Elastoplastic response and recoil of honeycomb lattices

This paper presents elasto-plastic response and recoil analysis of two-dimensional honeycombs. The architecture studied here possesses cell wall bending as the dominant mechanism of deformation. Elasto-plastic analysis of cell walls, in conjunction with the kinematics of the deformation of the lattice, enables us to obtain closed form plastic response as well as recoil upon unloading. Elastic-perfectly plastic cell wall material is considered. A smooth apparent structural response is observed although the material model is piece-wise linear. The apparent Poisson's ratio of the porous honeycomb material, in the plastic regime, is derived from the lateral response calculation. In the non-linear regime of deformation, the Poisson's ratio of honeycombs remains independent of the apparent strain of the lattice. A parametric study of the non-linear response involving systematic changes in the parameters is carried out. This suggests the existence of non-dimensional groups that could provide response relationship valid for all geometric and material parameters. Scaling arguments are developed and a scaling ansatz is proposed which leads to data collapse, based upon which, a family of honeycombs can be analytically characterised for elasto-plastic response. Data collapse thus obtained provides a master-curve for structure property relationship for plasticity of honeycombs which separates the individual cell wall mechanics from the lattice kinematics.