Hamiltonian and onsageristic approaches in the nonlinear theory of fluid-permeable elastic continua

摘要

A new system of equations governing nonlinear dynamics of fluid-permeable poro- elastic media is derived on the basis of Hamilton's principle for reversible effects and the Onsager- Sedov approach for irreversible effects. The equations are in Eulerian variables, suitable for dealing with fluid and solid phenomena simultaneously. The classical (Murnaghan-like) equations of nonlinear elasticity, as well as the governing equations of the ideal and Navier-Stokes fluids are shown to be special cases of the general governing system. It is well-known that the Navier- Stokes equations of compressible fluid provide a correct self-consistent basis for studying a wide variety of nonlinear effects in fluids. The authors believe that the governing system proposed here provides the same opportunities for various nonlinear effects in poro-elastic fluid-penetrable media.