A shell model allowing folds

Starting from the Kirchhoff-Love model, we formulate a new thin shell model in linearized
elasticity which can be applied to folded shells.
The presence of a fold is solely characterized by an additonal
constraint in the variational space.
The strain energy contains a membrane-bending coupling term and a new bending strain tensor $ chi_{ alpha beta}(u)$ which measures the
infinitesimal variations of the principal curvatures of a surface.
We establish a uniqueness and existence result for shells whose midsurfaces are of class $ mathcal{G}^1$, which includes curvature discontinuities.
We give explicit relative error estimates, which are of order $h^2$, on the difference between the solution of our model and the solution of the Kirchhoff-Love shell model.