On the mechanics of tetrakis-like lattices in the stretch-dominated regime

We derive general conditions for the design of two-dimensional stiffest elastic networks with tetrakis-like (or 'Union Jack'-like) topology. Upon generalizing recent results for tetrakis structures composed of two different rod geometries (length and cross-sectional area), we derive the elasticity tensor of a lattice with generalized tetrakis architecture, which is composed of three kinds of rods and generally exhibits anisotropic response. This study is accompanied by an experimental verification of the theoretical prediction for the longitudinal modulus of the lattice. In addition, the introduction of a third rod geometry allows to extend considerably the possible lattice geometries for isotropic, stiffest elastic lattices with tetrakis-like topology. The potential of the analyzed structures as innovative metamaterials featuring extremely high elastic moduli vs. density ratios is highlighted.