TECHNICAL PAPERS
Sep 1, 1986

Bounding Surface Plasticity. I: Mathematical Foundation and Hypoplasticity

Publication: Journal of Engineering Mechanics
Volume 112, Issue 9

Abstract

The mathematical foundation of the general bounding surface constitutive formulation in plasticity is presented. Along these lines the concept of hypoplasticity is formally introduced, and it is shown that a particular class of hypoplastic formulations arises naturally from certain bounding surface models, with the distinguishing feature being the dependence of the elastoplastic moduli and/or the plastic strain rate direction on the stress rate direction. The general analytical perspective allows the better understanding and improvement of existing bounding surface plasticity and hypoplasticity models, which are briefly discussed, and suggests the proper way to construct new ones for future applications.

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References

1.
Aboim, C. A., and Roth, W. H., “Bounding‐surface‐plasticity Theory Applied to Cyclic Loading of Sand,” Proceedings, International Symposium on Numerical Models in Geomechanics, R. Dungar, G. N. Pande, and J. A. Studer, Eds., A. A. Balkema, Zurich, Switzerland, Sept., 1982, pp. 65–72.
2.
Bardet, J. F., “Application of Plasticity Theory to Soil Behavior: A New Sand Model,” thesis presented to the California Institute of Technology, at Calif., in 1983, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
3.
Bažant, Z. P., “Endochronic Inelasticity and Incremental Plasticity,” International Journal of Solids Structures, Vol. 14, 1978, pp. 691–714.
4.
Bažant, Z. P., “Work Inequalities for Plastic Fracturing Materials,” International Journal of Solids Structures, Vol. 16, 1980, pp. 873–901.
5.
Besseling, J. F., “A Theory of Elastic, Plastic and Creep Deformations of an Initially Isotropic Material,” Journal of Applied Mechanics, ASME, Vol. 25, 1958, pp. 529–536.
6.
Bruhns, O. T., and Müller, R., “Some Remarks on the Application of a Two‐Surface Model in Plasticity,” Acta Mechanica, Vol. 53, 1984, pp. 81–100.
7.
Christoffersen, J., and Hutchinson, J. W., “A Class of Phenomenological Corner Theories of Plasticity,” Journal of Mechanics and Physical Solids, Vol. 27, 1979, pp. 465–487.
8.
Dafalias, Y. F., “On Cyclic and Anisotropic Plasticity,” thesis presented to the University of California, at Berkeley, Calif., in 1975, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
9.
Dafalias, Y. F., and Popov, E. P., “A Model of Nonlinearly Hardening Materials for Complex Loading,” Acta Mechanica, Vol. 21, 1975, pp. 173–192.
Also abstract in Proceedings, 7th U.S. National Congress of Applied Mechanics, Boulder, Colo., June, 1974, p. 149.
10.
Dafalias, Y. F., and Popov, E. P., “Plastic Internal Variables Formalism of Cyclic Plasticity,” Journal of Applied Mechanics, ASME, Vol. 43, 1976, pp. 645–651.
11.
Dafalias, Y. F., and Popov, E. P., “Cyclic Loading for Materials with a Vanishing Elastic Region,” Nuclear Engineering and Design, Vol. 41, 1977, pp. 293–302.
12.
Dafalias, Y. F., “A Model for Soil Behavior Under Monotonic and Cyclic Loading Conditions,” Transactions, 5th International Conference, on SMiRT, Vol. K, paper No. K 1/8, West Berlin, Germany, Aug., 1979.
13.
Dafalias, Y. F., “The Concept and Application of the Bounding Surface in Plasticity Theory,” Physical Non‐Linearities in Structural Analysis, IUTAM Symposium, Senlis, France, May, 1980, J. Hult and J. Lemaitre, Eds., Springer Verlag, Berlin, W. Germany, 1981, pp. 56–63.
14.
Dafalias, Y. F., “A Novel Bounding Surface Constitutive Law for the Monotonic and Cyclic Hardening Response of Metals,” Transactions, 6th International Conference on SMiRT, Vol. 1, paper No. L 3/4, Paris, France, Aug., 1981.
15.
Dafalias, Y. F., discussion of “Bounding Surface Plasticity. Part 2: Application to Isotropic Cohesive Soils,” by K. Hashiguchi, Journal of Applied Mechanics, ASME, Vol. 48, 1981, pp. 211–212.
16.
Dafalias, Y. F., “Realistic Constitutive Description for Finite Elastoplastic Deformations,” Proceedings, Plasticity of Metals at Finite Strain: Theory, Experiment and Computation, E. H. Lee and R. L. Mallett, Eds., RPI, Troy, N.Y., 1982, pp. 505–511.
17.
Dafalias, Y. F., and Herrmann, L. R., “Bounding Surface Formulation of Soil Plasticity,” Soil Mechanics—Transient and Cyclic Loads, G. N. Pande and O. C. Zienkiewicz, Eds., John Wiley and Sons, Chichester, U.K., 1982, pp. 253–282.
18.
