Geometric variational approach to the dynamics of porous medium, filled with incompressible fluid

@article{Farkhutdinov2020GeometricVA,
  title={Geometric variational approach to the dynamics of porous medium, filled with incompressible fluid},
  author={Tagir Farkhutdinov and Franccois Gay-Balmaz and Vakhtang Putkaradze},
  journal={Acta Mechanica},
  year={2020},
  pages={1-28}
}
We derive the equations of motion for the dynamics of porous medium, filled with incompressible fluid. We use a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the elastic matrix, and the kinetic energy of the fluid, coupled through the constraint of incompressibility. As an illustration of the method, the equations of motion for both the elastic matrix and the fluid are derived in the spatial (Eulerian) frame. Such an approach… Expand

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