Guided Impact Mitigation in 2D and 3D Granular Crystals

Abstract

We simulate the dynamics of impacts on 1D, 2D and 3D arrays of metallic spheres in order to design novel granular protection systems. The dynamics of these highly organized systems of spheres, commonly called granular crystals, are governed by the contact law that describes how each particle interacts with the others. We use our recently developed force-displacement model of the dynamic compression of elastic-plastic spheres as the building block to investigate the response of systems comprised of metallic spheres to an impact. We first provide preliminary experimental results using a drop tower as validation of our numerical approach for 2D and 3D systems. We then use simulations of large periodic granular crystals in order to determine which particle properties govern the velocity of stress waves in these materials. We show that the properties of 1D systems can be scaled to predict the behavior of more complex 2D and 3D granular crystals. Because we can choose the material properties of each of the constituent particles and design how the particles are geometrically packed, we can leverage the heterogeneity of the system to create materials with unique properties such as anisotropic local stiffnesses and wave propagation velocities. We show that these materials allow us to design the dispersion and dissipation properties within the material in order to influence the propagation of a stress wave. Using these materials, we can therefore design protection systems or armor that directs damage away from sensitive parts or localizes damage to an unimportant area after impact from a projectile or a blast.