On the homogenization of hexagonal honeycombs under axial and shear loading. Part I: Analytical formulation for free skin effect

In the present paper the skin effect is neglected, and a general parameterization of a hexagonal honeycomb, valid for constant wall thickness, double vertical walls (commercial), or for any combination of cell walls is generated. Thus, two new analytical models are proposed: generalized Malek and Gibson and correction of Gibson and Ashby. Description of the existing (Malek and Gibson, 2015 and classical relations established by Gibson and Ashby, 1997) and proposed models is done in detail. All nine effective elastic properties are obtained analytically using the beam and membrane plate theory in which more attention is paid to account for the nodes at the intersection of the vertical and inclined cell walls. The numerical modeling of honeycomb structures is too tedious and time consuming. The homogenization of honeycombs enables to obtain an equivalent orthotropic homogeneous solid and its elastic effective properties making thus possible very efficient finite element analyses. Such simulations are also used to establish the distribution of the stresses in nodes in order to validate the hypotheses used for determining the analytical relations. The existing and proposed analytical models are compared to the FEA solutions through two examples: one for a regular, and the other for a re-entrant honeycomb. The numerical results obtained as a reference for the effective elastic constants are discussed by comparing them to the ones given by the analytical models, and the advantages and pitfalls of each model are discussed and explained. The results provide new insights into understanding the mechanics of honeycombs and designing new types of cellular materials including composite hexagonal cell cores.