MathLab seminar announcement

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT



Title: Shocks in fragile matter
Speaker: Vincenzo Vitelli (Leiden University)
Date: Wednesday, 17 April, 2013 - 13:00
Room: SISSA - Santorio A - room 4

Abstract: Non-linear sound is an extreme phenomenon typically observed 
in solids after violent explosions. But granular media are different. 
Right when they unjam, these fragile and disordered solids exhibit 
vanishing elastic moduli and sound speed, so that even tiny mechanical 
perturbations form supersonic shocks. Here, we perform simulations in 
which two-dimensional jammed granular packings are continuously 
compressed, and demonstrate that the resulting excitations are strongly 
nonlinear shocks, rather than linear waves. We capture the full 
dependence of the shock speed on pressure and compression speed by a 
surprisingly simple analytical model. We also treat 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.