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In this study, microscopic buckling of elastic square honeycombs subject to in-plane compression is analyzed using a two-scale theory of the up-dated Lagrangian type. The theory allows us to analyze microscopic bifurcation and post-bifurcation behavior of periodic cellular solids. Cell aggregates are taken to be periodic units so that we can discuss the dependence of buckling stress on periodic length. Then, it is shown that microscopic buckling occurs at a lower compressive load as periodic length increases, and that long-wave buckling occurs just after the onset of macroscopic instability if the periodic length is sufficiently long. It is further shown that the macroscopic instability is of the shear type, leading to a simple formula to evaluate the lowest in-plane buckling stress of elastic square honeycombs. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]