A unified hyperbolic formulation for viscous fluids and elastoplastic solids

A unified hyperbolic formulation for viscous fluids and elastoplastic solids Full article

Journal

Springer Proceedings in Mathematics and Statistics
ISSN: 2194-1009 , E-ISSN: 2194-1017

Output data

Year: 2018, Volume: 237, Pages: 451-463 Pages count : 13 DOI: 10.1007/978-3-319-91548-7_34

Tags

Hyperbolic equations; Unified flow theory; Viscous fluids Elastoplasticity

Authors

Dumbser M. ¹ , Peshkov I. ^2,3 , Romenski E. ^3,4

Affiliations

1	Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, Trento, 38123, Italy
2	Institut de Mathématiques de Toulouse, Université Toulouse III, Toulouse, 31062, France
3	Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, Novosibirsk, 630090, Russian Federation
4	Novosibirsk State University, 2 Pirogova Str, Novosibirsk, 630090, Russian Federation

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.

Dumbser M. , Peshkov I. , Romenski E.
A unified hyperbolic formulation for viscous fluids and elastoplastic solids
Springer Proceedings in Mathematics and Statistics. 2018. V.237. P.451-463. DOI: 10.1007/978-3-319-91548-7_34 Scopus OpenAlex

Scopus:	2-s2.0-85049444041
OpenAlex:	W3121917360

DB	Citing
Scopus	16
OpenAlex	17