Plastic buckling of columns at the micron scale

Clamped-clamped compressed wide metal columns with length to thickness ratios such that they undergo plastic buckling are considered. Further, the thickness of the columns is assumed to be in the range of microns to tens of microns, typical of elements comprising some of the small-scale lattice materials currently being produced. The strengthening effects associated with plastic strain gradients are expected to influence buckling behavior, and the columns are analyzed using several versions of the available strain gradient plasticity theories. The columns are assumed to be infinitely wide and subject to plane strain deformations. Approximate one-dimensional and exact two-dimensional analyses are presented. The primary focus is the onset of plastic buckling as predicted by bifurcation from the state of uniform compression. However, a numerical post-buckling study is carried out for one class of strain gradient theories for columns with initial imperfections to ascertain if the buckling predictions stemming from this class of theory are realistic. The paper highlights the fact that one class of strain gradient theories does not appear to be adequate for analyzing plastic buckling.