On the response and stability of an inflated toroidal membrane under radial loading

• Inflation of an intrinsically and extrinsically flat toroidal membrane considered.
• Response and stability of torus subjected to radial force at inner boundary studied.
• Forcing under constant pressure and constant amount of gas conditions considered.
• Below the pressure limit point, wrinkling and pull-in stability boundaries revealed.
• Force–deflection characteristics exhibit a power law behaviour.

Two flat annular hyperelastic membranes, stacked and bonded together at both the boundaries (equators), form a closed inflatable structure of toroidal topology. The response and stability of the inflated toroidal structure subjected to a radial line force distribution at the inner boundary are studied. The forcing is considered under constant pressure and constant amount of gas inflation conditions. Two hyperelastic models described by the corresponding relaxed strain energy density functions are considered for the membrane material. The influence of geometry, material and level of inflation on the response and stability of the structure under load has been brought out. The structure exhibits pressure limit points with increasing levels of inflation. The force–deflection (stiffness) behaviour is found to be qualitatively different below and above the pressure limit points. Below the pressure limit point, wrinkling and pull-in under loading are revealed for different inflation conditions, and the stability boundaries are determined. Under certain conditions, a counter-intuitive stretch-softening behaviour is also observed.