An extensible-membrane model for the mylar balloon and tendon-reinforced inflatables

Inflatable structures have a wide range of applications, including high-altitude balloons, soft robotics, and biomedical devices. In general, inflatables exhibit coupling between geometry and membrane stresses: the inflated shape determines the stress field, while the stress field dictates the shape. Analytical approaches commonly assume inextensible membranes to simplify the problem, neglecting material strain. However, membrane materials often exhibit significant deformation under relatively small loads. Here, we present an analytical model for extensible membranes illustrated using the simple case of the Mylar "party" balloon, made from two circular films sealed at the edge. We expand on prior models for inextensible membranes by incorporating both linear and bi-linear elasto-plastic constitutive models. Our results show how extensibility alters the equilibrium shape, stress distribution, and the extent of wrinkling for the inflated balloon. A nondimensional formulation generalizes the results across scales, materials, and pressures. We validate our model experimentally using 3D scanning to capture the inflated geometry, and digital image correlation to measure the membrane's strain field. We further extend this work to tendon-reinforced "pumpkin" balloons, where tendons carry loading in the meridional direction. This shifts the load carried by the membrane to the circumferential direction, allowing the balloon to withstand higher pressures while adding minimal mass.