Buckling and zipping of a magnetic ring under gravity

Assemblies of magnetic beads, also called magnetostructures, exhibit interesting mechanical properties, adapting orientations of the dipoles to minimize the dipolar energy. A ring made of N spherical magnetic beads behaves like an elastic annulus. This elastic-like property is due to the dipolar nature of the particles. When submitted to gravity and as a function of its size, the initial circular shape of a magnetic ring is seen to experience flattening. This capsule-like shape appears when the number N of magnets reaches a critical point scaling with the Bond number N_{f}∝Bo^{-1/3}. When the number of magnets increases more and more, the ring starts to buckle and a flat object appears at a second critical point N_{z}∝Bo^{-1}+b. There, a zipping state corresponding to the attraction of two opposite sides is formed. We propose a theoretical approach to capture these scaling laws in agreement with experimental data. All shapes are also numerically obtained in a discrete element model confirming our findings.