TY - JOUR
T1 - Hyperbolic PDEs Across Gasdynamics, Plasticity, and Granular Plasticity
AU - Hoffman , Peter
JO - International Journal of Numerical Analysis and Modeling
VL - 4-5
SP - 564
EP - 578
PY - 2018
DA - 2018/04
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12531.html
KW - Prandtl fan, gasdynamics, plasticity, granular plasticity, Euclidean.
AB - <p style="text-align: justify;">This expository paper is presented in celebration of Professor Layton’s 60th birthday.
In mathematics genealogy, he is the gg-grandson of Göttingen’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.</p>