  We study the equilibrium configurations related to the growth of an elastic
fibre in a confining flexible ring. This system represents a paradigm for a
variety of biological, medical, and engineering problems. We consider a
simplified geometry in which initially the container is a circular ring of
radius $R$. Quasi-static growth is then studied by solving the equilibrium
equations as the fibre length $l$ increases, starting from $l = 2R$.
Considering both the fibre and the ring as inextensible and unshearable, we
find that beyond a critical length, which depends on the relative bending
stiffness, the fibre buckles. Furthermore, as the fibre grows further it folds,
distorting the ring until it induces a break in mirror symmetry at $l>2 \pi R$.
We get that the equilibrium shapes depend only on two dimensionless parameters:
the length ratio $\mu = l/R$ and the bending stiffnesses ratio $\kappa$. These
findings are also supported by finite element simulation. Finally we
experimentally validate the theoretical results showing a very good
quantitative prediction of the observed buckling and folding regimes at
variable geometrical parameters.
