Multiple scale computational model for damage in composite materials

Computer Methods in Applied Mechanics and Engineering

Volumn 172, Issue 1-4, 1999, Pages 175-201

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

^a Ohio State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041191199     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (43)

1. [1] A. Benssousan, J.L. Lions and G. Papanicoulau, Asymptotic Analysis for Periodic Structures (North Holland, Amsterdam, 1978).
2. [2] E. Sanchez-Palencia, Non-homogeneous media and vibration theory, Lecture Notes in Physics, Vol. 127 (Springer-Verlag, Berlin Heidelberg, 1980).
3. [3] V.Z. Parton and B.A. Kudryavtsev, Engineering Mechanics of Composite Structure (CRC Press, 1993).
4. [4] N.S. Bakhvalov and G.P. Panasenko, Homogenization in Periodic Media, Mathematical Problems of the Mechanics of Composite Materials (Nauka, Moscow, 1984).
5. [5] J. Fish and V. Betsky, Multigrid method for periodic heterogeneous media, part II: multiscale modeling and quality control in multidimensional case, Comput. Methods Appl. Mech. Engrg. 126 (1995) 17-38.
6. [6] J. Fish and A. Wagiman, Multiscale finite element method for a locally nonperiodic heterogeneous medium, Comput. Mech. 12 (1993) 164-180.
7. [7] 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.
8. [8] 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).
9. [9] J. Fish, K. Shek, M. Pandheeradi and M. S. Shephard, Computational plasticity for composite structures based on mathematical homogenization: theory and practice, Comput. Methods Appl. Mech. Engrg. 148 (1997) 53-73.
10. [10] J.M. Guedes, Nonlinear computational model for composite material using homogenization, Ph.D. Dissertation, University of Michigan, MI, 1990.
11. [11] C.-H. Cheng, Modeling of the elasto-plastic behavior for composite materials using homogenization method, Ph.D. Dissertation, University of Michigan, MI, 1992.
12. [12] F. Lene, Damage constitutive relations for composite materials, Engrg. Fract. Mech. 25(5) (1986) 713-728.
13. [13] F. Devries, H. Dumontet, G. Duvaut and F. Lene, Homogenization and damage for composite structures, Int. J. Numer. Methods Engrg. 27 (1989) 285-298.
14. [14] J. Fish, M. Pandheeradi and V. Belsky, An efficient multilevel solution scheme for large scale non-linear systems, Int. J. Numer. Methods Engrg. 38 (1995) 1597-1610.
15. [15] J. Fish, P. Nayak and M.H. Holmes, Microscale reduction error indicators and estimators for a periodic heterogeneous medium, Comput. Mech. 14 (1994).
16. [16] T.I. Zohdi, J.T. Oden and G.J. Rodin, Hierarchical modeling of heterogeneous bodies, TICAM Report, Vol. 96-21, The University of Texas, Austin, 1996.
17. [17] J.T. Oden and T.I. Zohdi, Analysis and adaptive modeling of highly heterogeneous elastic structures, TICAM Report, Vol. 96-56, The University of Texas, Austin, 1996.
18. [18] S. Moorthy and S. Ghosh, A Model for analysis of arbitrary composite and porous microstructures with Voronoi cell finite elements, Int. J. Numer. Methods Engrg. 39 (1996) 2363-2398.
19. [19] S. Moorthy and S. Ghosh, A Voronoi cell finite element model for particle cracking in composite materials, Comput. Methods Appl. Mech. Engrg. 151 (1998) 377-400.
20. [20] S. Ghosh, Z. Nowak and K. Lee, Quantitative characterization and modeling of composite microstructures by Voronoi cells, Acta Metall. Mater. 45(6) (1997) 2215-2234.
21. [21] S. Ghosh and Y. Liu, Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials, Int. J. Numer. Methods Engrg. 38 (1995) 1361-1398.
