Homogenization of nonlinear inextensible pantographic structures by Γ-convergence

We prove the Γ-convergence of a pantographic microstructured sheet with inextensible fibers to a 2D generalized continuum model. Large deformations considered as geometrical nonlinearities are taken into account, and the Γ-convergence argument is developed in terms of convergence of measure functionals. We also prove a relative compactness property for the sequence of discrete energy functionals