Boundary layers and stress concentration in the circular shearing of annular thin films

This work addresses a generalization of Dean's classical problem, which sought to explain how an annular thin elastic plate buckles under uniform shearing forces applied around its edges. We adapt the original setting by assuming that the outer edge is radially stretched while the inner rim undergoes in-plane rotation through some small angle. Boundary-layer methods are used to investigate analytically the deformation pattern which is set up and localized around the inner hole when this angle reaches a well-defined critical wrinkling value. Linear stability theory enables us to identify both the critical load and the preferred number of wrinkles appearing in the deformed configuration. Our asymptotic results are compared with a number of direct numerical simulations.