  We study the behaviour of circular flexible loops sedimenting in a viscous
fluid by numerical simulations and linear stability analysis. The numerical
model involves a local slender-body theory approximation for the flow coupled
to the Euler-Bernoulli elastic forces for an inextensible fibre. Starting from
an inclined circle, we simulate the dynamics using truncated Fourier modes to
observe three distinct regimes of motion: absolute stability, two-, and
three-dimensional dynamics, depending on therelative importance of elastic and
gravitational forces. We identify the governing parameter and develop a simple
semi-analytic stability criterion, which we verify numerically. In all cases,
sedimenting loops converge to stable, planar shape equilibria with one free
parameter related to the initial conditions and material properties of the
fibre.
