Sensitivity and randomness in homogenization of periodic fiber-reinforced composites via the response function method

International Journal of Solids and Structures

Volumn 46, Issue 3-4, 2009, Pages 923-937

  Kamiński, Marcin ^a  

^a LODZ UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Finite element method; Homogenization technique; Periodic composites; Response function method; Sensitivity analysis; Stochastic perturbation technique; Symbolic analysis

Indexed keywords

CARBON FIBER REINFORCED PLASTICS; ELASTICITY; FINITE ELEMENT METHOD; FUNCTIONS; HOMOGENIZATION METHOD; NUMERICAL ANALYSIS; NUMERICAL METHODS; PERTURBATION TECHNIQUES; PROBABILITY; PROBABILITY DENSITY FUNCTION; SENSITIVITY ANALYSIS; TENSORS;

HOMOGENIZATION TECHNIQUE; PERIODIC COMPOSITES; RESPONSE FUNCTION METHOD; STOCHASTIC PERTURBATION TECHNIQUE; SYMBOLIC ANALYSIS;

METHOD OF MOMENTS;

EID: 58149333408     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2008.10.003     Document Type: Article

References (46)

1. Abell, M.L., Braselton, A.P., 1994. The MAPLE V Handbook, AP Professional, Boston.
2. Bathe K.J. Finite Element Procedures (1996), Prentice-Hall, Englewood Cliffs, NJ
3. Bendat J.S., and Piersol A.G. Random Data: Analysis and Measurement Procedures (1971), Wiley, New York
4. Bensoussan, A., Lions, J.L., Papanicolaou, G., 1978. Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam.
5. Bhangale R.K., and Ganesan N. Static analysis of simply supported functionally graded and layered magneto-electro-elastic plates. International Journal of Solids and Structures 43 (2006) 3230-3253
6. Castaneda P.P., and Suquet P.M. Nonlinear Composites. In: Van Der Giessen E., and Wu T.Y. (Eds). Advances in Applied Mechanics vol. 34 (1998), Academic Press, New York
7. Chellappa S., Diaz A.R., and Bendsoe M. Layout optimization of structures with finite-sized features using multiresolution analysis. Structural and Multidisciplinary Optimization 26 (2004) 77-91
8. Christensen R.M. Mechanics of Composite Materials (1979), Wiley, New York
9. Clayton J.D., and Chung P.W. An atomistic-to-continuum framework for nonlinear crystal mechanics based on asymptotic homogenization. Journal of Mechanics and Physics of Solids 54 (2006) 1604-1639
10. Cruz M.E., and Patera A.T. A parallel Monte-Carlo finite element procedure for the analysis of multicomponent media. International Journal of Numerical Methods in Engineering 38 (1995) 1087-1121
11. Feller W. An Introduction to Probability Theory and Its Applications (1965), Wiley, New York
12. Fish J., and Ghouali A. Multiscale analytical sensitivity analysis for composite materials. International Journal of Numerical Methods in Engineering 50 (2001) 1501-1520
13. Florence C., and Sab K. A rigorous homogenization method for the determination of the overall ultimate strength of periodic discrete media and an application to general hexagonal lattices of beams. European Journal of Mechanics A/Solids 25 (2006) 72-97
14. Friebel C., Doghri I., and Legat V. General mean-field homogenization schemes for viscoelastic composites containing multiple phases of coated inclusions. International Journal of Solids and Structures 43 (2006) 2513-2541
15. Ghanem R.G., and Spanos P.D. Spectral techniques for stochastic finite elements. Archives of Computer Methods in Engineering 4 1 (1997) 63-100
16. Gitman I.M., Gitman M.B., and Askes H. Quantification of stochastically stable representative volumes for random heterogeneous media. Archive of Applied Mechanics 75 (2006) 79-92
17. Haftka R.T., and Gürdal Z. Elements of Structural Optimization (1992), Kluwer Academic Publications, Dordrecht
18. Idiart M.I., et al. Macroscopic behavior and field fluctuations in viscoplastic composites: second order estimates versus full-field simulations. Journal of Mechanics and Physics of Solids 54 (2006) 1029-1063
19. In: Jeulin D., and Ostoja-Starzewski M. (Eds). Mechanics of Random and Multiscale Structures. CISM Courses and Lectures vol. 430 (2001), Springer Wien, New York
20. Kamiński M. Multiscale homogenization of n-component composites with semi-elliptical stochastic interface defects. International Journal of Solids and Structures 42 11-12 (2005) 3590-3751
21. Kamiński M. Sensitivity studies for the effective characteristics of periodic multicomponent. International Journal of Engineering Science 44 11-12 (2006) 757-777
