Elastic networks to model auxetic properties of cellular materials

Elastic networks model that is used to model a class of two-dimensional cellular structures including re-entrant and regular honeycombs is considered. Two mechanical parameters (longitudinal stiffness and torsional stiffness) are used to describe the interaction between the nodes in a lattice for a given geometry. Effective properties with emphasis on the auxeticy of solid materials corresponding to the considered microstructures are investigated. A method based on comparison of the strain energies at macro- and microscale is proposed to determine the effective properties of continuum and can be applied to other cellular materials. All components of stiffness tensor are determined as functions of interaction parameters. Thus, the general parametric study of the honeycomb structures is made possible. Re-entrant honeycomb structures demonstrate the auxetic properties at any combination of parameters whereas the regular honeycombs can have both positive and negative Poisson's ratios. Comparison with other model shows that the 2-parameter elastic networks can successfully describe isotropic materials. However in cases of higher anisotropy this model can be used within certain limitations.