Elastic stiffness and yield strength of periodic closed-cell honeycombs

The multiscale modeling idea applied to formulate an effective model of elastic behaviour of closed-cell honeycombs is presented. Essential macroscopic features of mechanical behaviour are inferred from the deformation response of a representative volume element. The structural mechanics methods are applied to the plate model of a skeleton. An analytical formulation of force-displacement relations for the skeleton elements is found by considering the affinity of nodal displacements in tensile, bending and shear deformations. The stiffness tensor for anisotropic solid may be determined depending on material properties of the solid phase and topological arrangement of cellular structure, using micro-macro transition based on micromechanical approach. Macroscopic yield condition is predicted on the basis of energy yield criterion for anisotropic solid. The study based on the assumption of linear elasticity leads to analytical formulae. The proposed theoretical framework may be extended to nonlinear behaviour, plasticity and failure analysis with the use of numerical approach.