Contact problems of hyperelastic membranes: Existence theory

In this paper we describe the pressure-driven inflation of an incompressibl e isotropic hyperelastic membrane into a rigid mould by a variational inequ ality and consider the existence of a solution in the case of various, suit ably modified, strain energy functions of the Ogden form. The variational i nequality description is applicable to the case of perfect sliding contact of the membrane with the mould and the modification to the strain energy fu nction is according to tension field theory which rules out compressive str esses. The modified or relaxed strain energy functions obtained are shown, in our examples, to be polyconvex and in some cases convex. Using such prop erties, the main result of the paper is an existence theorem for a solution of the variational inequality. Copyright (C) 2000 John Wiley & Sons, Ltd.