Inflation of elastic membranes in contact with rigid or deformable surfaces

In this paper we address the problem of determining the equilibrium configuration of elastic membranes which enter in contact with rigid or elastic surfaces during the inflation process. The state of stress in the membrane is assessed through a simple mechanical model recently proposed by the authors to study the equilibrium shapes of highly pressurized elastic membranes. The geometrical non-linearities (local buckling and wrinkling phenomena) promoted by the small values of the membrane thickness are taken into account by means of an equivalent physical non-linearity, following an approximated but easy to handle approach. In particular, we assume the material behaves elastically when is stretched but, at the same time, it is unable to transmit any stress when it is contracted. The evolution of the wrinkled regions as well as that of the contact zones is accurately monitored for increasing inflating pressures. The numerical results, obtained by an expressly developed incremental-iterative algorithm, concern cases of contact with plane surfaces, rigid or flexible, with or without friction, thus constituting a first preliminary parametric study of the influence of the main geometrical and mechanical parameters characterizing the problem.