additional dipole–quadrupole corrections leave global magnetization and the onset of bifurcation largely unchanged but increase the contact fraction and promote thicker particle-chain clustering near contact.
SN - 0022-5096
ER -