Internal length scale in dynamic strain localization of multiphase porous media

In this paper, a length scale included in multiphase materials such as saturated and partially saturated porous media is discussed, where the viscous terms are introduced naturally by the fluid mass balance equations. The discussion is limited to the dynamic case. The characteristic stability equation is given in explicit form for one-dimensional wave propagation. It is shown that for axial waves a wave number domain exists for which the material model is dispersive when softening behaviour occurs for solid skeleton and that an internal length scale can be derived, while for ideal shear propagation this is not the case. Numerical examples are given to corroborate the validity of the expressions derived.