Some Aspects on Basic Theories of Strain Localization Analysis of Multiphase Porous Media with Regularized Constitutive Model

摘要

This paper discusses some theoretical aspects of strain localization analysis of multiphase porous media, particularly when regularized constitutive models such as the gradient dependent and time dependent models are used. Stability and hyperbolicity of the governing equations are studied and the relationships between permeability and the wave number where a real wave speed exists are investigated numerically. The results obtained will be very useful for a good understanding of the mechanical behavior of the problem. It will be also shown that a possible wave number domain exists where the wave speed vanishes but the problem will be still stable. Particular attention is focused on the two cases of wave number ~(K+0) and ~(K→∞) of the perturbation waves and the interaction between the different internal length scale parameters during dynamic strain localisation in multiphase porous materials are also studied. It is pointed out that the consideration of fluid interaction is necessary for the prediction of the internal length when regularization through a constitutive model is introduced in the numerical model to overcome mesh dependence in a finite element solution.