(2008-10-14) Lewicka, Marta; Mora, Maria Giovanna; Pakzad, Mohammad Reza
Using the notion of \Gamma-convergence, we discuss the limiting behavior of the 3d nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like h^\beta with 2 < \beta < 4. We establish that, for
the given scaling regime, the limiting theory reduces to the linear pure bending. Two major
ingredients of the proofs are: the density of smooth infinitesimal isometries in the space of W^{2,2} first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with
exact isometric immersions on smooth elliptic surfaces.