Two non-associated isotropic elastoplastic hardening models for frictional materials

Acta Mechanica

Volumn 135, Issue 1, 1999, Pages 73-90

  Lambrecht, M ^a   Miehe, C ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DEFORMATION; DIFFERENTIATION (CALCULUS); ELASTOPLASTICITY; FUNCTIONS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; SOIL MECHANICS; TENSILE STRESS;

DRUCKER-PRAGER FUNCTION; ELASTOPLASTIC CONSTITUTIVE MODELS;

FRICTION MATERIALS;

EID: 0032672526     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01179047     Document Type: Article

References (31)

1. de Boer, R.: On plastic deformation of soils. Int. J. Plasticity 4, 371-391 (1988).
2. de Borst, R.: Non-linear analysis of frictional materials. Ph. D. Diss., Teschnische Hogeschool Delft 1986.
3. Bronstein, I. N., Semendjajew, K. A.: Taschenbuch der Mathematik. Zürich Frankfurt/M.: Harri Deutsch 1971.
4. Chen, W. F., Saleeb, A. F.: Constitutive equations for engineering materials. New York: Wiley-Interscience 1982.
5. Chen, W. F., Mizuno, E.: Nonlinear analysis in soil mechanics. In: Developments in geotechnical engineering 53. New York: Elsevier 1990.
6. Coleman, B. D., Gurtin, M. F.: Thermodynamics with internal state variables. J. Chem. Phys. 47, 597-613 (1969).
7. Desai, C. S.: A general basis for yield, failure and potential functions in plasticity. Int. J. Num. Anal. Meth. Geomech. 4, 361-375 (1980).
8. Drucker, D. C.: A more fundamental approach to plastic stress-strain relations. In: Proceedings of the first U.S. National Congress of Applied Mechanics, Chicago, June 11-16, 1951, pp. 487-491.
9. Drucker, D. C.: Update of conventional and unconventional plastic response and representation. Appl. Mech. Rev. Ann. Suppl. 1996, 48, No. 10, Part 2, 92-100 (1996).
10. Drucker, D. C., Li, M.: Triaxial test instability of a nonassociated flow-rule model. ASCE J. Eng Mech. Div. 119, 1188-1204 (1993).
11. Drucker, D. C., Li, M.: Stable response in the plastic range with local instability. ZAMP 46, 375-385 (1995).
12. Drucker, D. C., Prager, W.: Soil mechanics and plastic analysis or limit design. Q. J. Appl. Math. 10, 157-165 (1952).
13. Duxbury, P., Xikui, L.: Development of elasto-plastic material models in a natural coordinate system. Comp. Meth. Appl. Mech. Eng 135, 283-306 (1996).
14. Ehlers, W.: A single-surface yield function for geomaterials. Arch. Appl. Mech. 65, 246-259 (1995).
15. Gudehus, G.: Elastoplastische Stoffgleichungen für trockenen Sand. Ing. Arch. 42, 151-169 (1973).
16. Hill, R.: The mathematical theory of plasticity. Oxford: Clarendon Press 1950.
17. Koiter, W. T.: General theorems of elastic-plastic solids. In: Progress in solid mechanics (Sneddon, I. N., Hill, R. eds.). North Holland 1960.
18. Krenk, S., Borup, M., Hedegaard, J.: A triaxial characteristic state model for sand. Engineering Mechanics Paper 24, Department of Building Technology and Structural Engineering, Aalborg Universitet 1994.
19. Lade, P. V.: Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces. Int. J. Solids Struct. 13, 1019-1035 (1977).
20. Lade, P. V., Kim, M. K.: Single hardening constitutive model for frictional materials, II. Yield criterion and plastic work contours. Comp. Geotechn. 6, 13-29 (1988).
21. Lade, P. V., Kim, M. K.: Single hardening constitutive model for soil, rock and concrete. Int. J. Solids Struct. 32, 1963-1978 (1994).
22. Leroy, Y., Ortiz, M.: Finite element analysis of strain localization in frictional materials. Int. J. Num. Anal. Meth. Geomech. 13, 53-74 (1989).
23. Li, M., Drucker, D. C.: Instability and bifurcation of a non-associated extended Mises model in the hardening regime. J. Mech. Phys. Solids. 42, 1883-1904 (1995).
24. Lubliner, I.: Plasticity theory. New York: Macmillan 1990.
25. Miehe, C.: Multisurface thermoplasticity for single crystals at large strains in terms of Eulerian vector updates. Int. J. Solids Struct. 33, 1981-2004 (1996).
26. Roscoe, K. H., Burland, J. B.: On the generalized stress-strain behavior of 'wet' clay. In: Engineering plasticity, pp. 535-609. Cambridge: Cambridge University Press 1968.
27. Simó, J. C., Kennedy, J. G., Govindjee, S.: Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms. Int. J. Num. Meth. Eng 26, 2161-2185 (1988).
28. Simó, J. C., Meschke, G.: A new class of algorithms for classical plasticity extended to finite strains. Application to geomaterials. Comp. Mech. 11, 253-278 (1993).
29. Vermeer, P. A.: A double hardening model for sand. Géotechnique 28, 413-433 (1978).
30. Vermeer, P. A., de Borst, R.: Non-associated plasticity for soils, concrete and rock. HERON 29, No. 3 (1984).
31. Wood, D. M.: Soil behaviour and critical state soil mechanics. Cambridge: Cambridge University Press 1990.