Buckling morphology of an elastic ring confined in an annular channel

This paper studies the buckling morphology transition of an elastic ring confined in an annular channel. Under uniform axial strain, the ring would first form one inward blister and then transit to an "S" shape, but does not induce more blisters due to an energy barrier caused by the annular shape of the channel. In order to overcome the energy barrier, external perturbation is employed and a stable morphology with multiple blisters may be obtained. A theoretical framework is then established to calculate the bifurcation points of the shape transition, which agrees well with finite-element (FEM) simulation results. The diagrams of the stable buckling morphologies with respect to the geometrics of the elastic rings are presented, which may provide useful insights for practical applications, for example, the design of a peristaltic pump.