Finite Indentation of an Elastic Membrane by a Spherical Indenter

Rotatlonally Symmetrie stresses and deformations are considered for a prestressed elastic sheet of circular outer boundary loaded transversely by a centered indenter with a hemispherical tip. A nonlinear membrane solution is obtained for the portion of the sheet that is in frictionless contact with the rigid tip of the indenter. This solution and the solution that was previously obtained for a prestressed annular membrane [Ref. 1] are used to obtain the exact solution for stresses and deflections in the indented membrane. Simpler, limiting expressions for stresses and deflections are also obtained for sufficiently large and sufficiently small indenter loads. Comparison of computed results from this analysis with the experimental results of Jahsman, Field and Holmes [Ref. 2] on stretched mylar membranes shows good agreement except in the immediate neighborhood of the indenter. The theory shows that yielding and plastic deformation of the membrane is incipient for a relatively small value of the Indenter load, and, for these experiments, this limiting value is less than the least value of indenter load for which data was reported.