Bending of thin periodic plates

We show that nonlinearly elastic plates of thickness h→0 with an ε -periodic structure such that ε−2h→0 exhibit non-standard behaviour in the asymptotic two-dimensional reduction from three-dimensional elasticity: in general, their effective stored-energy density is “discontinuously anisotropic” in all directions. The proof relies on a new result concerning an additional isometric constraint that deformation fields must satisfy on the microscale.