  Motivated by applications to seed germination, we consider the transverse
deflection that results from the axisymmetric indentation of an elastic
membrane by a rigid body. The elastic membrane is fixed around its boundary,
with or without an initial pre-stretch, and may be initially curved prior to
indentation. General indenter shapes are considered, and the load-indentation
curves that result for a range of spheroidal tips are obtained for both flat
and curved membranes. Wrinkling may occur when the membrane is initially
curved, and a relaxed strain-energy function is used to calculate the deformed
profile in this case. Applications to experiments designed to measure the
mechanical properties of seed endosperms are discussed.
