Mesoscale probabilistic models for the elasticity tensor of fiber reinforced composites: Experimental identification and numerical aspects

Mechanics of Materials

Volumn 41, Issue 12, 2009, Pages 1309-1322

  Guilleminot, Johann ^a   Soize, Christian ^a   Kondo, Djimedo ^b  

^a Université Paris Est Créteil   (France)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPIC MICROSTRUCTURES; CHAOS COEFFICIENTS; ELASTICITY TENSOR; EXPERIMENTAL IDENTIFICATION; FIBER REINFORCED COMPOSITES; IDENTIFICATION STRATEGIES; MESOSCALE; MESOSCOPICS; MICRO-MECHANICAL; MONTE CARLO NUMERICAL SIMULATIONS; NON DESTRUCTIVE; NUMERICAL ASPECTS; PARAMETRIC ANALYSIS; PROBABILISTIC MODELS; RANDOM FIELDS; REINFORCED COMPOSITES; STOCHASTIC REPRESENTATIONS;

COMPUTER SIMULATION; ELASTICITY; MICROSTRUCTURE; TESTING; ULTRASONIC TESTING;

TENSORS;

EID: 70349789075     PISSN: 01676636     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechmat.2009.08.004     Document Type: Article

References (27)

1. Baxter S.C., Hossain M.I., and Graham L.L. Micromechanics based random material property fields for particulate reinforced composites. Int. J. Solids Struct. 38 (2001) 9209-9220
2. Desceliers C., Ghanem R., and Soize C. Maximum likelihood estimation of stochastic chaos representations from experimental data. Int. J. Numer. Methods Eng. 66 (2006) 978-1001
3. Ghanem R., and Spanos P. Stochastic Finite Elements: A Spectral Approach (1991), Springer, New-York
4. Graham L.L., Arwadea S.R., Corrb D.J., Gutierrez M.A., Breyssed D., Grigoriu M., and Zabaras N. Probability and materials. from nano- to macro-scale: a summary. Prob. Eng. Mech. 21 3 (2006) 193-199
5. Graham L.L., and Baxter S.C. Simulation of local material properties based on moving-window GMC. Prob. Eng. Mech. 16 (2001) 295-305
6. Guilleminot J., Soize C., Kondo D., and Binetruy C. Theoretical framework and experimental procedure for modelling mesoscopic volume fraction stochastic fluctuations in fiber reinforced composites. Int. J. Solids Struct. 45 (2008) 5567-5583
7. Huet C. Application of variational concepts to size effects in elastic heterogeneous bodies. J. Mech. Phys. Mater. 38 6 (1990) 813-841
8. Jaynes E.T. Information theory and statistical mechanics. Phys. Rev. 106 4 (1957) 620-630
9. Jaynes E.T. Information theory and statistical mechanics. Phys. Rev. 108 2 (1957) 171-190
10. Jeulin D. Morphological characterization and models of random structures. Homogenization in Mechanics of Materials (2009), ISTE Ltd. and John Wiley & Sons
11. Lewis R.M., and Torczon V. Pattern search algorithms for bound constrained minimization. SIAM J. Optim. 9 4 (1999) 1082-1099
12. Lewis R.M., and Torczon V. A globally convergent augmented lagrangian pattern search algorithm for optimization with general constraints and simple bounds. SIAM J. Optim. 12 4 (2002) 1075-1089
13. Loève M. Probability Theory. fourth ed. (1977), Springer Verlag, New-York
14. Ostoja-Starzewski M. Microstructural Randomness and Scaling in Mechanics of Materials (2008), Chapman & Hall-CRC-Taylor & Francis
15. Poirion F., and Soize C. Numerical methods and mathematical aspects for simulation of homogeneous and nonhomogeneous gaussian vector fields. In: KrTe W., and Wedig W. (Eds). Probabilistic Methods in Applied Physics, Lecture Notes in Physics (1995), Springer-Verlag, Berlin, Heidelberg 17-53
16. Sab K. On the homogenization and the simulation of random materials. Eur. J. Mech. A/Solids 11 5 (1992) 585-607
17. Serfling R.J. Approximation Theorems of Mathematical Statistics (1980), John Wiley & Sons
18. Serra J. Image Analysis and Mathematical Morphology (1982), Academic Press, London
19. Shannon C.E. A mathematical theory of communication. Bell Syst. Tech. J. 27 (1948) 379-423 pp. 623-659
20. Shinozuka M. Simulations of multivariate and multidimensional random processes. J. Acoust. Soc. Amer. 39 1 (1971) 357-367
21. Silverman B.W. Density Estimation for Statistics and Data Analysis (1986), Chapman & Hall CRC
22. Soize C. Non-gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators. Comput. Methods Appl. Mech. Eng. 195 (2006) 26-64
23. Soize C. Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size. Prob. Eng. Mech. 23 (2008) 307-323
24. Soize C., and Ghanem R. Physical systems with random uncertainties: chaos representations with arbitrary probability measure. SIAM J. Sci. Comput. 26 2 (2004) 395-410
25. Torquato S. Random Heterogeneous Materials: Microstructure and Macroscopic Properties (2002), Springer, New-York
26. Wiener N. The homogeneous chaos. Amer. J. Math. 60 (1938) 897-936
27. Xu X.F., and Chen X. Stochastic homogenization of random elastic multi-phase composites and size quantification of representative volume element. Mech. Mater. 41 (2009) 174-186