Numerical analysis and large strain elastic-viscoplastic behavior of hydrostatic stress-sensitive metals

International Journal of Solids and Structures

Volumn 38, Issue 4, 2001, Pages 635-656

  Brünig, Michael ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; ELASTOPLASTICITY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PLASTIC FLOW; PROBLEM SOLVING; STRAIN; STRESS ANALYSIS; VISCOPLASTICITY;

GENERALIZED MACROSCOPIC THEORY; HYDROSTATIC STRESS-SENSITIVE METALS;

STRUCTURAL ANALYSIS;

EID: 0035193159     PISSN: 00207683     EISSN: None     Source Type: None    
DOI: 10.1016/S0020-7683(00)00092-5     Document Type: Article

References (55)

1. Anand, L., 1985. Constitutive equations for hot-working metals. Int. J. Plasticity 1, 213-231.
2. Arya, V.K., 1996. Efficient and accurate explicit integration algorithms with application to viscoplastic models. Int. J. Numer. Meth. Engng. 39, 261-279.
3. Argyris, J.H., Vaz, L.E., Willam, K.J., 1978. Improved solution methods for rate problems. Comp. Meth. Appl. Mech. Engng. 16, 231-277.
4. Asaro, R.J., 1983. Micromechanics of crystals and polycrystals. Adv. Appl. Mech. 23, 2-115.
5. Auricchio, F., Taylor, R.L., 1994. A generalized viscoplastic model and its algorithmic implementation. Comput. and Struct. 53, 637-647.
6. Bazant, Z.P., Lin, F.B., 1988. Non-local yield limit degradation. Int. J. Numer. Meth. Engng. 26, 1805-1823.
7. Bodner, S.R., Partom, Y., 1975. Constitutive equations for elastic-viscoplastic strain-hardening materials. J. Appl. Mech. 42, 385-389.
8. de Borst, R., Pamin, J., 1996. Some novel developments in finite element procedures for gradient-dependent plasticity. Int. J. Numer. Meth. Engng. 39, 2477-2505.
9. Brünig, M., 1996. Macroscopic theory and nonlinear finite element analysis of micromechanics of single crystals at finite strains. Comput. Mech. 18, 471-484.
10. Brünig, M., 1997. Numerical modelling of finite elastic-plastic deformations of crystalline solids including non-Schmid effects. In: Owen, D.R.J., Oñate, E., Hinton, E. (Eds.), Computational Plasticity 5 - Fundamentals and Applications, CIMNE, Barcelona, 907-912.
11. Brünig, M., 1998. Microscopic modelling of volume expansion and pressure dependence of plastic yielding in crystalline solids. Archive Appl. Mech. 68, 71-84.
12. Brünig, M., 1999a. Large strain elastic-plastic theory and nonlinear finite element analysis based on metric transformation tensors. Comput. Mech. 24, 187-196.
13. Brünig, M., 1999b. Formulation and numerical treatment of incompressibility constraints in large strain elastic-plastic analysis. Int. J. Numer. Meth. Engng. 45, 1047-1068.
14. Brünig, M., 1999c. Numerical simulation of the large elastic-plastic deformation behavior of hydrostatic stress-sensitive solids. Int. J. Plasticity 15, 1237-1264.
15. Brünig, M., Obrecht, H., 1998. Finite elastic-plastic deformation behavior of crystalline solids based on a non-associated macroscopic flow rule. Int. J. Plasticity 14, 1189-1208.
16. Brünig, M., Obrecht, H., Speier, L., 1995. Finite deformation elastic-plastic analysis based on a plastic predictor method. In: Owen, D.R.J., Oñate, E. (Eds.), Computational Plasticity 4 - Fundamentals and Applications, Pineridge Press, Swansea, 141-152.
17. Cormeau, I.C., 1975. Numerical stability of quasi-static elasto/visco-plasticity. Int. J. Numer. Meth. Engng. 9, 109-127.
18. Fotiu, P.A., Nemat-Nasser, S., 1996. A universal integration algorithm for rate-dependent elastoplasticity. Comput. and Struct. 59, 1173-1184.
19. Eterovic, A.L., Bathe, K.-J., 1990. A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropickinematic hardening using logarithmic stress and strain measures. Int. J. Numer. Methods Eng. 30, 1099-1114.
20. Hill, R., 1950. The Mathematical Theory of Plasticity. Oxford University Press, Oxford.
21. Hill, R., 1962. Acceleration waves in solids. J. Mech. Phys. Solids 10, 1-16.
22. Hutchinson, J.W., 1976. Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. Lond. A. 348, 101-127.
23. Khan, A.S., Huang, S., 1995. Continuum Theory of Plasticity. Wiley, New York.
24. Lee, E.H., 1969. Elastic-plastic deformations at finite strains. J. Appl. Mech. 36, 1-6.
25. Lehmann, Th., 1982a. Some remarks on the decomposition of deformations and mechanical work. Int. J. Eng. Sci. 20, 281-288.
26. Lehmann, Th., 1982b. Some theoretical considerations and experimental results concerning elastic-plastic stress-strain relations. Arch. Appl. Mech. (Ingenieur-Archiv) 52, 391-403.
27. Lush, A.M., Weber, G., Anand, L., 1989. An implicit time-integration procedure for a set of Internal variable constitutive equations for isotropic elasto-viscoplasticity. Int. J. Plasticity 5, 521-549.
