Perturbation based stochastic finite element method for homogenization of two-phase elastic composites

Computers and Structures

Volumn 78, Issue 6, 2000, Pages 811-826

  Kamiński, Marcin ^a   Kleiber, Michal ^b  

^a Rice University   (United States)

^b INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; ELASTIC MODULI; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MONTE CARLO METHODS; PERTURBATION TECHNIQUES; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; RANDOM PROCESSES; STRUCTURAL ANALYSIS; TENSORS;

HOMOGENIZATION METHODS; STOCHASTIC FINITE ELEMENTS; STOCHASTIC PERTURBATION METHODS;

COMPOSITE STRUCTURES;

EID: 0342955063     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(00)00116-4     Document Type: Article

References (39)

1. Arminjon M. Limit distributions of the states and homogenization in random media. Acta Mech. 88:1991;27-59.
2. Avellaneda M. Optimal bounds and microgeometries for elastic two-phase composites. SIAM J Appl Math. 47:1987;1216-1228.
3. Bahei-El-Din Y.A. Finite element analysis of viscoplastic composite materials and structures. Int J Comp Mat Struct. 3:1996;1-28.
4. Bathe KJ. Finite element procedures. Engelwood Cliffs, NJ: Prentice-Hall; 1996.
5. Bendat JS, Piersol AG. Random data: analysis and measurement procedures. New York: Wiley; 1971.
6. Beran MJ. Application of statistical theories for the determination of thermal, electrical and magnetic properties of heterogeneous materials. In: Broutman LJ, Kroch RH, editors, Mechanics of composite materials. New York: Academic Press; 1974.
7. Boswell MT, et al. The art of computer generation of random variables. In: Rao CR, editor, Handbook of statistics, Computational Statistics, vol. 9. Amsterdam: Elsevier; 1991. p. 662-721.
8. Braides A., Piat V.C. Remarks on the homogenization of connected media. Nonlinear Anal Theor Meth Appl. 22(4):1994;391-407.
9. Castaneda PP, Suquet PM. Nonlinear Composites. In: Van Der Giessen E, Wu TY, editors, Advances in Applied Mechanics, vol. 34. Academic Press, 1998.
10. Chang S., Chao S.J., Chang Y. Estimates of elastic moduli for granular material with anisotropic random packing structure. Int J Solids Struct. 32:1995;1989-2008.
11. Christensen RM. Mechanics of Composite Materials. New York: Wiley-Interscience; 1979.
12. Cruz M.E., Patera A.T. A parallel Monte-Carlo finite element procedure for the analysis of multicomponent media. Int J Num Meth Engng. 38:1995;1087-1121.
13. Fish J, editor. Computational advances in modeling composites and heterogeneous materials. Comput Meth Appl Mech Engng 1999;172.
14. 2 and applications. Arch Rational Mech Anal. 131:1995;305-333.
15. Frantziskonis G, Renaudin P, Breysse D. Heterogeneous solids. Part I: analytical and numerical 1-D results on boundary effects. Eur J Mech A/Solids 1997;16(3):409-23.
16. Ghanem R.G., Spanos P.D. Spectral techniques for stochastic finite elements. Arch Comput Meth Engng. 4(1):1997;63-100.
17. Ghosh S., Lee K., Moorthy S. Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element method. Int J Solids Struct. 32:1995;27-62.
18. Grigoriu M. Stochastic mechanics. Int J Solids Struct. 37:2000;197-214.
19. Gutierrez M.A., de Borst R. Numerical analysis of localization using a viscoplastic regularization: influence of stochastic materials defects. Int J Num Meth Engng. 44:1999;1823-1841.
20. Hashin Z., Shtrikman S. A variational approach to the theory of the elastic behavior of multiphase materials. J Mech Phys Sol. 11:1963;127-140.
21. Hurtado J.E., Barbat A.H. Monte-Carlo techniques in computational stochastic mechanics. Arch Comput Meth Engng. 5(1):1998;3-30.
22. Kalamkarov AL, Kolpakov AG. Analysis, Design and Optimization of Composite Structures. New York: Wiley; 1997.
23. Kaminski M. Homogenization in random elastic media. Comput Ass Mech Engng Sci. 3(1):1996;9-22.
24. Kaminski M. Homogenized properties of n-component composite materials. Int J Engng Sci. 38(4):2000;405-427.
25. Kaminski M., Kleiber M. Numerical homogenization of n-phase composites including stochastic interface defects. Int J Num Meth Engng. 47:2000;1001-1025.
26. Kaminski M, Kleiber M. Stochastic finite element method in random non-homogeneous media. In: Desideri JA, et al., editor, Numerical Methods in Engineering'96. New York: Wiley; 1996, p. 35-41.
27. Kaminski M., Kleiber M. Stochastic structural interface defects in composite materials. Int J Solids Struct. 33(20-22):1996;3035-3056.
28. Kleiber M, Hien TD. The stochastic finite element method. Basic perturbation technique and computer implementation. New York: Wiley; 1992.
29. Kohn RV. Recent progress in the mathematical modeling of composite materials. In: Sih G, et al., editors. Composite materials response. Constitutive relations and damage mechanisms. Amsterdam: Elsevier; 1988. p. 155-77.
30. Kröner E. Effective moduli of random elastic media- unified calculation of bounds and self-consistent values. Mech Res Comm. 4:1977;389-393.
31. Ostoja-Starzewski M, Jasiuk I. Micromechanics of random media. Proc Symp 'Micromechanics of Random Media' MEET'N'93. Appl Mech Rev 1994;47(1).
32. Pedersen J, editor. Optimal design with advanced materials. Amsterdam: Elsevier; 1993.
33. Renaudin P, Breysse D, Frantziskonis G. Heterogeneous solids. Part II: numerical 2-D results on boundary and other relevant phenomena. Eur J Mech A/Solids 1997;16(3):425-43.
34. Sab K. On the homogenization and the simulation of random materials. Eur J Mech Sol. 11:1992;585-607.
35. Schellekens JCJ. Computational strategies for composite structures. Delft University of Technology, 1990.
36. Suquet P. A dual method in homogenization: application to elastic media. J Mech Theor Appl 1992;79-98.
37. Taliercio A, Sagramoso P. Uniaxial strength of polymeric-matrix fibrous composites predicted through a homogenization approach. Int J Solids Struct 1995;32(14):2095-123.
38. Terada K, Miura T, Kikuchi N. Digital image-based modeling applied to the homogenization analysis of composite materials. Comput Mech 1997;20:331-46.
39. Vanmarcke E. Random fields. Analysis and synthesis. Cambridge, MA: MIT Press; 1983.