A Note on Convergence of Low Energy Critical Points of Nonlinear Elasticity Functionals, for Thin Shells of Arbitrary Geometry

We prove that the critical points of the 3d nonlinear elasticity functional on shells of small thickness h, around the mid-surface S of arbitrary geometry, converge as h → 0 to the critical points of the von Kármán functional on S, recently derived in [14]. We prove the same convergence result for the weak solutions to the static equilibrium equations (formally the EulerLagrange equations associated to the elasticity functional). These convergences hold provided the elastic energy of the 3d deformations scale like h and the external body forces scale like h.