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On elastic spherical membranes, there is no stress induced by the bendingenergy and the corresponding Laplace-Young law does not involve the elasticbending stiffness. However, when considering an axially symmetricalperturbation that pinches the sphere, it induces nontrivial stresses on theentire membrane. In this paper we introduce a theoretical framework to examinethe stress induced by perturbations of geometry around the sphere. We find thelocal balance force equations along the normal direction to the vesicle, andalong the unit binormal, tangent to the membrane; likewise, the global balanceforce equation on closed loops is also examined. We analyze the distribution ofstresses on the membrane as the budding transition occurs. For closed membraneswe obtain the modified Young-Laplace law that appears as a consequence of thisperturbation.

Induced stresses in quasi-spherical elastic vesicles: local and global Laplace-Young law