Long-wave buckling of elastic square honeycombs subject to in-plane biaxial compression

In this study, long-wave and short-wave buckling of elastic square honeycombs subject to in-plane biaxial compression are analyzed using a two-scale theory of the updated Lagrangian type. By taking cell aggregates to be periodic units, the bifurcation and post-bifurcation behavior are analyzed so that the dependence of buckling stress on periodic length can be discussed. It is shown that buckling stress decreases as periodic length increases, and that very-long-wave buckling occurs just after the onset of macroscopic instability if the periodic length is sufficiently long. Then, a simple formula to evaluate the very-long-wave buckling stress under in-plane biaxial compression is derived by exploring the macroscopic instability condition in the light of the two-scale analysis. The resulting formula is verified using an energy method.