Dynamic Strain Localization in Fluid‐Saturated Porous Media

Abstract

The fluid‐saturated medium is viewed as a two‐phase continuum consisting of a solid porous skeleton with interconnected voids that are filled with a perfect fluid, and the formulation based on the theory of mixtures. Conditions for dynamic strain localization to occur in the rate‐independent elastic‐plastic saturated porous solid are first discussed. In particular, it is shown that the existence of a stationary discontinuity is only dependent upon the material properties of the underlying drained porous solid skeleton. Viscoplasticity is then introduced as a general procedure to regularize the elastic‐plastic porous solid, especially for those situations in which the underlying inviscid drained material exhibits instabilities that preclude meaningful analysis of the initial‐value problem. Rate‐dependency naturally introduces a length scale that sets the width of the shear bands in which the deformations localize and high strain gradients prevail. Then, provided that the element size is appropriate for an adequate description of the shear band geometry, the numerical solutions are shown to be pertinent. Stable and convergent solutions with mesh refinements are obtained that are shown to be devoid of spurious mesh length‐scale effects. Also, the effects of permeability on shear band development are studied and discussed. It is shown that low permeabilities delay considerably the growth of the shear band instabilities in agreement with Rice's (1975) predictions. Finally, the effect of the specimen geometry on the pattern of shear banding is illustrated.