Tailored multiscale instabilities in a grid metamaterial

In this study, we investigate a plane metamaterial made up of a periodic grid of shear-deformable rods with rigid finite-size joints, subjected to a biaxial macro-stress state. We derive closed-form solutions for the stability domains by means of Floquet-Bloch theory. Remarkably, this analytical modeling enable us to determine how the size of the rigid joints yields to transition from macroscopic to microscopic critical modes (i.e. pattern transformation) for specific macro-stress states. We also examine a minimum weight problem for this class of metamaterials. The analytical model predictivity in describing multiscale instabilities is validated by comparisons with experimental findings and numerical analyses.