A generalized approach to formulate the consistent tangent stiffness in plasticity with application to the GLD porous material model

International Journal of Solids and Structures

Volumn 42, Issue 1, 2005, Pages 103-122

  Kim, Jinkook ^a   Gao, Xiaosheng ^a  

^a The University of Akron   (United States)

Author keywords

Anisotropic plasticity; Backward Euler method; Consistent tangent moduli; Ductile fracture; Implicit finite element method; The Gologanu Leblond Devaux model

Indexed keywords

ANISOTROPY; CONVERGENCE OF NUMERICAL METHODS; DUCTILE FRACTURE; FINITE ELEMENT METHOD; ITERATIVE METHODS; MATRIX ALGEBRA; POROUS MATERIALS; STIFFNESS;

ANISOTROPIC PLASTICITY; BACKWARD EULER METHOD; CONSISTENT TANGENT MODULI; IMPLICIT FINITE ELEMENT METHOD; THE GOLOGANU-LEBLOND-DEVAUX MODELS;

PLASTICITY;

EID: 5644246472     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2004.07.011     Document Type: Article

References (23)

1. ABAQUS/Theory Manual, 2001. Version 6.2, 2001. Hibbit, Karlsson and Sorensen Inc.
2. Aravas, N., 1987. On the numerical integration of a class of pressure-dependent plasticity models. Int. J. Numer. Methods Eng. 24, 1391-1416.
3. Benzerga, A.A., 2000. Rupture ductile des tôles anisotropes. Ph.D. Thesis (parts in English). Ecole des Mines de Paris.
4. Faleskog, J., Gao, X., Shih, C.F., 1998. Cell model for nonlinear fracture analysis - I. Micromechanics calibration. Int. J. Fract. 89, 355-373.
5. Gao, X., Faleskog, J., Shih, C.F., 1998a. Cell model for nonlinear fracture analysis - II. Fracture-process calibration and verification. Int. J. Fract. 89, 375-398.
6. Gao, X., Faleskog, J., Shih, C.F., Dodds, R.H., 1998b. Ductile tearing in part-through cracks: experiments and cell-model predictions. Eng. Fract. Mech. 59, 761-777.
7. Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing nonspherical voids - case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723-1754.
8. Gologanu, M., Leblond, J.B., Devaux, J., 1994. Approximate models for ductile metals containing nonspherical voids - case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Tech. 116, 290-297.
9. Gologanu, M., Leblond, J.B., Perrin, G., Devaux, J., 1995. Recent extensions of Gurson's model for porous ductile metals. In: Suquet, P. (Ed.), Continuum Micromechanics. Springer-Verlag, Berlin.
10. Gologanu, M., Leblond, J.B., Perrin, G., Devaux, J., 2001. Theoretical models for void coalescence in porous ductile solids. I. Coalescence "in layers". Int. J. Solids Struct. 38, 5581-5594.
11. Gurson, A.L., 1977. Continuum of ductile rupture by void nucleation and growth: part I - yield criteria and flow rules for porous ductile media. J. Eng. Mater. Tech. 99, 2-55.
12. Lee, J.H., Zhang, Y., 1991. On the numerical integration of a class of pressure-dependent plasticity models with mixed hardening. Int. J. Numer. Methods Eng. 32, 419-438.
13. Muhlich, U., Brocks, W., 2003. On the numerical integration of a class of pressure-dependent plasticity models including kinematic hardening. Comput. Mech. 31, 479-488.
14. Needleman, A., Tvergaard, V., 1987. An analysis of ductile rupture modes at a crack tip. J. Mech. Phys. Solids 35, 151-183.
15. Ortiz, M., PoPov, E.P., 1985. Accuracy and stability of integration algorithms for elastoplastic constitutive relations. Int. J. Numer. Methods Eng. 21, 1561-1576.
16. Pardoen, T., Hutchinson, J.W., 2000. An extended model for void growth and coalescence. J. Mech. Phys. Solids 48, 2467-2512.
17. Pardoen, T., Hutchinson, J.W., 2003. Micromechahics-based model for trends in toughness of ductile metals. Acta Mater. 51, 133-148.
18. Pardoen, T., 2003. Private communication.
19. Ruggieri, C., Panontin, T.L., Dodds, R.H., 1998. Numerical modeling of ductile crack growth in 3-D using computational cell elements. Int. J. Fract. 82, 95-97.
20. Simo, J.C., Taylor, R.L., 1985. Consistent tangent operators for rate-independent elastoplasticity. Comput. Methods Appl. Mech. Eng. 48, 101-118.
21. Tvergaard, V., 1982. On Localization in ductile materials containing spherical voids. Int. J. Fract. 18, 237-252.
22. Xia, L., Shih, C.F., Hutchinson, J.W., 1995. Computational approach to ductile crack growth under large scale yielding conditions. J. Mech. Phys. Solids 43, 389-413.
23. Zhang, Z.L., 1995. Explicit consistent tangent moduli with a return mapping algorithm for pressure-dependent elastoplasticity models. Comput. Methods Appl. Mech. Eng. 121, 29-44.