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Volume 15, Issue 4-5
Hyperbolic PDEs Across Gasdynamics, Plasticity, and Granular Plasticity

Peter Hoffman

Int. J. Numer. Anal. Mod., 15 (2018), pp. 564-578.

Published online: 2018-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

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.

  • Keywords

Prandtl fan, gasdynamics, plasticity, granular plasticity, Euclidean.

  • AMS Subject Headings

35L02, 76N15, 74C15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

peter.hoffman@ucdenver.edu (Peter Hoffman)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-564, author = {Hoffman , Peter}, title = {Hyperbolic PDEs Across Gasdynamics, Plasticity, and Granular Plasticity}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {4-5}, pages = {564--578}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12531.html} }
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 -

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.

Hoffman , Peter. (2018). Hyperbolic PDEs Across Gasdynamics, Plasticity, and Granular Plasticity. International Journal of Numerical Analysis and Modeling. 15 (4-5). 564-578. doi:
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