On the controllability of a creasing singularity in a nonlinear elastic circular sector

The deformation of a circular sector into a full self-contacting circle can be sustained in all homogeneous, isotropic, incompressible materials by surface tractions alone. In this class of nonlinear elastic materials, this works investigates the controllability of such a peculiar mapping having uniform constant strains and a creasing singularity. By performing a perturbative analysis based on small–on–large incremental methods, we determine the critical conditions for the normal traction load to trigger a morphological transition from the circular ground state to an elliptic shape. Such predictions are given for neo-Hookean, Gent and polynomial material models to illustrate how both geometrical and physical nonlinearities concur to this elastic instability.