28. Miller, A.K., 1976. An inelastic constitutive model for monotonic, cyclic and creep deformation. Part I. Equations development and analytical procedures. Trans. ASME J. Engng. Mater. Technol. 98, 106-113.
29. Mühlhaus, H.B., 1989. Application of Cosserat theory in numerical solutions of limit load problems. Archive Appl. Mech. (Ing.- Archiv) 59, 124-137.
30. Mühlhaus, H.B., Aifantis, E.C., 1991. A variational principle for gradient plasticity. Int. J. Solids Struct. 28, 845-857.
31. Müller-Hoeppe, N., Wriggers, P., 1992. Numerical integration of viscoplastic material laws at large strains with application to impact problems. Comput. and Struct. 45, 165-171.
32. Needleman, A., 1988. Material rate dependence and mesh sensitivity in localization problems. Comp. Meth. Appl. Mech. Engng. 67, 69-85.
33. Needleman, A., Tvergaard, V., 1984. Limits to formability in rate-sensitive metal sheets. In: Carlsson, J., Ohlson, N.G. (Eds.), Mechanical Behavior of Materials, Pergamon Press, Oxford, pp. 51-65.
34. Nemat-Nasser, S., Chung, D.T., 1992. An explicit constitutive algorithm for large-strain, large-strain-rate elastic-viscoplasticity. Comp. Meth. Appl. Mech. Engng. 95, 205-219.
35. Nemat-Nasser, S., Li, Y.F., 1992. A new explicit algorithm for finite-deformation elastoplasticity and elastoviscoplasticity: performance evaluation. Comput. and Struct. 44, 937-963.
36. Nishiguchi, I., Sham, T.-L., Krempl, E., 1990. A finite deformation theory of viscoplasticity based on overstress: part I - Constitutive equations. J. Appl. Mech. 57, 553-561.
37. Pan, J., Rice, J.R., 1983. Rate sensitivity of plastic flow and implications for yield-surface vertices. Int. J. Solids Struct. 19, 973-987.
38. Peirce, D., Shih, N., Needleman, A., 1984. A tangent modulus method for rate dependent solids. Comput. and Struct. 18, 875-887.
39. Perić, D., Owen, D.R.J., Honnor, M.E., 1992. A model for finite strain elasto-plasticity based on logarithmic strains: Computational issues. Comp. Meth. Appl. Mech. Engng. 94, 35-61.
40. Perzyna, P., 1966. Fundamental problems in viscoplasticity. Adv. Appl. Mech. 9, 243-377.
41. Rice, J.R., 1970. On the structure of stress-strain relations for time-dependent plastic deformations in metals. ASME J. Appl. Mech. 37, 728-737.
42. Rice, J.R., 1971. Inelastic constitutive relations for solids: An Internal variable theory and its applications to metal plasticity. J. Mech. Phys. Solids 19, 433-455.
43. Rice, J.R., 1977. The localization of plastic deformation. In: Koiter, W.T. (Ed.), Proc., 14th Int. Congr. Theoret. Appl. Mech., North- Holland, Amsterdam, pp. 207-220.
44. Rouainia, M., Perić, D., 1998. A computational model for elasto-viscoplastic solids at finite strain with reference to thin shell applications. Int. J. Numer. Meth. Engng. 42, 289-311.
45. Sansour, C., Kollmann, F.G., 1997. On theory and numerics of large viscoplastic deformation. Comput. Meth. Appl. Mech. Engng. 146, 351-369.
46. Spitzig, W.A., Richmond, O., 1984. The effect of pressure on the flow stress of metals. Acta Metall. 32, 457-463.
47. Spitzig, W.A., Sober, R.J., Richmond, O., 1975. Pressure dependence of yielding and associated volume expansion in tempered martensite. Acta Metall. 23, 885-893.
48. Spitzig, W.A., Sober, R.J., Richmond, O., 1976. The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory. Metall. Trans. A 7A, 1703-1710.
49. Taylor, L.M., Becker, E.B., 1983. Some computational aspects of large deformation, rate-dependent plasticity problems. Comput. Meth. Appl. Mech. Engng. 41, 251-277.
50. Wang, W.M., Sluys, L.J., Borst, R., 1996. Interaction between material length scale and imperfection size for localization phenomena in viscoplastic media. Eur. J. Mech. A Solids 15, 447-464.
51. Weber, G., Anand, L., 1990. Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic- viscoplastic solids. Comput. Meth. Appl. Mech. Engng. 79, 173-202.
52. Wilkins, M.L., 1964. Calculation of elastic-plastic flow. In: Alder, B. et al. (Eds.), Meth. Comp. Physics, vol. 3. Academic Press, New York.
53. Zabaras, N., Arif, F.M., 1992. A family of integration algorithms for constitutive equations in finite deformation elasto-viscoplasticity. Int. J. Numer. Meth. Engng. 33, 59-84.
54. Zienkiewicz, O.C., Cormeau, I.C., 1974. Viscoplasticity, plasticity and creep in elastic solids - a unified numerical solution approach. Int. J. Numer. Meth. Engng. 8, 821-845.
55. Zirky, M.A., 1994. An accurate and stable algorithm for high strain-rate finite strain plasticity. Comput. and Struct. 50, 337-350.