### Abstract or Additional Information

The nonlinear bending theory for plates describes the mechanics of a thin inextensible and incompressible film. It features a highly non-convex isometry constraint and a quadratic cost on second-order terms. This talk will be about modern developments in deriving an extension of the nonlinear bending theory for new materials, in a mathematically general and rigorous way using Gamma-convergence. I will begin by deriving a nonlinear bending theory for prestrained thin films, using convex-integration solutions to the Monge--Ampere equation. I will also discuss extensions to microheterogeneous prestrained plates with different aspect ratio; and to liquid crystal elastomer bilayers, including ongoing work on a variational relaxation problem as the regularizing Oseen-Franck term vanishes.