Dynamic Strain Localization in Fluid‐Saturated Porous Media
Publication: Journal of Engineering Mechanics
Volume 117, Issue 4
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.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Biot, M. A. (1956). “Theory of propagation of elastic waves in a fluid saturated porous solid.” J. Acoust. Soc. Am., 28(1), 168–191.
2.
Bowen, R. M. (1976). “Theory of mixtures.” Continuum physics, A. C. Eringen, ed., Academic Press, New York, N.Y., 1–127.
3.
Duvaut, G., and Lions, J. L. (1972). Les inéquations en Mécanique et en physique, Dunod, Paris, France (in French).
4.
Flanagan, D. P., and Belytschko, T. (1981). “A uniform strain hexahedron and quadrilateral with orthogonal hourglass control.” Int. J. Numer. Methods Engrg., 17(5), 679–706.
5.
Hadamard, J. (1903). Lecons sur la propagation des ondes et les equations de I'hydrodynamique. Librairie Scientifique A., Hermann, Paris, France (in French).
6.
Hill, R. (1962). “Acceleration waves in solids.” J. Mech. Phys. Solids, 10(1), 1–16.
7.
Hughes, T. J. R. (1980). “Generalization of selective reduced integration procedures to anisotropic nonlinear media.” Int. J. Numer. Methods Engrg., 15(9), 1413–1418.
8.
Hughes, T. J. R. (1987). The finite element method. Prentice‐Hall, Englewood Cliffs, N.J.
9.
Hughes, T. J. R., and Liu, W. K. (1978). “Implicit‐explicit finite elements in transient analysis.” J. Appl. Mech., 45, 371–378.
10.
Loret, B. (1990). “Acceleration waves in elastic‐plastic porous media: Interlacing and separation properties.” Int. J. Engrg. Sci., 28(12), 1315–1320.
11.
Loret, B., and Prevost, J. H. (1990). “Dynamic strain localization in elasto‐(visco‐) plastic solids—Part 1: General formulation and one‐dimensional examples.” Comp. Meth. Appl. Mech. Engrg., 83, 247–273.
12.
Loret, B., and Prevost, J. H. (1986), “Accurate numerical solutions for Drucker‐Prager elastic‐plastic models,” Comput. Methods Appl. Mech. Engrg., 54(3), 259–277.
13.
Loret, B., Prevost, J. H., and Harireche, O. (1990). “Loss of hyperbolicity in elasticplastic solids with deviatoric associativity.” Eur. J. Mech.: A/Solids, 9(3), 225–ndash;231.
14.
Mandel, J. (1963). “Propagation des surfaces de discontinuite dans un milieu elastoplastique.” Proc. IUTAM Symp. on Stress Waves in Inelastic Solids, H. Kolsky and W. Prager, eds., Springer‐Verlag, Berlin, Germany, 337–344.
15.
Needleman, A. (1988). “Material rate dependence and mesh sensitivity in localization problems.” Comput. Methods Appl. Mech. Engrg., 67, 69–85.
16.
Needleman, A. (1989). “Dynamic shear band development in plane strain.” J. Appl. Mech., 56(1), 1–9.
17.
Prevost, J. H., and Loret, B. (1990). “Dynamic strain localization in elasto‐(visco‐) plastic solids—Part 2: Plane strain examples.” Comput. Methods Appl. Mech. Engrg., 83, 275–294.
18.
Prevost, J. H. (1982). “Non‐linear transient phenomena in saturated porous media.” Comput. Methods Appl. Mech. Engrg., 30, 3–18.
19.
Prevost, J. H. (1985). “Wave propagation in fluid‐saturated porous media: An efficient finite element procedure.” Int. J. Soil Dyn. Earthquake Engrg., 4(4), 183–202.
20.
Prevost, J. H. (1980). “Mechanics of continuous porous media.” Int. J. Engrg. Sci., 18(5), 787–800.
21.
Rice, J. R. (1975). “On the stability of dilatant hardening for saturated rock masses.” J. Geophys. Res., 80(11), 1531–1536.
22.
Rice, J. R. (1976). “The localization of plastic deformation.” Proc. 14th IUTAM Congress; Theoretical and applied mechanics, W. T. Koiter, ed., North‐Holland Publ., Amsterdam, Netherlands, 207–220.
23.
Rudnicki, J. W. (1984). “Effect of dilatant hardening on the development of concentrated shear‐deformation in fissured rock masses.” J. Geophys. Res., 89(B11), 9259–9270.
24.
Sandler, I., and Wright, J. P. (1984). “Strain‐softening.” Theoretical foundation for large scale computations for nonlinear material behavior, S. Nemat‐Nasser, R. J. Asaro and G. A. Hegemier, eds., Martinus Nijhoff Publishers, Dordrecht, the Netherlands, 285–290.
25.
Simo, J. C., Kennedy, J. G., Govindjee, S., and Hughes, T. J. R. (1987). “Unconditionally convergent algorithms for non‐smooth multi‐surface plasticity amenable to exact linearization.” Advances in inelastic analysis AMD‐Vol. 88, S. Nakazawa, K. William, and N. Rebello, eds., ASME, 87–96.
26.
Terzaghi, K. (1943). Theoretical soil mechanics. John Wiley and Sons, New York, N.Y.
27.
Thomas, T. Y. (1961). Plastic flow and fracture in solids. Academic Press, New York, N.Y.
28.
Truesdell, C., and Toupin, R. (1960). “The classical field theories.” Handbook of physics, 3, S. Flügge, ed., Springer‐Verlag, Berlin, Germany.
29.
Vardoulakis, I. (1986). “Dynamic stability analysis of undrained simple shear on water‐saturated granular soils.” Int. J. Numer. Anal. Meth. Geomech., 10(2), 177–190.
30.
Wu, F. H., and Freund, L. B. (1984). “Deformation trapping due to thermoplastic instability in one‐dimensional wave propagation.” J. Mech. Phys. Solids, 32(2), 119–132.
Information & Authors
Information
Published In
Copyright
Copyright © 1991 ASCE.
History
Published online: Apr 1, 1991
Published in print: Apr 1991
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.