Dynamic Strain Localization in Fluid‐Saturated Porous Media

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 ...

[1]  C. Truesdell,et al.  The Classical Field Theories , 1960 .

[2]  R. M. Bowen.  Part I – Theory of Mixtures , 1976 .

[3]  T. Hughes.  Generalization of selective integration procedures to anisotropic and nonlinear media , 1980 .

[4]  Thomas J. R. Hughes,et al.  Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory , 1978 .

[5]  A. Needleman.  Material rate dependence and mesh sensitivity in localization problems , 1988 .

[6]  Jean-Herve Prevost,et al.  Accurate numerical solutions for Drucker-Prager elastic-plastic models , 1986 .

[7]  R. Hill.  Acceleration waves in solids , 1962 .

[8]  T. Belytschko,et al.  A uniform strain hexahedron and quadrilateral with orthogonal hourglass control , 1981 .

[9]  Acceleration waves in elastic-plastic porous media : interlacing and separation properties , 1990 .

[10]  L. B. Freund,et al.  Deformation trapping due to thermoplastic instability in one-dimensional wave propagation , 1984 .

[11]  K. Terzaghi.  Theoretical Soil Mechanics , 1943 .

[12]  Richard Bellman,et al.  Plastic Flow and Fracture in Solids , 1962 .

[13]  M. Biot.  Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range , 1956 .

[14]  J. Lions,et al.  Les inéquations en mécanique et en physique , 1973 .

[15]  Jean H. Prevost,et al.  Dynamic strain localization in elasto-(visco-)plastic solids, Part 2. Plane strain examples , 1990 .

[16]  Jean-Herve Prevost,et al.  Wave propagation in fluid-saturated porous media: An efficient finite element procedure , 1985 .

[17]  John R. Rice,et al.  On the Stability of Dilatant Hardening for Saturated Rock Masses , 1975 .

[18]  Alan Needleman,et al.  Dynamic Shear Band Development in Plane Strain , 1989 .

[19]  J. Prévost.  Mechanics of continuous porous media , 1980 .

[20]  J. Prévost,et al.  Loss of hyperbolicity in elastic-plastic solids with deviatoric associativity , 1990 .

[21]  J. Prévost,et al.  Dynamic strain localization in elasto-(visco-)plastic solids, Part 1. General formulation and one-dimensional examples , 1990 .

[22]  J. Prévost.  Nonlinear transient phenomena in saturated porous media , 1982 .

[23]  J. Rice.  Localization of plastic deformation , 1976 .

[24]  Siavouche Nemat-Nasser,et al.  Theoretical foundation for large-scale computations for nonlinear material behavior , 1984 .

[25]  I. Vardoulakis.  Dynamic stability analysis of undrained simple shear on water‐saturated granular soils , 1986 .

[26]  J. Rudnicki.  Effects of dilatant hardening on the development of concentrated shear deformation in fissured rock masses , 1984 .