HYPERBOLIC PDES ACROSS GASDYNAMICS, PLASTICITY, AND GRANULAR PLASTICITY

This expository paper is presented in celebration of Professor Layton's 60th birthday. In mathematics genealogy, he is the gg-grandson of Gottingen's Ludwig Prandtl (1875-1953), who contributed enormously to both fluid and solid mechanics. The Prandtl-Meyer fan is a simple tool to visualize solutions of hyperbolic PDEs in the context of gasdynamics. In later years, Prandtl adapted the fan to visualize solutions of hyperbolic PDEs in the context of plasticity in metals. By 1960, the fan had been used by Sokolovskii in the context of granular plasticity. Because the last introduces logarithms into plasticity's equivalent of the Riemann invariant, granular materials exhibit unexpected behaviors that are being ignored by the construction community with costly consequences. Interestingly, one of the consequences for soil is analogous to the Rankine-Hugoniot relation in gasdynamics.