Parametric variational principle based elastic-plastic analysis of heterogeneous materials with Voronoi finite element method

Applied Mathematics and Mechanics (English Edition)

Volumn 27, Issue 8, 2006, Pages 1037-1047

  Zhang, Hong Wu ^a   Wang, Hui ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Parametric variational principle; Quadratic programming method; Voronoi finite element

Indexed keywords

COMPUTER SIMULATION; MATERIALS; MECHANICAL PROPERTIES; QUADRATIC PROGRAMMING; TWO DIMENSIONAL;

ELASTIC PLASTIC ANALYSIS; ELASTIC PLASTIC EQUATIONS; FINITE ELEMENT FORMULATIONS; HETEROGENEOUS MATERIALS; MICROSCOPIC HETEROGENEITIES; NUMERICAL SIMULATION; PARAMETRIC VARIATIONAL PRINCIPLE; STANDARD QUADRATIC PROGRAMMING MODEL; VORONOI CELL FINITE ELEMENT METHOD (VCFEM);

FINITE ELEMENT METHOD;

EID: 33750216920     PISSN: 02534827     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10483-006-0804-1     Document Type: Article

References (21)

1. Brockenbrough J R, Suresh S, Wienecke H A. Deformation of metal-matrix composites with continuous fibers: geometrical effects of fiber distribution and shape[J]. Acta Metall Mater, 1991, 39(5): 735-752.
2. Christman T, Needleman A, Suresh S. An experimental and numerical study of deformation in metal-ceramic composites[J]. Acta Metall Mater, 1989, 37(11): 3029-3050.
3. Hashin Z, Strikman S. A variational approach to the theory of the elastic behavior of multiphase materials[J]. J Mech Phys Solids, 1963, 11(2): 127-140.
4. Chen H S, Acrivos A. The effective elastic moduli of composite materials containing spherical inclusions at non-dilute concentrations[J]. Int J Solids Structures, 1978, 14(3): 349-364.
5. Hill R. A self consistent mechanics of composite materials[J]. J Mech Phys Solids, 1965, 13(4): 213-222.
6. Hori M, Nemat-Nasser S. Double inclusion model and overall moduli of multiphase composites[J]. J Mech Phys Solids, 1993, 14(2): 189-206.
7. Bao G, Hutchinson J W, McMeeking R M. Plastic reinforcement of ductile matrices against plastic flow and creep[J]. Acta Metall Mater, 1991, 39(5): 1871-1882.
8. Ghosh S, Mukhopadhyay S N. A material based finite element analysis of heterogeneous media involving Dirichlet tessellations[J]. Comput Methods Appl Mech Engrg, 1993, 104(3/4): 211-247.
9. Pian T H H. Derivation of element stiffness matrices by assumed stress distribution[J]. AAIA J, 1964, 2(5): 1333-1336.
10. Zhang J, Katsube N. Problems related to application of eigenstrains in a finite element analysis[J]. Int J Numer Methods Eng, 1994, 37(18): 3185-3193.
11. Zhang J, Katsube N. A hybrid finite element method for heterogeneous materials with randomly dispersed rigid inclusions[J]. Int J Numer Methods Eng, 1995, 38(10): 1635-1653.
12. Ghosh S, Moorthy S. Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi cell finite element method[J]. Comput Methods Appl Mech Engrg, 1995, 121(1/4): 373-409.
13. Ghosh S, Lee K, Moorthy S. Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element method[J]. Int J Solids Structures, 1995, 32(1): 27-62.
14. Grujicic M, Zhang Y. Determination of effective elastic properties of functionally graded materials using Voronoi cell finite element method[J]. Materials Science and Engineering, Ser A, 1998, 251(1): 64-76.
15. Lee K, Ghosh S. A microstructure based numerical method for constitutive modeling of composite and porous materials[J]. Materials Science and Engineering, Ser A, 1999, 272(1): 120-133.
16. Raghavan P, Li S, Ghosh S. Two scale response and damage modeling of composite materials[J]. Finite Elements in Analysis and Design, 2004, 40(12): 1619-1640.
17. Zhong Wanxie. On parametric complementary energy variational principle in soil mechanics[J]. Acta Mechanica Sinica, 1986, 18(3): 253-258 (in Chinese).
18. Zhong Wanxie, Zhang Hongwu, Wu Chengwei. Parametric Variational Principles and Its Application in Engineering[M]. Scientific and Technical Publishers, Beijing, 1997 (in Chinese).
19. Zhang H W, Xu W L, Di S L, et al. Quadratic programming method in numerical simulation of metal forming process[J]. Comput Methods Appl Mech Engrg, 2002, 191(49): 5555-5578.
20. Zhang H W, Zhang X W, Chen J S. A new algorithm for numerical solution of dynamic elasticplastic hardening and softening problems[J]. Computers and Structures, 2003, 81(17): 1739-1749.
21. Zhang H W, Schrefler B A. Gradient-dependent plasticity model and dynamic strain localization analysis of saturated and partially saturated porous media: one dimensional model[J]. European Journal of Solid Mechanics A/Solids, 2000, 19(3): 503-524.