We derive a dimensionally reduced model for a thin film prestrained with a given incompatible Riemannian metric:
where is the thickness of the film. The problem is studied rigorously by using a variational approach and establishing the -convergence of the non-Euclidean version of the nonlinear elasticity functional. It is shown that the residual nonlinear elastic energy scales as as .
"Relative bending energy for weakly prestrained shells." Rocky Mountain J. Math. 50 (3) 1001 - 1020, June 2020. https://doi.org/10.1216/rmj.2020.50.1001