Tailored instabilities at different scales in a metamaterial
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Mechanical metamaterials made up of a beams square lattice exhibit a fi rst critical mode related to macroscopic deformations. Here, we analyze a class of metamaterials in which the fi rst critical mode is related to a microscopic instability not involving deformations at the macroscale. In particular, a periodic two-dimensional lattice composed by a square mesh of beams with rigid fi nite-size nodes has been analyzed and the closed form solution of the stability domain of the lattice subjected to a plane macro-stress has been obtained, by means of Floquet-Bloch wave analysis. It has been shown that the size of nodes can be varied in order to obtain microscopic critical modes instead of macroscopic ones (i.e. pattern transformation), for different macro-stress states. Weight minimization has been also carried out. Numerical analyses and experimental tests on a selected metamaterial specimen have been performed in order to verify the assumptions made in our analytical model, showing a remarkable agreement with our theoretical results. We argue that the obtained results can be useful for the development of innovative dissipative metamaterials.
