"Shocks in fragile matter"

In ordinary solids, acoustic shocks are extreme mechanical phenomena: they occur when rigid materials are subjected to violent impacts. But in soft materials things are different. Granular media, foams and polymer networks can all be prepared in a state of vanishing rigidity in which even the tiniest perturbation elicits an extreme mechanical response. When that happens these materials are not just soft, they have become fragile.

In this talk, we present simulations in which two-dimensional jammed granular packings are dynamically compressed, and demonstrate that the elementary excitations are strongly nonlinear shocks, rather than ordinary phonons. We capture the full dependence of the shock speed on pressure and impact intensity by a surprisingly simple analytical model.

We also discuss shear shocks within a simplified viscoelastic model of nearly-isostatic random networks comprised of harmonic springs. In this case, anharmonicity does not originate locally from nonlinear interactions between particles, as in granular media. Instead, it emerges from the global architecture of the network. As a result, the diverging width of the shear shocks bears a nonlinear signature of the diverging isostatic length associated with the loss of rigidity in these floppy networks.