Dafalias, Y. F., “The Plastic Spin,” Journal of Applied Mechanics, ASME, Vol. 52, 1985, pp. 865–871.
19.
Dafalias, Y. F., and Herrmann, L. R., “Bounding Surface Plasticity. 2: Application to Isotropic Cohesive Soils,” Journal of Engineering Mechanics, ASCE, in press.
20.
Darve, F., “Contribution a la Determination de la Loi Rehologique Incrementale des Sols,” thesis presented to the Universite de Grenoble, at Grenoble, France, in 1974, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
21.
Fardis, M. N., Alibe, B., and Tassoulas, J. L., “Monotonic and Cyclic Constitutive Law for Concrete,” Journal of Engineering Mechanics, ASCE, Vol. 109, EM4, Apr., 1983, pp. 516–536.
22.
Hashiguchi, K., and Ueno, M., “Elasto‐plastic Constitutive Laws of Granular Materials,” Proceedings, Constitutive Equations of Soils, Specialty Session 9, 9th International Conference on Soil Mechanics and Foundation Engineering, Tokyo, Japan, 1977, pp. 73–82.
23.
Hashiguchi, K., “Constitutive Equations of Elastoplastic Materials with Elastic‐Plastic Transition,” Journal of Applied Mechanics, ASME, Vol. 47, 1980, pp. 266–272.
24.
Hashiguchi, K., “Constitutive Equations of Elastoplastic Materials with Anisotropic Hardening and Elastic‐Plastic Transition,” Journal of Applied Mechanics, ASME, Vol. 48, 1981, pp. 297–301.
25.
Iwan, W. D., “On a Class of Models for the Yielding Behavior of Continuous and Composite Systems,” Journal of Applied Mechanics, ASME, Vol. 34, 1967, pp. 612–617.
26.
Krieg, R. D., “A Practical Two‐Surface Plasticity Theory,” Journal of Applied Mechanics, ASME, Vol. 42, 1975, pp. 641–646.
27.
Lubliner, J., “On Loading, Yield and Quasi‐Yield Hypersurfaces in Plasticity Theory,” International Journal of Solids Structures, Vol. 11, 1976, pp. 1011–1016.
28.
McVay, M., and Taesiri, Y., “Cyclic Behavior of Pavement Base Materials,” Journal of Geotechnkal Engineering, ASCE, Vol. 111, No. 1, Jan., 1985, pp. 1–17.
29.
Mroz, Z., “On Forms of Constitutive Laws for Elastic‐Plastic Solids,” Arch. Mech. Stos., Vol. 18, 1966, pp. 3–35.
30.
Mroz, Z., “On the Description of Anisotropic Workhardening,” Journal of the Mechanics and Physics of Solids, Vol. 15, 1967, pp. 163–175.
31.
Mroz, Z., Norris, V. A., and Zienkiewicz, O. C., “Application of an Anisotropic Hardening Model in the Analysis of Elastoplastic Deformation of Soils,” Geotechnique, Vol. 29, 1979, pp. 1–34.
32.
Mroz, Z., and Zienkiewicz, O. C., “Uniform Formulation of Constitutive Equations for Clays and Sands,” Mechanics of Engineering Materials, C. S. Desai and R. H. Gallagher, Eds., John Wiley and Sons, Chichester, U.K., 1984, pp. 415–449.
33.
Phillips, A., and Sierakowski, R. L., “On the Concept of the Yield Surface,” Acta Mechanica, Vol. I/1, 1965, pp. 29–35.
34.
Phillips, A., “On Rate‐Independent Continuum Theories of Graphite and their Experimental Verification,” Nuclear Engineering and Design, Vol. 18, 1972, pp. 203–211.
35.
Phillips, A., and Lee, C. W., “Yield Surfaces and Loading Surfaces. Experiments and Recommendations,” International Journal of Solids Structures, Vol. 15, 1979, pp. 715–729.
36.
Popov, E. P., and Ortiz, M., “Macroscopic and Microscopic Cyclic Metal Plasticity,” Proceedings, 3rd Engineering Mechanics Division Specialty Conference, ASCE, Austin, Tex., 1979, pp. 303–330.
37.
Tseng, N. T., and Lee, G. C., “Simple Plasticity Model of Two‐Surface Type,” Journal of Engineering Mechanics, ASCE, Vol. 109, June, 1983, pp. 795–810.
38.
Valanis, K. C., and Lee, C. F., “Some Recent Developments of the Endochronic Theory with Applications,” Nuclear Engineering and Design, Vol. 69, 1982, pp. 327–344.
39.
Wang, Z., Shen, C. K., Dafalias, Y. F., Yang, H. W., and Li, X. S., “The Role of Relative Density in a Bounding Surface Plasticity Model for Sand,” Proceedings, 2nd International Conference on Soil Dynamics and Earthquake Engineering, On board the liner QE2, Brebbia, C. A. et al., Eds., Springer, New York, N.Y., 1985, pp. 2177–2192.
40.
Yang, B. L., Dafalias, Y. F., and Herrmann, L. R., “A Bounding Surface Plasticity Model for Concrete,” Journal of Engineering Mechanics, ASCE, Vol. 111, 1985, pp. 359–380.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 112Issue 9September 1986
Pages: 966 - 987

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Published online: Sep 1, 1986
Published in print: Sep 1986

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Yannis F. Dafalias, M. ASCE
Prof. of Engrg. Sci., Dept. of Civ. Engrg., Univ. of California, Davis, CA 95616

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