In-plane homogenization of commercial hexagonal honeycombs considering the cell wall curvature and adhesive layer influence

In the present paper a general parameterization of a periodic hexagonal honeycomb with double vertical walls (commercial honeycomb) is proposed and a new analytic model is established. More attention is paid to account for the radius of curvature of the inclined walls, the adhesive layer thickness, and adhesive fillet at nodes. Then, neglecting the skin effect, in plane elastic constants is obtained analytically using the beam theory. The deformation mechanisms of the honeycomb cells include flexure, stretching, shearing and hinging. The mechanism of hinging is included through small fictitious beams in order to balance the local effects which cannot be captured using the beam theory. Hinging can be neglected when the thickness of these beams becomes infinite or optimally chosen by a proper thickness as to minimize the cumulative errors of the analytical assumptions. The new analytic model presented in this paper can be particularized to the extended Balawi and Abot model if some parameters are adequately modified. The finite element modeling of a representative volume element is used for model calibration and validation considering different relative densities of real honeycombs. The numerical results obtained as a reference for the effective elastic constants are discussed by comparing them to the ones given by the analytic model; its advantages and pitfalls are discussed and explained through a case study and some sensitivity analyses. Numerical simulations are also done in order to establish the distribution of the stresses in cell walls and nodes to confirm the hypotheses used for determining the analytical relations and to explain some limits of the analytic model. The results provide new insights into understanding the mechanics of honeycombs and facilitate the design of new types of cellular materials, including composite hexagonal cell cores. (C) 2018 Elsevier Ltd. All rights reserved.