Inhomogeneous spherical configurations of inflated membranes

Based on physically meaningful choice of the strain measures, we study the equilibrium and stability of an inflated spherical membrane. First, we obtain general results deduced by global geometric properties and then we analyze the possibility of inhomogeneous configurations. The stability analysis shows that under special constitutive assumptions the global energy minimum can be attained by inhomogeneous spherical configurations that we analytically describe. We argue that these deformations can reproduce well-known experimental results.