Multifunctional disordered elastic networks: Designed response of mechanical metamaterials*

We design intelligent protocols to tune the elastic response of metamaterials with flexible mechanical properties. We discuss phonon and elastic properties of randomly diluted twisted-Kagome lattices with tunable structures that include auxetics with negative Poisson ratios. 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. These models exhibit rich critical phenomena that include rigidity percolation, jamming, shear-jamming, and double-jamming. We also discuss extensions of our models to include anisotropy, spatial dependence and generalizations to three dimensions.