Basic theories for strain localization analysis of porous media with gradient dependent plasticity model

The interaction between the two kinds of internal length scales is analyzed when the gradient-dependent plasticity is introduced to a multiphase material model to study the dynamic strain localization phenomenon of saturated and partially saturated porous media. The stability analysis demonstrates that the resulting enhanced porous media model preserves the well-posedness of the initial value problem for both axial and shear waves because an internal length scale dependent on the gradient parameter is introduced. On the other hand, the seepage process of the water also provides an internal length scale for strain localization analysis via the Darcy's law but only in the case of compression wave propagation (and not in the shear wave case). It is thus that the length scale introduced by the gradient dependent model and that naturally contained in the governing equations of fully and partially saturated model can interact with each other in a finite element analysis. A basic method is presented to investigate the internal length scale of the porous media under the interaction of these two kinds of length scale parameters. Material stability analysis is carried out for a certain permeability from which the results of wave number domain with real wave speed are distinguished.