Buckling of lattice columns made from three-dimensional chiral mechanical metamaterials

The three-dimensional (3D) chiral mechanical metamaterials were found to exhibit unique compression-twisting coupling effect. The metamaterial will twist in addition to axial shortening when subjected to the external compressive load. For a slender structure made from 3D chiral mechanical metamaterial, global buckling may occur if the compressive load exceeds the critical value. In this work we investigated the buckling strength of the chiral lattice columns which were constructed by periodically placing the inclined straight beams in a chiral manner. Based on the Cosserat rod theory, a novel constitutive model with a new parameter governing the compression-twisting coupling was built to describe the deformation of 3D chiral metamaterial. A semi-analytical homogenization method was proposed to connect the stiffness parameters of arbitrary sized lattice column to the properties of the unit cell. The constitutive model together with the homogenization method well interpreted and quantified the size dependency of the chirality. The fourth-order governing equations of buckling were developed and solved analytically to predict the critical buckling load of 3D chiral metamaterial. The effects of chirality on the buckling strength and buckling mode were revealed.