Elastic stability of a lattice of cross-braced shear deformable beams

Abstract

A plane metamaterial made up of a periodic square grid of shear deformable beams has been braced by crossing cables. This coupling, widely adopted in structural engineering, is here applied with the aim of enhancing the stability performance of a periodic material. Under suitable assumptions, analytical solutions for a rich variety of critical modes and the stability domain are determined by the Bloch wave approach and the effectiveness of our analytical results has been verified by numerical simulations. Furthermore, the experimental response of a specimen, in which hierarchical beams composed by lower order elements are modeled as equivalent shear deformable beams, has shown a satisfactory agreement with our analytical solutions. We argue that our analytical model can be efficiently used to tailor the buckling response of various new metamaterials under general plane stress states.