Michael G. Grinfeld
Andrew N. Norris
Dept. of Mech. and Aerospace Eng., Rutgers Univ., Piscataway, NJ 08855-0909
A new nonlinear governing system for poroelastic fluid-permeable media in Eulerian variables is derived on the basis of Hamilton's principle for reversible effects and the Onsager--Sedov approach for irreversible effects. The classical (Murnaghan-like) equations of nonlinear elasticity, as well as the governing equations of the ideal and Navier--Stokes fluids, appear to be some special cases of the general governing system. It is well known that the Navier--Stokes equations for compressible fluids 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 poroelastic fluid-penetrable media. In particular, it allows one to study the internal structure of shock waves and flutterlike phenomena among others. [Work was supported by ONR.]