Homogenized elastic properties of honeycomb sandwich with skin effect

The adaptation of homogenization theory to periodic plates is presented and extended to include transverse shear deformation theory for a honeycomb sandwich. Based on the scaling asymptotic expansions about plate thickness δ for sandwiches with comparable characteristic periodicity ε, the homogenization functions Π, U, and V are formulated implicitly in 3-D elliptical equations corresponding to the modes of transverse shear, in-plane stretch and out-plane bending. The solutions of these periodic functions are analytically obtained through a multi-pass homogenization technique that includes the first pass of a geometry-to-material transformation model and the second pass of 2-D unit cell homogenization. The derivation not only leads to analytical formulas of homogenized (To distinguish the homogenization between micro-scale and meso-scale, the term `homogenized' or `equivalent' is hereby used in meso-scale, corresponding to the term `effective' for micro-scale.) elastic stiffness of honeycomb sandwiches, but also demonstrates the significance of usually neglected skin effect on honeycomb computations. Finally, a periodic unit cell finite element modeling technique is developed to validate the analytical approach and further complement it with skin rigidity considered.