Nonlinear and semilinear dynamic poroelasticity with microstructure (Q760223)

Nonlinear equations for wave propagation through dry or fluid-saturated porous elastic media are derived using a variational formulation. The method presented is very similar to the approach of Bedford and Drumheller [\textit{A. Bedford} and \textit{D. S. Drumheller}, Int. J. Solids Struct. 15, 967-980 (1979; Zbl 0411.73088)], including microinertia terms for local density fluctuations of fluid and solid. One major difference is the choice of a Lagrangian (rather than Eulerian) reference frame locked to the solid constituent. This choice of reference frame is preferable for porous solids and also allows direct comparison to Biot's theories of nonlinear and semilinear rheology of porous solids.