Contact problems of hyperelastic membranes: Existence theory

In this paper we describe the pressure-driven inflation of an incompressible isotropic hyperelastic mem brane into a rigid mould by a variational inequality and consider the existence of a solution in the case of various, suitably modified, strain energy functions of the Ogden form. The variational inequality description is applicable to the case of perfect sliding contact of the membrane with the mould and the modification to the strain energy function is according to tension field theory which rules out compressive stresses. The modified or relaxed strain energy functions obtained are shown, in our examples, to be polyconvex and in some cases convex. Using such properties, the main result of the paper is an existence theorem for a solution of the variational inequality.