Waves from a suddenly punched hole in an elastic sheet subjected to finite simple tension

We consider the plane stress unloading waves emanating from a suddenly punched circular hole in a thin elastic sheet, subjected to an initial finite deformation simple tension. The sheet is assumed to be hyperelastic, isotropic, incompressible and thin enough that the generalized plane stress approximation is valid. It is further assumed that the plugging of the hole is due to normal impact of a cylindrical projectile and that the impact velocity of the projectile is sufficiently high that the plugging can be assumed instantaneous. The governing equations of the problem are obtained in Lagrangian form with respect to a reference configuration that is the initial stretched configuration. A numerical scheme is proposed for the solution of the governing equations, and numerical results are obtained for the neo-Hookean strain energy function. However with some additional complication other isotropic strain energy functions can be considered.