Finite strain generalization of small-strain constitutive relations for any finite strain tensor and additive volumetric-deviatoric split

International Journal of Solids and Structures

Volumn 33, Issue 20-22, 1996, Pages 2887-2897

  Bažant, Zdeněk P ^a  

^a NORTHWESTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATERIALS TESTING; MATHEMATICAL TRANSFORMATIONS; STRAIN GAGES; STRAIN RATE; STRESS CONCENTRATION; TENSORS;

DEVIATORIC STRAIN TENSOR; FINITE STRAIN GENERALIZATION; FINITE STRAIN TENSOR; GREEN LAGRANGE STRAIN TENSOR; ISOTROPIC MATERIALS; MULTIPLICATIVE DECOMPOSITION; SMALL STRAIN CONSTITUTIVE EQUATIONS; TRANSFORMATION TENSOR; VOLUMETRIC STRAIN TENSOR;

STRAIN;

EID: 0030212344     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/0020-7683(96)00002-9     Document Type: Article

References (36)

1. Atluri, S. N. (1984). Alternate stress and conjugate strain measures, and mixed variational formulations involving rigid rotations, for computational analyses of finitely deformed solids, with application to plates and shells - I. Theory. Computers and Structures 18, 93-116.
2. Bažant, Z. P. (1971). A correlation study of incremental deformations and stability of continuous bodies. J. Appl. Mech. Trans. ASME 38, 919-928.
3. Bažant, Z. P. and Cedolin, L. (1991). Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories. Oxford University Press, New York.
4. Bažant, Z. P. (1994) Finite strain generalization of small-strain constitutive relations and volumetric-deviatoiic split. Report 94/C425f, Dept. of Civil Engrg, Northwestern University, Evanston, IL.
5. Bažant, Z. P. (1995). Additive volumetric-deviatoric split of finite strain tensor and its implication for cracking models. Proc. 2nd Int. Conf. on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS2) (Edited by F. H. Wittmann), Zürich, July 1995, pp. 1021-1026.
6. Bažant, Z. P., Bishop, F. C. and Chang, T.-P. (1986). Confined compression tests of cement paste and concrete up to 300 ksi. J. Am. Concrete Inst. 83, 553-560.
7. Bažant, Z. P., Xiang, Y. and Prat, P. C. (1995). Microplane model for concrete: I. Stress-strain boundaries and finite strain. ASCE J. Engng Mech. 121 (in press).
8. Biot, M. (1965). Mechanics of Incremental Deformations. John Wiley, New York.
9. Doyle, T. C. and Ericksen, J. L. (1956). Non-linear elasticity. Advances in Applied Mech. 4, 53-115.
10. Flory, T. J. (1961). Thermodynamic relations for high elastic materials. Trans. Faraday Soc. 57, 829-838.
11. Fox, N. (1968). On the continuum theories of dislocations and plasticity. Quart. J. Appl. Math. 21, 67-75.
12. Green, A. P. and Naghdi (1971). Intern. J. Engng Sci. 9, 1219.
13. Gurtin, M. E. and Spear, K. (1983). On the relationship between the logarithmic strain rate and the stretching tensor. Int. J. Solids Structures 19, 437-444.
14. Hill, R. (1966). Generalized constitutive relations for incremental deformations of metal crystals by multi-slip. J. Mech. Phys. Solids 14, 95-102.
15. Hill, R. (1968). On constitutive inequalities for simple materials. J. Mech. Phys. Solids 16, 229-242, 315-322.
16. Hill, R. (1970). Constitutive inequalities for isotropic solids under finite strain. Proc. Roy. Soc. London A 314, 457.
17. Kröner, E. (1960). Allgemeine Kontinuumstheorie der Versetzungern und Eigenspannungen. Arch. Ration. Mech. Anal. 4, 273-334.
18. Lee, E. H. (1969). Elastic-plastic deformations in finite strains. ASME J. Applied Mech. 36, 1-60.
19. Lee, E. H. and Liu, D. T. (1967). Finite-strain elastic-plastic theory with application to plane-wave analysis. J. Appl. Phys. 38, 19-27.
20. Lubliner, J. (1986). Normality rules in large-deformation plasticity. Mech. Materials 5, 29-34.
21. Lubliner, J. (1990). Plasticity Theory. Macmillan, New York (Section 8.2).
22. Malvern, L. E. (1969). Introduction to the Mechanics of a Continuous Medium. Prentice Hall, Englewood Cliffs, NJ.
23. Mandel, J. (1973). Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques. Int. J. Solids Structures 9, 725-740.
24. Mandel, J. (1976). Adaptation d'une structure écrouissable. Mech. Res. Comm. 3, 251-258, 483-488.
25. Mandel, J., Zarka, J. and Halpen, B. (1977). Adaptation d'une structure élastoplastique à écrouissage cinématique. Mech. Res. Comm. 4, 309-314.
26. McMeeking, R. M. and Rice, J. R. (1975). Finite element formulations for problems of large elasto-plastic deformation. Int. J. Solids Structures 11, 601-616.
27. Ogden, R. W. (1984). Non-linear Elastic Deformations. Ellis Horwood, U.K.
28. Pinski, P. M., Ortiz, M. and Pister, K. S. (1983). Numerical integration of rate constitutive equations in finite deformation analysis. Computer Meth. in Appl. Mech. Engng 40, 137-158.
29. Rice, J. R. (1970). On the structure of stress-strain relations for time-dependent plastic deformation of metals. ASME J. Applied Mech. 37, 728-737.
30. Rice, J. R. (1993). Mechanics of solids. In Encyclopedia Brittanica (15th edn), Vol. 23, pp. 737-747 and 773.
31. Rubinstein, R. and Atluri, S. N. (1983). Objectivity of incremental constitutive relations over finite time steps in computational finite deformation analyses. Computer Meth. in Appl. Mech. Engng 36, 277-290.
32. Sidoroff, F. (1974). Un modèle viscoélastique non linéaire avec configuration intermédiaire. J. de Mécanique 13, 679-713.
33. Simo, J. C. (1985). On the computational significance of the intermediate configuration and hyperelastic constitutive equations. Mechanics of Materials 4, 439-451.
34. Simo, J. C. (1988). A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. Computer Methods in Appl. Mech. Engng 66, 199-219 and 68, 1-31.
35. Simo, J. C. (1988). A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. Computer Methods in Appl. Mech. Engng 66, 199-219 and 68, 1-31.
36. Simo, J. C. and Ortiz M. (1985). A unified approach to finite deformation elasto-plasticity based on the use of hyperelastic constitutive equations. Computational Meths. in Applied Mech. Engng 49, 177-208.