On the Föppl-von Kàrmàn theory for elastic prestrained films with varying thickness

We derive the variational limiting theory of thin films, parallel to the Föppl-von Kàrmàn theory in the nonlinear elasticity, for films that have been prestrained and whose thickness is a general non-constant function. Using $\Gamma$-convergence, we extend the existing results to the variable thickness setting, calculate the associated Euler-Lagrange equations of the limiting energy, and analyze convergence of equilibria. The resulting formulas display the interrelation between deformations of the geometric mid-surface and components of the growth tensor.