Size effects of elastic properties for auxetic cellular structures: bending energy-based method

Auxetic cellular structures have attracted growing attention due to their distinctive mechanical properties including increased stiffness, energy absorption capacity and high strength-to-weight ratio. In this paper, the size effects of elastic properties for a double-arrowed auxetic honeycomb (DAAH) has been investigated. With the microscopic size of DAAH taken into account, analytical models predicting the in-plane effective Young's modulus and Poisson's ratio have been established by adopting a bending energy-based method (BEM) and a strain-based expansion homogenization method (HM), respectively. Further, an integrated experimental and simulation approach has been conducted to validate the analytical models. The comparison shows that the bending energy-based method can reveal the size effects of elastic properties for DAAH with an acceptable accuracy. Further, a variety of analytical results have been presented to investigate the size effects. It is shown that with the increase of scale factor, the predicted elastic properties prove to feature a monotonic change and then tend to a convergence. Finally, the influence of volume fraction on the size effects has been discussed. It is believed that this work can greatly expand the engineering application of auxetic structures with stable mechanical properties in various scales.