On Percolation, Jamming, and Shock Waves in Solids

For many materials the shock wave speed in uniaxial strain compression increases linearly with increasing particle velocity with a slope generally characterized by s. From the Rankine-Hugoniot jump relations, the longitudinal compressive stress behind the shock wave becomes infinite at a critical compressive strain epsilon(c) = 1/s. This paper raises the possibility that such behavior could be indicative of a jamming transition that occurs near a percolation threshold pc. Motivation for this line of inquiry comes from the results of pressure-shear plate impact (PSPI) experiments on polyurea, a block co-polymer comprised of hard and soft polymeric regions. At the high shear strain rates (10(5) - 10(6) s(-1)) of these PSPI experiments the shearing resistance increases proportionately, and strongly, with increasing pressure - suggesting the possibility that the response of polyurea may have similarities with that of a lubricated granular medium. The strong resistance would be due to interaction of the hard regions, whereas the apparent viscosity would be due to the lubrication provided by the soft regions.