22. Kamiński M. Determination of sensitivity coefficients of the elastic effective properties for periodic fiber-reinforced composites using the response function method. Computational Materials Science 43 (2008) 829-841
23. Kanit T. Apparent and effective physical properties of heterogeneous materials: representativity of samples of two materials from food industry. Computer Methods in Applied Mechanics and Engineering 195 (2006) 3960-3982
24. Kleiber M., et al. Parameter Sensitivity in Nonlinear Mechanics (1997), Wiley, New York
25. Lefik M., and Schrefler B.A. 3-D finite element analysis of composite beams with parallel fibres, based on homogenization theory. Computational Mechanics 14 (1994) 2-15
26. Luciano R., and Willis J.R. Hashin-Shtrikman based FE analysis of the elastic behaviour of finite random composite bodies. International Journal of Fracture 137 (2006) 261-273
27. Lux J., et al. Macroscopic thermal properties of real fibrous materials: volume averaging method and 3D image analysis. International Journal of Heat and Mass Transfer 49 (2006) 1958-1973
28. Ma W., and Hu G. Influence of fiber's shape and size on overall elastoplastic property for micropolar composites. International Journal of Solids and Structures 43 (2006) 3025-3043
29. Markovic D., and Ibrahimbegovic A. Complementary energy based FE modeling of coupled elasto-plastic and damage behavior for continuum microstructure computations. Computer Methods in Applied Mechanics and Engineering 195 (2006) 5077-5093
30. Matache A.M., Babuska I., and Schwab C. Generalized p-FEM in homogenization. Numerische Mathematik 86 (2000) 319-375
31. Milton G. The Theory of Composites (2002), Cambridge University Press, Cambridge
32. Noor A.K., and Shah R.S. Effective thermoelastic and thermal properties of unidirectional fiber-reinforced composites and their sensitivity coefficients. Composite Structures 26 (1993) 7-23
33. Ponte Castañeda P., and Suquet P.M. Nonlinear composites. Advances in Applied Mechanics 34 (1998) 171-302
34. Rohan E., Cimrman R., and Lukes V. Numerical modeling and homogenized constitutive law of large deforming fluid saturated heterogeneous solids. Computers and Structures 84 (2006) 1095-1114
35. Samaey G., Kevrikidis I.G., and Roose D. Patch dynamics with buffers for homogenization problems. Journal of Computational Physics 213 (2006) 264-287
36. Sanchez-Palencia E. Non-homogeneous Media and Vibration Theory. Lecture Not. Phys. No. 127 (1980), Springer, Berlin
37. Sigmund O. Materials with prescribed constitutive parameters: an inverse homogenization problem. International Journal of Solids and Structures 31 (1994) 2313-2329
38. Song Y.S., and Youn J.R. Evaluation of effective thermal conductivity for carbon nanotube/polymer composites using control volume finite element method. Carbon 44 (2006) 710-717
39. Steeves C.A., and Fleck N.A. In-plane properties of composite laminates with through-thickness pin reinforcement. International Journal of Solids and Structures 43 (2006) 3197-3212
40. Vanmarcke E. Random Fields. Analysis and Synthesis (1983), MIT Press, Cambridge
41. Wang W.X., et al. New solution method for homogenization analysis and its application to the prediction of macroscopic elastic constants of materials with periodic microstructures. Computers and Structures 84 (2006) 991-1001
42. Xiu-Li G., and Melchers R.E. Effect of response surface parameter variation on structural reliability estimates. Structural Safety 23 (2002) 429-444
43. Xu X.F., and Graham-Brady L. A stochastic computational method for evaluation of global and local behavior of random elastic media. Computer Methods in Applied Mechanics and Engineering 194 (2005) 4362-4385
44. Zhang H., et al. Multiple spatial and temporal scales method for numerical simulation of non-classical heat conduction problems: one dimensional case. International Journal of Solids and Structures 42 (2005) 877-899
45. Zhang H.W., et al. Thermo-mechanical analysis of periodic multiphase materials by a multiscale asymptotic homogenization approach. International Journal of Numerical Methods in Engineering 69 1 (2007) 87-113
46. Zienkiewicz O.C., and Taylor R.L. Finite Element Method for Solid and Structural Mechanics. sixth ed. (2005), Elsevier, Amsterdam