SUMMARYWe establish a version of the inÿnitesimal rigid displacement lemma in curvilinear Lipschitz coordinates. We give an application to linearly elastic shells whose midsurface and normal vector are both Lipschitz.

In surgical practice, with the parameters of our experimental Wistar rats model (vessel diameter, length of dissection), it is fundamental to be below 105 degrees of torsion angle for the vein microanastomosis, in order to decrease its risk of failure.

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We present an existence theorem for a large class of nonlinearly elastic shells with low regularity in the framework of a two-dimensional theory involving the mean and Gaussian curvatures. We restrict our discussion to hyperelastic materials, that is to elastic materials possessing a stored energy function. Under some specific conditions of polyconvexity, coerciveness and growth of the stored energy function, we prove the existence of global minimizers. In addition, we define a general class of polyconvex stored energy functions which satisfies a coerciveness inequality.Comment: 13 page