Plastic deformation modes of regular hexagonal honeycombs under in-plane biaxial compression

A limit analysis approach is employed to identify the plastic deformation modes of regular hexagonal honeycombs with relatively large wall-thickness-to-length ratios under in-plane biaxial compression. An infinite block of honeycomb material is considered and a representative block consisting of four hexagonal cells is defined when assuming the kinematic admissibility of the modes and a periodic repeatability of the representative block in both spatial directions. In general, three plastic collapse modes are found to be preferable depending on the direction of loading, and in some particular cases they are similar to the modes that occur elastically under stress or strain controlled in-plane biaxial compression. It is shown that the critical forces at the onset of the plastic collapse depend on the assumed constraints for the deformation of the representative block. The results obtained from the theoretical analysis and the numerical simulations are compared and discussed.