Bending of thin periodic plates

Abstract

We show that nonlinearly elastic plates of thickness $h\to 0$ with an $\epsilon$-periodic structure such that ${\epsilon }^{-2}h\to 0$ 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.

35 pages

References in corpus (1)

• High contrast homogenisation in nonlinear elasticity under small loads