Instabilities and discontinuities in two-phase media

Within the framework of the generalised theory of heterogeneous media, the complete set of equations is derived for a three-dimensional, fluid-saturated porous medium. Analytical and numerical investigations have been carried out into the wave propagation characteristics for the case of a skeleton which exhibits strain softening. Wave propagation has a dispersive character in this medium, but the internal length scale associated with it vanishes in the short wave-length limit, which has the implication that localisation in a zero width will occur and no regularisation will be present, unless the solid phase is augmented with a so-called localisation limiter. Alternatively, all damage can be lumped in a discrete interface. The second part of the contribution therefore focuses on the modelling of arbitrary discontinuities in a fluid-saturated porous medium.