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

This paper analyzes the interaction between two kinds of internal length scales when the rate dependen plasticity is introduced to a multiphase material model to study the dynamic strain localization phenomenon of satu rated and partially saturated porous media. The stability analysis demonstrates that the enhanced porous media mode preserves the well-posedness of the initial value problem for both axial and shear waves because an internal length scale parameter is introduced in the visco-plasticity model. On the other hand, the interaction between the length scale intro duced by the rate dependent model and that naturally con tained in the governing equations of fully and partially satu rated model will take place. A basic method is presented to investigate the internal length scale of the multiphase porou 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. A one dimen sional example is given to illustrate the theoretical findings.