  We study the deformations of elastic filaments confined within
slowly-shrinking circular boundaries, under contact forces with friction. We
perform computations with a spring-lattice model that deforms like a thin
inextensible filament of uniform bending stiffness. Early in the deformation,
two lobes of the filament make contact. If the friction coefficient is small
enough, one lobe slides inside the other; otherwise, the lobes move together or
one lobe bifurcates the other. There follows a sequence of deformations that is
a mixture of spiraling and bifurcations, primarily the former with small
friction and the latter with large friction. With zero friction, a simple model
predicts that the maximum curvature and the total elastic energy scale as the
wall radius to the -3/2 and -2 powers respectively. With nonzero friction, the
elastic energy follows a similar scaling but with a prefactor up to 8 times
larger, due to delayering and bending with a range of small curvatures. For
friction coefficients as large as 1, the deformations are qualitatively similar
with and without friction at the outer wall. Above 1, the wall friction case
becomes dominated by buckling near the wall.
