Free and constrained inflation of elastic membranes in relation to thermoforming — non-axisymmetric problems

Abstract

This paper deals with the inflation of elastic membranes of general shapes in the context of thermoforming of heated polymeric sheets against relatively cold moulding surfaces. A previous paper (1) has dealt with axisymmetric problems. As before, both theoretical and experimental investigations are reported. The theoretical part consists of a self-contained finite element formulation for large deformation, free and constrained inflation of isotropic elastic membranes. The computer program developed on the basis of presented formulation is applied to free and constrained inflation of plane elliptical membranes of aspect ratios 2 and 4. The material model adopted is that of a single constant neo-Hookean elastic material. The constrained analyses are carried out for inflation against: (a) cylindrical walls (90 degree elliptical cones), (b) 60 degree elliptical cones, and (c) horizontal plates. Separate analyses are performed by assuming the contact to be either slipless or frictionless. The theoretical results are compared with the experimental ones for free inflation and constrained inflation cases (a) and (c).