A Green-function-based multiscale method for uncertainty quantification of finite body random heterogeneous materials

Computers and Structures

Volumn 87, Issue 21-22, 2009, Pages 1416-1426

  Xu, X Frank ^a   Chen, Xi ^a   Shen, Lihua ^a,b  

^a STEVENS INSTITUTE OF TECHNOLOGY   (United States)

^b CAPITAL NORMAL UNIVERSITY   (China)

Author keywords

Boundary value problems; Green function based multiscale method; Random heterogeneous materials; Scale coupling; Uncertainty quantification

Indexed keywords

CLASSICAL CONTINUUM THEORY; COUPLING PROBLEM; COUPLING SYSTEMS; DETERMINISTIC PROBLEMS; ENGINEERING PRACTICES; FAILURE PROBLEMS; FINE-SCALE MICROSTRUCTURES; FINITE BODIES; GENERALIZED VARIATIONAL PRINCIPLE; GREEN-FUNCTION-BASED MULTISCALE METHOD; LARGE-SCALE SEPARATION; MULTISCALE METHOD; NUMERICAL EXAMPLE; RANDOM HETEROGENEOUS MATERIALS; RANDOM MICROSTRUCTURE; SCALE-COUPLING; UNCERTAINTY QUANTIFICATION; UNCERTAINTY QUANTIFICATIONS;

BOUNDARY VALUE PROBLEMS; CONTINUUM MECHANICS; MICROSTRUCTURE; VARIATIONAL TECHNIQUES;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 70349504357     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2009.05.009     Document Type: Article

References (29)

1. Glimm J., and Sharp D. Stochastic partial differential equations: selected applications in continuum physics. In: Carmona R.A., and Rozovskii B.L. (Eds). Stochastic partial differential equations: six perspectives. Mathematical surveys and monographs (1998), American Mathematical Society, Providence 03-44
2. Coveney P.V. Self-organization and complexity: a new age for theory, computation and experiment. Phil Trans: Math Phys Eng Sci (Ser A) 361 1807 (2003) 1057-1079
3. Bensoussan A., Lions J.L., and Papanicolaou G. Asymptotic analysis for periodic structures (1978), Amsterdam, North-Holland
4. Sanchez-Palencia E. Nonhomogeneous media and vibration theory. Lecture notes in physics vol. 127 (1980), Springer, Berlin
5. c, Physics: Long Island City, NY, vol. 2; 1966. p. 263.
6. Wilson K.G. The renormalization group: critical phenomena and the Kondo problem. Rev. Mod. Phys. 47 4 (1975) 773
7. Brant J. Multiscale solvers and systematic upscaling in computational physics. Comput Phys Commun 169 1-3 (2005) 438-441
8. E W, Engquist B, Li X, Ren W, Vanden-Eijnden E. Heterogeneous. Multiscale methods: a review. Comput Phys Commun 2007;2(3):367-450.
9. Weibull W. A statistical distribution function of wide applicability. J Appl Mech 18 (1951) 293-297
10. Bazant Z.P., Pang S.-D., Voechovsky M., and Novak D. Energetic-statistical size effect simulated by SFEM with stratified sampling and crack band model. Int J Numer Methods Eng 71 11 (2007) 1297-1320
11. Sornett D. Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes, and human birth. PNAS 99 3 (2002) 2522-2529
12. Bathe K. On reliable finite element methods for extreme loading conditions. NATO Sec Sci Ser C: Environ Sec (2007) 71-102
13. Xu X.F. A multiscale stochastic finite element method on elliptic problems involving uncertainties. Comput Methods Appl Mech Eng 196 25-28 (2007) 2723-2736
14. Xu XF. Generalized variational principles for uncertainty quantification of boundary value problems of random heterogeneous materials. ASCE J Eng Mech, in press.
15. Xu X.F., and Chen X. Stochastic homogenization of random multi-phase composites and size quantification of representative volume element. Mech Mater 41 2 (2009) 174-186
16. Charmpis D.C., Schueller G.I., and Pellissetti M.F. The need for linking micromechaincs of materials with stochastic finite elements: a challenge for material science. Comput Mater Sci 41 (2007) 27-37
17. Maute K., and Frangopol D.M. Reliability-based design of MEMS mechanisms by topology optimization. Comput Struct 81 8-11 (2003) 813-824
18. Atkinson K. The numerical solution of integral equations of the second kind (1997), Cambridge University Press, Cambridge
19. Ghanem R.G., and Spanos P.D. Stochastic finite element: a spectral approach (1991), Springer-Verlag, New York
20. Luciano R., and Willis J. FE analysis of stress and strain fields in finite random composite bodies. J Mech Phys Solids 53 (2005) 1505-1522
21. Eyre D.J., and Milton G.W. A fast numerical scheme for computing the response of composites using grid refinement. Eur Phys J AP 6 (1999) 41-47
22. Xu X.F., and Graham-Brady L. Computational stochastic homogenization of random media elliptic problems using Fourier Galerkin method. Finite Elem Anal Des (Special issue on 17th Melosh Competition) 42 7 (2006) 613-622
23. Hashin Z., and Shtrikman S. A variational approach to the theory of the elastic behavior of multiphase materials. J Mech Phys Solids 11 (1962) 127-140
24. Romkes A., Oden J.T., and Vemaganti K. Multi-scale goal-oriented adaptive modeling of random heterogeneous materials. Mech Mater 38 8-10 (2006) 859-872
25. Ganapathysubramanian B., and Zabaras N. A stochastic multiscale framework for modeling flow through random heterogeneous porous media. J Comput Phys 228 2 (2009) 591-618
26. Nolen J., Papanicolaou G., and Pironneau O. A framework for adaptive multiscale methods for elliptic problems. Multiscale modeling and simulation 7 1 (2008) 171-196
27. Masud A., and Franca L.P. A hierarchical multiscale framework for problems with multiscale source terms. Comput Methods Appl Mech Eng 197 33-40 (2008) 2692-2700
28. Miehe C., and Bayreuther C.G. On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers. Int J Numer Methods Eng 71 10 (2007) 1135-1180
29. Acharjee S., and Zabaras N. A non-intrusive stochastic Galerkin approach for modeling uncertainty propagation in deformation processes. Comput Struct 85 5-6 (2007) 244-254