Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model

Computer Methods in Applied Mechanics and Engineering

Volumn 132, Issue 1-2, 1996, Pages 63-116

  Ghosh, Somnath ^a   Lee, Kyunghoon ^a   Moorthy, Suresh ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; ELASTOPLASTICITY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MICROSTRUCTURE; POROUS MATERIALS;

ASYMPTOTIC HOMOGENIZATION THEORY; SOFTWARE PACKAGE ABAQUS; VORONOI CELL FINITE ELEMENT MODEL (VCFEM);

COMPOSITE MATERIALS;

EID: 0030143667     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/0045-7825(95)00974-4     Document Type: Article

References (42)

1. T. Christman, A. Needleman and S. Suresh, An experimental and numerical study of deformation in metal-ceramic composites, Acta Metall. Mater. 37 (1989) 3029-3050.
2. Z. Hashin and S. Strikman, A variational approach to the theory of the elastic behavior of multiphase materials, J. Mech. Phys. Solids 11 (1963) 127-140.
3. S. Nemat-Nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials (North-Holland, Amsterdam, 1993).
4. H.S. Chen and A. Acrivos, The effective elastic moduli of composite materials containing spherical inclusions at non-dilute concentrations, Int. J. Solids Struct. 14 (1978) 349-364.
5. R. Hill, A self consistent mechanics of composite materials, J. Mech. Phys. Solids 13 (1965) 213-222.
6. B. Budiansky, On the elastic modulii of some heterogeneous materials, J. Mech. Phys. Solids 13 (1965) 223-227.
7. R.M. Christensen and K.H. Lo, Solutions for effective shear properties in three phase sphere and cylinder models, J. Mech. Phys. Solids 27 (1979) 315-330.
8. G.P. Tandon and G.J. Weng, A theory of particle reinforced plasticity, J. Appl. Mech. 55 (1988) 126-135.
9. G. Dvorak and Y.A. Bahei-el-din, Plasticity analysis of fibrous composites, J. Appl. Mech. 49 (1982) 327-335.
10. G. Dvorak and Y.A. Bahei-el-din, A bimodal plasticity theory of fibrous composite materials, Acta Mech. 69 (1987) 219-241.
11. M. Paley and J. Aboudi, Micromechanical analysis of composites by the generalized cell model, Mech. Mater. 14 (1992) 127-139.
12. S. Nemat-Nasser, T. Iwakuma and M. Hejazi, On composites with periodic structure, Mech. Mater. 1 (1982) 239-267.
13. G. Bao, J.W. Hutchinson and R.M. McMeeking. Plastic reinforcement of ductile matrices against plastic flow and creep, Acta Metallur. Mater. 39 (1991) 1871-1882.
14. V. Tvergaard Analysis of tensile properties for a whisker-reinforced metal matrix composite, Acta Metall. Mater. 38 (1990) 185-194.
15. A. Benssousan, J.L. Lions and G. Papanicoulau, Asymptotic Analysis for Periodic Structures (North Holland, Amsterdam, 1978).
16. E. Sanchez-Palencia, Non-homogeneous media and vibration theory, Lecture notes in Physics, 127 (Springer-Verlag, Berlin Heidelberg, 1980).
17. A. Toledano and H. Murakami, A high order mixture model for periodic particulate composites, Int. J. Solids. Struct. 23(7) (1987) 989-1002.
18. J.M. Guedes and N. Kikuchi, Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods, Comput. Methods Appl. Mech. Engrg. 83 (1991) 143-198.
19. P. Suquet, Local and global aspects in the mathematical theory of plasticity, in: A. Sawczuk and G. Bianchi, eds., Plasticity Today - Modeling Methods and Applications (Elsevier, London, 1985).
20. J.M. Guedes, Non-linear computational model for composite material using homogenization, Ph.D. Dissertation, University of Michigan, MI, 1990.
21. C.-H. Cheng, Modeling of the elasto-plastic behavior for composite materials using homogenization method, Ph.D. Dissertation, University of Michigan, MI, 1992.
22. V.Z. Parton and B.A. Kudryavtsev, Engineering Mechanics of Composite Structure (CRC Press, Boca Raton, FL, 1993).
23. S.J. Hollister and N. Kikuchi, A comparison of homogenization and standard mechanics analyses for periodic porous composites, Comput. Mech. 10 (1992) 73-95.
24. N.S. Bakhvalov and G.P. Panasenko, Homogenization in periodic media. Mathematical Problems of the Mechanics of Composite Materials, Nauka, Moscow, 1984.
25. F. Devries, H. Dumontet. G. Duvant and F. Lene, Homogenization of damage for composite structures, Int. J. Numer. Methods Engrg. 27 (1989) 285-298.
26. S. Ghosh and S. Moorthy, Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi cell finite element method, Comput. Methods Appl. Mech. Engrg. 121 (1995) 373-409.
27. S. Moorthy and S. Ghosh, A model for analysis of arbitrary composite and porous microstructures with Voronoi cell finite elements, Int. J. Numer. Mech. Engrg., in press.
28. S. Ghosh, K. Lee and S. Moorthy, Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element method, Int. J. Solids Struct. 32(1) (1995) 27-62.
29. S. Ghosh and Y. Liu, Voronoi cell finite element method for micropolar thermo-elastic heterogeneous materials, Int. J. Numer. Methods Engrg. 38(8) (1995) 1361-1398.
30. S. Ghosh and S.N. Mukhopadhyay, A two dimensional automatic mesh generator for finite element analysis of random composites, Comput. Struct. 41 (1991) 245-256.
31. ABAQUS/Standard User's Manual, Version 5.4 Hibbit Karlsson and Sorensen Inc., 1994.
32. P. Suquet, Elements of homogenization theory for inelastic solid mechanics, in: E. Sanchez-Palencia and A. Zaoui, eds., Homogenization Techniques for Composite Media (Springer-Verlag, New York, 1987) 194-278.
33. T.H.H. Pian, Derivation of element stiffness matrices by assumed stress distribution, AIAA J. 2 (1964) 1333-1336.
34. S.N. Atluri, On the hybrid finite element model for incremental analysis of large deformation problems, Int. J. Solids Struct. 9 (1973) 1177-1191.
35. S.N. Atluri, On some new general and complimentary energy theorems for the rate problems in finite strain, classical elastoplasticity, J. Struct. Mech. 8(1) (1980) 61-92.
36. P. Tong, T.H.H. Pian and S.J. Lasry, A hybrid-element approach to crack problems in plane elasticity, Int. J. Numer. Methods Engrg. 7 (1973) 197-308.
37. R. Piltner, Special finite elements with holes and internal cracks, Int. J. Numer. Methods Engrg. 21 (1973) 197-308.
38. V. Tvergaard, Influence of voids on shear band instability under plane strain conditions, Int. J. Fracture 17 (1981) 389-407.
39. V. Tvergaard, Material failure by void coalescence in localized shear bands, Int. J. Solids Struct. 18 (1982) 659-672.
40. N. Aravas, On the numerical integration of a class of pressure-dependent plasticity models, Int. J. Numer. Methods Engrg. 24 (1987) 1395-1416.
41. Y.H. Zhao and G.J. Weng. Theory of plasticity for inclusion and fiber-reinforced composite in: G.J. Weng, M. Taya and H. Abe, eds., Micromechanics and Inhomogeneity, The Toshio Mura Anniversary Volume (Springer-Verlag, Berlin, 1989) 599-622.
42. D.F. Adams, Inelastic analysis of a unidirectional composite subjected to transverse normal loading, J. Comput. Mater. 4 (1970) 310-328.