Long-wave in-plane buckling of elastoplastic square honeycombs

In this study, two formulae derived for very long-wave in-plane buckling of elastic square honeycombs are extended and examined in the elastoplastic case. To this end, microscopic buckling and post-buckling behavior of elastoplastic square honeycombs subject to in-plane compression are numerically analyzed using a homogenization theory of the updated Lagrangian type. It is thus demonstrated that very long-wave buckling occurs just after the onset of macroscopic instability if periodic length is sufficiently long, and that plasticity can cause the localization of microscopic buckling accompanied by a significant decrease in macroscopic compressive stress. Then, the very long-wave buckling stresses computed are predicted by incorporating the effect of plasticity in the two formulae of elastic square honeycombs. It is shown that the resulting formulae are successful in predicting the very long-wave buckling stresses in the plastic range as well as in the elastic range.