Honeycomb structures are essentially constituted of a repetition of regularly-arranged and loaded sub-structures. The present study carries out a parametrically investigation of the behavior of a multi re-entrant honeycomb structure with variable stiffness and Poisson's ratio effects. A refined analytical model is specifically developed and compared to full-scale numerical simulations. The analytical model developed is based on energy theorems and takes into full consideration bending, shearing and membrane effects. The influence of the cell walls thickness on the elastic homogenized constants is investigated. The results obtained show a good agreement between the refined analytical approach developed and the numerical computations carried out.

We propose in this paper analytical and numerical models that describe the in‐plane uniaxial elastic properties (Young's moduli and Poisson's ratios) of a honeycomb structure with curved walls. We perform a parametric analysis of the mechanical performance of this honeycomb also by taking into account the different types of deformations acting inside the cell walls. The curved wall honeycomb possesses higher magnitudes of the Poisson's ratio ν12 in the auxetic configuration compared to classical center symmetric configuration with straight cell wall. The presence of the curvature also allows creating configurations with positive Poisson's ratio even for negative internal cell angles, and makes this honeycomb design attractive for mechanical tailoring.

Purpose The purpose of this paper is to study the effect of the relative density and geometric parameters on the homogenised in-plane elasticity modulus of a cellular honeycomb structure using analytical and numerical approaches. Design/methodology/approach In this work, the mechanical behaviour of a new design of the honeycomb is analysed through a refined analytical model that is developed based on the energy theorems by considering the shearing and stretching effects in addition to bending. Findings By taking into account the various deformation mechanisms (MNT), the obtained results show that the values of elasticity modulus are the same for low relative densities, but the difference becomes remarkable for higher densities. Moreover, it is difficult to judge the effect of the relative density and anisotropy of the cellular structure on the values of the homogenised elasticity modulus without considering all the three deformation mechanisms in the analytical model. It is shown that conventional models overestimate the elasticity modulus, especially for high relative densities. Originality/value In this paper, a refined model that takes into account the three deformation mechanisms (MNT) is developed to predict the in-plane elasticity modulus of a honeycomb cellular material. It is shown that analytical models that describe the anisotropic behaviour of honeycomb cells can be improved by considering the three deformation mechanisms, which are bending, stretching, and shearing deformations.