Spring back of infinite honeycomb sheets beyond plastic deformation

Cellular structures are promising for applications where high stiffness and strength are required with the minimal use of material. They are often used in applications where the plastic deformation plays an important role, such as those involving crashworthiness, energy absorption, and stents. The elastic analysis of a honeycomb sheet has been carried out in the past [1]. The present analysis extends this classical work in the elasto-plastic regime. Recoil analysis due to elastic recovery is absent from the published literature. This work aims to develop an analytical model to calculate the spring back for a simplified case, that of an infinite honeycomb sheet. An elastic-perfectly plastic material model is assumed. The recoil for a clamped beam with a load and moment applied at the free edge is analytically calculated first. This is carried out by relating the stress distribution of the cross section to the final deformed shape. The part corresponding to the elastic contribution is subsequently subtracted in order to obtain the final configuration after the external load is removed. This simple elasto-plastic analysis is then incorporated into the analysis of an infinite sheet made of uniform hexagonal cells. The translational symmetry of the lattice is exploited along with the analysis of a beam under tip loading through to plastic stage and recoil. The final shape of the struts upon the removal of the remote stress is completely determined by the plastic deformation which cannot be recovered. The expression for the beam thus obtained is then used to build an analytical model for an infinite honeycomb sheet loaded in both directions.