A unified hyperbolic formulation for viscous fluids and elastoplastic solids

Michael Dumbser, Ilya Peshkov, Evgeniy Romenski

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

7 Citations (Scopus)

Abstract

We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics and solid dynamics. The fundamental difference from the classical continuum models, such as the Navier–Stokes, for example, is that the finite length scale of the continuum particles is not ignored but kept in the model in order to semi-explicitly describe the essence of any flows, that is the process of continuum particles rearrangements. To allow the continuum particle rearrangements, we admit the deformability of particle which is described by the distortion field. The ability of media to flow is characterized by the strain dissipation time which is a characteristic time necessary for a continuum particle to rearrange with one of its neighboring particles. It is shown that the continuum particle length scale is intimately connected with the dissipation time. The governing equations are represented by a system of first-order hyperbolic PDEs with source terms modeling the dissipation due to particle rearrangements. Numerical examples justifying the reliability of the proposed approach are demonstrated.

Original languageEnglish
Title of host publicationTheory, Numerics and Applications of Hyperbolic Problems II
EditorsC Klingenberg, M Westdickenberg
PublisherSpringer New York LLC
Pages451-463
Number of pages13
Volume237
ISBN (Print)9783319915470
DOIs
Publication statusPublished - 1 Jan 2018
Event16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 - Aachen, Germany
Duration: 1 Aug 20165 Aug 2016

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSPRINGER
Volume237
ISSN (Print)2194-1009

Conference

Conference16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016
CountryGermany
CityAachen
Period01.08.201605.08.2016

Keywords

  • Hyperbolic equations
  • Unified flow theory
  • Viscous fluids Elastoplasticity
  • Elastoplasticity
  • SOUND
  • Viscous fluids
  • HIGH-VELOCITY IMPACT
  • NONLINEAR MODEL
  • SCHEMES

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