22. [22] S. Ghosh, K. Lee and S. Moorthy, Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model, Comput. Methods Appl. Mech. Engrg. 132 (1996) 63-116.
23. [23] 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.
24. [24] S. Ghosh and S. Moorthy, Particle fracture simulation in non-uniform microstructures of metal-matrix composites, Acta Mater. 46(3) (1998) 965-982.
25. [25] N.I. Muskhelishvili, Some Basic Problems in the Mathematical Theory of Elasticity (P. Nordhoff Ltd., 1961).
26. [26] S. Moorthy, The Voronoi cell finite element method for response and damage analysis of arbitrary heterogeneous media, Ph.D. Thesis, Ohio State University, 1997.
27. [27] W.H. Hunt, J.R. Brockenbrough and P.E. Magnusen, An Al-Si-Mg composite model system: Microstructural effects on deformation and damage evolution, Scripta Metall. Mater. 25 (1991) 15-20.
28. [28] W.H. Hunt, Microstructural damage processes in an aluminum matrix-silicon particle composite model, Ph.D. Thesis, Carnegie Mellon University, 1992.
29. [29] M.T. Kiser, F.W. Zok and D.S. Wilkinson, Plastic flow and fracture of a particulate metal matrix composite, Acta Metall. Mater. 9 (1996) 3465-3476.
30. [30] W.A. Curtin, In situ fiber strengths in ceramic-matrix composites from fracture mirrors, J. Am. Cer. Soc. 77 (1994) 1075-1078.
31. [31] M. Li, S. Ghosh, T.N. Rouns, H. Weiland, O. Richmond and W. Hunt, Serial sectioning method in the construction of 3-D microstructures for particle reinforced MMCs, Mater. Charac. 41(2-3) (1998) 81-95.
32. [32] A.L. Gurson, Continuum theory of ductile rupture by void nucleation and Growth-I, Yield criteria and flow rules for porous ductile media, J. Engrg. Mater. Technol. 99 (1977) 2-15.
33. [33] R. Becker, A. Needleman, O. Richmond and V. Tvergaard, Void growth and failure in notched bars, J. Mech. Phys. Solids, 36 (1989) 201-217.
34. [34] M. Xie and D. Adams, A plasticity model for unidirectional composite materials and its applications in modeling composite testing, Comput. Sci. Tech. 54 (1995) 11-21.
35. [35] R. Mahnken and E. Stein, Parameter identification for viscoplastic models based on analytical derivation of a least-square functional and stability investigations, Int. J. Plasticity 12(4) (1996) 451-479.
36. [36] K. Terada and N. Kikuchi, Nonlinear homogenization method for practical applications, in: S. Ghosh and M. Ostoja-Starzewski, eds., Computational Methods in Micromechanics, ASME AMD 212 (1995) 1-16.
37. [37] G.J. Dvorak, Transformation field analysis for inelastic composite materials, Proc. R. Soc. Lond, A 437 (1992) 311-327.
38. [38] G.J. Dvorak and Y. Benveniste, On transformation strains and uniform fields in multiphase elastic media, Proc. R. Soc. Lond. A 437 (1992) 291-310.
39. [39] R. Hill, The Mathematical Theory of Plasticity (Oxford Press, 1971).
40. [40] N. Aravas, On the numerical integration of a class of pressure-dependent plasticity model, Int. J. Numer. Methods Engrg. 24 (1987) 1395-1416.
41. [41] J.Z. Zhu and O.C. Zienkiewicz, Adaptive techniques in the finite element method, Comm. Appl. Numer. Methods 4 (1988) 197-204.
42. [42] R.J. Melosh and P.V. Marcal, An energy basis for mesh refinement of structural continua, Int. J. Numer. Methods Engrg. 11(7) (1977) 1083-1092.
43. [43] L. Demkowicz, Ph. Devloo and J.T. Oden, On an h type mesh refinement strategy based on a minimization of interpolation error, Comput. Methods Appl. Mech. Engrg. 3 (1985) 67-89.