Multi-functional Tw-Kagomé lattices: Tuning by pruning mechanical metamaterials

We study phonon and elastic properties of randomly-diluted twisted-Kagome lattices with tunable structures that include auxetics with negative Poisson ratios. Intelligent protocols to tune the Poisson ratio of elastic networks can be used in the design of metamaterials with flexible mechanical properties. Here we introduce two periodic lattice models that access negative values of the Poisson ratio, one of which accesses the full range from -1 to +1. Besides tunable auxetic transitions, these models exhibit rich critical phenomena that include rigidity percolation (where both the bulk B and shear G moduli continuously vanish), jamming (where B undergoes a discontinuous jump and G grows continuously from zero), shear-jamming (where G undergoes a discontinuous jump and B grows continuously from zero), and “double jamming” (where both B and G undergo a discontinuous jump).