Parametric stability investigations for hydro-statically loaded membranes

This paper discusses instabilities occurring in thin pressurized membranes, important in biological as well as in engineering contexts. The membranes are represented by only their in-plane stress components, for which an incompressible isotropic hyper-elastic behavior can be assumed. A hydro-static pressurization can give instabilities in the form of limit points with respect to a loading parameter, but also bifurcations and wrinkling. The hyper-elastic material model itself can also, under some circumstances, lead to a bifurcation situation. The instability situations can be included as constraints in a structural optimization. The paper discusses the formulation, the solution methods and some relevant instability situations. Numerical examples considering the pressurization of a flat and a cylindrical pre-stressed membrane illustrate some aspects of instability.