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.]

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