On Variation Models of the Irreversible Processes in Mechanics of Solids and Generalized Hydrodynamics

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.