Keywords: thin membrane, pressurization, hydro-static loading, instability, optimization, simulations..

This paper discusses instabilities occuring 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 hyperelastic behavior can be assumed. The inherently non-linear response to pressurization can give instabilities in the forms 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. A numerical example considering the internal pressurization of a cylindrical pre-stressed membrane illustrates some aspects of instability.

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