Packing a flexible fiber into a cavity

The insertion of an elastic rod or fiber into a confining cavity is studied. Such an insertion is a feature of a variety of problems, including packing and unpacking of DNA in viral capsids and the insertion of catheters during surgery. We consider a simplified geometry in which the container is a smooth (frictionless) circular cylinder of radius a. The fiber is pushed through a hole in the curved surface of the cylinder and is then assumed to stay in a cross-sectional plane perpendicular to the cylinder axis. A solution is found for the fiber shape in which most of the fiber lies against the curved interior surface of the cylinder, apart from the final end section of the fiber, of length 2.0888a, which crosses the interior of the cylinder before ending at the opposite side, which it meets at an angle 1.15 rad to the normal. The force required to push the fiber into the cylinder is EI/2a2, where E is the fiber's Young's modulus and I its cross-sectional moment of inertia. The shape of the final end section of the fiber is confirmed by experiment.