Abstract
Microscopic buckling and macroscopic instability of periodic cellular solids under uniaxial, as well as biaxial, compression are studied. To this end, a general framework of microscopic bifurcation and post-bifurcation analysis is established on the basis of an updated Lagrangian type, two-scale theory. Using the framework, cell aggregates of an elastoplastic honeycomb subject to in-plane compression are analyzed. We thus demonstrate the dependence of microscopic bifurcation on periodic length, the inherent multiplicity of long-wave microscopic bifurcation, the localizations of microscopic buckling in a cell row and in deltaic areas, and the change into an asymmetric, long-wave mode under equi-biaxial compression.
