Buckling of rectangular and hexagonal honeycomb under combined axial compression and transverse shear

One of the many uses of honeycomb is as core in sandwich plates, producing very high stiffness-to-weight ratio structures. The macroscopically observed crushing mechanism of these structures has its origin in instabilities at the local scale. Of particular interest here are the critical (i.e., onset of a buckling-type instability) loads and corresponding eigenmodes of honeycomb under general 3D loading involving simultaneous axial compression and transverse shear. Since the critical eigenmodes in honeycomb often involve more than one unit cell, numerical studies are limited by the size of the domain considered for their analyses. We propose a new theoretical approach to determine the critical loads and eigenmodes of perfect honeycomb of infinite extent under general loading conditions based entirely on unit-cell calculations. It combines Bloch wave representation theorem for the eigenmode with the analytical solution of the linearized von Karman plate equations for the walls. The proposed approach uses the fact that the honeycomb walls remain flat in the principal solution prior to the onset of the first instability and solves analytically the corresponding eigenvalue problem. Three different geometries are considered.: rectangular honeycomb with varying in-plane aspect ratios, an isotropic-section hexagonal honeycomb, and an anisotropic-section hexagonal honeycomb (resulting from its manufacturing process). Several different loading cases are investigated: axial compression under free or fully constrained lateral expansion, transverse shear and combined axial compression and transverse shear. The results show that the buckling mode is highly dependent on the type of loading: e.g., laterally unconstrained axial compression results in local critical eigenmodes, while constraining the lateral expansion leads to global ones. The addition of transverse shear not only reduces the critical axial strain, but also affects the wavelengths of the critical eigenmode. (C) 2013 Elsevier Ltd. All rights reserved.