On Variation Models of the Irreversible Processes in Mechanics of Solids and Generalized Hydrodynamics
- Authors: Belov P.A.1, Lurie S.A.1
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Affiliations:
- Institute of Applied Mechanics of Russian Academy of Sciences
- Issue: Vol 40, No 7 (2019)
- Pages: 896-910
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/204995
- DOI: https://doi.org/10.1134/S1995080219070060
- ID: 204995
Cite item
Abstract
It is proposed a procedure for constructing a non-integrable variational form, allowing to extend the procedure of formal construction of variational models of mechanics of deformable media to irreversible deformation processes. We introduce the non-integrable variational forms that determine possible dissipation channels depending on the list of generalized variables for a particular model of media. The problems of filtering of Biot models are considered and it is proved that non-integrable variational forms allow us to construct variational hydrodynamic models of Darcy, Navier-Stokes and Navier-Stokes-Darcy. It is shown that the equations of the Navier—Stokes—Darcy model contain the Helmholtz operator, which will allow to take into account the scale effects associated with the boundary layers.
About the authors
P. A. Belov
Institute of Applied Mechanics of Russian Academy of Sciences
Author for correspondence.
Email: belovpa@yandex.ru
Russian Federation, Moscow, 125040
S. A. Lurie
Institute of Applied Mechanics of Russian Academy of Sciences
Author for correspondence.
Email: salurie@mail.ru
Russian Federation, Moscow, 125040