Analytical Investigation on Elastic–Plastic Deformation of Reentrant Honeycomb Structures

Abstract

Analytical elastic–plastic analysis is presented to investigate the in-plane deformation of the reentrant honeycomb structures subjected to tension or compression. An analytical elastic–plastic deformation analysis is carried out and the nonlinear stress–strain relation of honeycombs is presented, reflecting the dependence of equivalent stress, equivalent Young’s modulus, and equivalent Poisson’s ratio on the deformation. The modified factors of the stress–strain relation are then presented, which depend on the shape and deformation of the honeycomb structure and are independent of the material Young’s modulus and the ratio of wall thickness to its length. It is found that, by adjusting the geometric or material parameters, we can enable this reentrant honeycomb structure to achieve a range of negative Poisson’s ratio and Young’s modulus values. A finite element model is used to indicate the effectiveness of the proposed model. A parametric study is finally carried out to investigate the effects of the geometric or material parameters on the reentrant honeycombs structure.