Elastic‐Viscoplastic Model for Large Deformation of Soils
Publication: Journal of Engineering Mechanics
Volume 116, Issue 9
Abstract
An elastic‐viscoplastic model for large deformation of metals (Rubin 1987b) has been generalized to include the major features of cap‐type models for geological materials. Specifically, the effects of shear‐enhanced compaction and dilation are conveniently modeled using kinematics that naturally separate plastic distortion from plastic dilatation (volume change). The constitutive equation for stress is hyperelastic in the sense that the stress is a function of elastic deformation and is equal to a derivative of the Helmholtz free energy. Although the theory is formulated without the explicit use of a yield function, the flow rule for plastic deformation rate can best be described as nonassociated. In this regard, special attention is focused on satisfying a physically plausible thermodynamic restriction on the constitutive equations, which ensures that the rate of plastic dissipation is nonnegative. Specific constitutive equations are proposed, and the material constants are determined by matching experimental data for Yuma clayey sand.
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References
1.
Bodner, S. R., and Partom, Y. (1972). “A large deformation elastic‐viscoplastic analysis of a thick‐walled spherical shell.” J. Appl. Mech., ASME, 39(3), 751–757.
2.
Bodner, S. R., and Partom, Y. (1975). “Constitutive equations for elastic‐viscoplastic strain‐hardening materials.” J. Appl. Mech., ASME, 42(2), 385–389.
3.
Chen, W. F., and Baladi, G. Y. (1985). Soil plasticity, theory and implementation, Elsevier, Amsterdam, The Netherlands.
4.
Drucker, D. C. (1951). “A more fundamental approach to stress‐strain relations.” Proc., 1st U.S. Congress on Applied Mechanics, 487–491.
5.
Flory, P. J. (1961). “Thermodynamic relations for high elastic materials.” Trans., Faraday Soc., 57, 829–838.
6.
Green, A. E., and Naghdi, P. M. (1965). “A general theory of an elastic‐plastic continuum.” Arch. Rational Mech. Anal., 18, 251–281.
7.
Green, A. E., and Naghdi, P. M. (1966). “A thermodynamic development of elasticplastic continua.” Proc., IUTAM Symposia, Vienna, Austria, 117–131.
8.
Green, A. E., and Naghdi, P. M. (1977). “On thermodynamics and the nature of the second law.” Proc., Royal Soc. Lond., Vol. A 357, 253–270.
9.
Green, A. E., and Naghdi, P. M. (1978). “The second law of thermodynamics and cyclic processes.” J. Appl. Mech., ASME, 45(3), 487–492.
10.
Il'yushin, A. A. (1961). “On the postulate of plasticity.” Prikl. Mat. Mekh., 25, 503–507.
11.
Lade, P. V. (1987). “Modelling the elastic behaviour of granular materials.” Int. J. Numer. Anal. Methods Geomech., 11, 521–542.
12.
Lade, P. V. (1988). “Effects of voids and volume changes on the behaviour of frictional materials.” Int. J. Numer. Anal. Methods Geomech., 12, 351–370.
13.
Lade, P. V., Nelson, R. B., and Marvin, Y. (1987). “Nonassociated flow and stability of granular materials.” J. Engrg. Mech., 113(9), 1302–1318.
14.
Lade, P. V., Nelson, R. B., and Marvin, Y. (1988). “Instability of granular materials with nonassociated flow.” J. Engrg. Mech., 114(12), 2173–2191.
15.
Naghdi, P. M., and Trapp, J. A. (1975). “Restrictions on constitutive equations of finitely deformed elastic‐plastic materials.” Q. J. Mech. Appl. Math., 28, 25–46.
16.
Nemat‐Nasser, S. (1983). “On finite plastic flow of crystalline solids and geomaterials.” J. Appl. Mech., 50(4b), 1114–1126.
17.
Rubin, M. B. (1986). “An elastic‐viscoplastic model for large deformation.” Int. J. Engrg. Sci., 24(7), 1083–1095.
18.
Rubin, M. B. (1987a). “An elastic‐viscoplastic model for metals subjected to high compression.” J. Appl. Mech., ASME, 54, 532–538.
19.
Rubin, M. B. (1987b). “An elastic‐viscoplastic model exhibiting continuitty of solid and fluid states.” Int. J. Engrg. Sci., 25(9), 1175–1191.
20.
Rubin, M. B. (1989). “A time integration procedure for large plastic deformation in elastic‐viscoplastic metals.” J. Appl. Math. and Physics, 40(6), 846–871.
21.
Rubin, M. B., and Chen, R. (1989). “Universal relations for elastically isotropic elastic‐plastic materials.” J. Appl. Mech., (in press).
22.
Schreyer, H. L. (1989). “Smooth limit surfaces for metals, concrete and geotechnical materials.” J. Engrg. Mech., ASCE, 115(9), 1960–1975.
23.
Simo, J. C., Taylor, R. L., and Pister, K. S. (1985). “Variational and projection methods for the volume constraint in finite deformation elasto‐plasticity.” Comp. Methods Appl. Mech. Engrg., 51, 177–208.
24.
Steinberg, D. J., Cochran, S. G., and Guinan, M. W. (1980). “A constitutive model for metals applicable at high‐strain rate.” J. Appl. Phys., 51(3), 1498–1504.
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Copyright © 1990 ASCE.
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Published online: Sep 1, 1990
Published in print: Sep 1990
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