Plane-stress Analysis of a Holed Membrane at Finite Equibiaxial Stretch

An equibiaxially stretched thin neo-Hookean circular membrane with a hole at its center under plane-stress condition is analyzed within the framework of finite deformation elasticity. Initially, we introduce a novel form for the differential governing equation to the problem. This enables the introduction of a closed-form solution in the limit of infinite stretch. Comparison of this solution to corresponding finite element simulations reveals a neat agreement for stretch ratios larger than 2.5. In the practically important case of a small hole, at the circumference of the hole, the stress concentration factor is 4 and the tangential stretch ratio is twice the applied far-field stretch ratio. These values are double the corresponding ratios in the well-known limit of infinitesimal deformation.