  We study the homogenization of the Thomas-Fermi-von Weizsacker (TFW) model
for 2D materials. It consists in considering 2D-periodic nuclear densities with
periods going to zero. We study the behavior of the corresponding ground state
electronic densities and ground state energies. The main result is that these
three dimensional problems converge to a limit model that is one dimensional.
We also illustrate this convergence with numerical simulations and estimate the
converging rate for the ground state electronic densities and the ground state
energies.
