Plastic behaviour of two-dimensional regular hexagonal structures with bilinear and uniaxial strength asymmetry in cellular materials

Abstract

An elasto-plastic micromechanical model of the two-dimensional regular hexagonal structure was developed. General analytical expressions for the incremental constitutive relations were derived in terms of parameters defining the architecture and material of an internal beam. Non-linearity of the structure was introduced by considering the elastic—linear strain hardening behaviour of each internal beam, in which uniaxial strength asymmetry of the cellular material was accounted for. The plastic stress—strain relationship of the structure under any loading conditions can therefore be analysed by localized beam deformation. The results show that the bending deformation of the internal beam dominates under uniaxial stress loading conditions, however, the axial displacement dominates under the uniaxial strain conditions. The structure will present different behaviours under different loading conditions. The corresponding stresses under the uniaxial strain condition are greater than those under the uniaxial stress condition. The analyses also show that the volume fraction is highly correlated with the elastic constants and yield stresses of the structure. The denser the structure, the higher the moduli and yield stresses.