Bending of thin periodic plates

Original · EN

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.