Mechanics of materially uniform thin films

A pure-bending model for thin films, accurate to leading order in film thickness, is rigorously established on the basis of the three-dimensional theory of materially uniform elastic bodies. A model accounting for both stretching and bending is also proposed. This incorporates a natural extension of Koiter’s theory. We show that the classical Kirchhoff–Love hypothesis, to the effect that material lines normal to the film remain so in the course of deformation, is not generally valid.