Stability domain and design of a plane metamaterial made up of a periodic mesh of rods with cross-bracing cables

In this work we examine a plane metamaterial subjected to a generic biaxial macrostress, obtained by coupling a periodic mesh of rods with a periodic mesh of extremely flexible cables. In particular, we couple a square mesh of rods with diagonal cables with the aim of enhancing the stability performance of the obtained metamaterial. By introducing appropriate restrictions on the feasible critical modes, the study can be framed into the context of the Eulerian stability analysis and then, by means of Floquet-Bloch theory, a closed form solution for the stability domain is determined. Finally, on the basis of the previous stability analysis the optimal design problem is addressed.