Some theoretical aspects of strain localization analysis of multiphase porous media with regularized constitutive models

This paper discusses some theoretical aspects of strain localiza- tion analysis in multiphase porous media, particularly when reg- ularized constitutive models such as the gradient-dependent and rate-dependent models are used. Stability and hyperbolicity of the governing equations are studied and the relations between permeability and the wave number where a real wave speed exists are investigated numerically. Particular attention is focused on the two cases of wave number K=0 and K→∞ of the perturbation waves. The interaction between the different internal length scale parameters during dynamic strain localization in multiphase porous materials is also studied. It is pointed out that the consideration of fluid interaction is necessary for the prediction of the internal length in a multiphase porous medium when regularization through a constitutive model is introduced in the numerical model to overcome mesh dependence in a finite element solution.