Stochastic homogenization of random elastic multi-phase composites and size quantification of representative volume element

Mechanics of Materials

Volumn 41, Issue 2, 2009, Pages 174-186

  Xu, X Frank ^a   Chen, Xi ^a  

^a STEVENS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AGGLOMERATION; AGGREGATES; BOUNDARY VALUE PROBLEMS; BUILDING MATERIALS; CONCRETE AGGREGATES; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; HOMOGENIZATION METHOD; INITIAL VALUE PROBLEMS; LEARNING SYSTEMS; SIZE DETERMINATION; THREE DIMENSIONAL; VARIATIONAL TECHNIQUES; VOLUME MEASUREMENT;

BOUNDARY VALUES; COMPUTATIONAL APPROACHES; CONCRETE MATERIALS; DEGREES OF FREEDOMS; DIMENSION REDUCTIONS; DIMENSIONAL PROBLEMS; EFFECTIVE PROPERTIES; ENERGY BOUNDS; ENGINEERING PRACTICES; FINITE ELEMENTS; FINITE-ELEMENT MODELING; GENERALIZED VARIATIONAL PRINCIPLES; HETEROGENEOUS MATERIALS; HETEROGENEOUS MEDIUMS; HOMOGENIZATION PROBLEMS; HOMOGENIZATION TECHNIQUES; MATERIAL CONSTANTS; MINIMUM SIZES; NUMERICAL CHARACTERIZATIONS; PHASE COMPOSITES; RANDOM HETEROGENEOUS MATERIALS; REPRESENTATIVE VOLUME ELEMENTS; SCALE SEPARATIONS; SIZE DEPENDENTS; SIZE EFFECTS; SMALL SCALES; STOCHASTIC BOUNDS; TWO-DIMENSIONAL PROBLEMS; UNCERTAINTY QUANTIFICATIONS;

SIZE SEPARATION;

EID: 56749163389     PISSN: 01676636     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechmat.2008.09.002     Document Type: Article

References (18)

1. Bensoussan A., Lions J.L., and Papanicolaou G. Asymptotic Analysis for Periodic Structures (1978), North-Holland, Amsterdam
2. Berryman J.G. Bounds and estimates for transport coefficients of random and porous media with high contrasts. J. Appl. Phys. 97 (2005) 063504
3. Cho S.W., and Chasiotis I. Elastic properties and representative volume element of polycrystalline silicon for MEMS. Exp. Mech. 47 (2007) 1741-2765
4. Drugan W.J., and Willis J.R. A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. J. Mech. Phys. Solids 44 (1996) 497-524
5. Graham-Brady L., and Xu X.F. Stochastic morphological modeling of random multiphase materials. J. Appl. Mech. 75 (2008) 061001
6. 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
7. Jiang B., and Weng G.J. A composite model for the grain-size dependence of yield stress of nano-grained materials. Metall. Mater. Trans. 34A (2003) 765-772
8. Liu C. On the minimum size of representative volume element: an experimental investigation. Exp. Mech. 45 (2005) 238-243
9. Milton G.W. The theory of composites (2002), Cambridge University Press
10. Nemat-Nasser S., and Hori M. Micromechanics: Overall Properties of Heterogeneous Materials (1999), North-Holland, Amsterdam
11. Ostoja-Starzewski M. Microstructural Randomness and Scaling in Mechanics of Materials (2008), Chapman & Hall/CRC
12. Ostoja-Starzewski M., Du X., Khisaeva Z., and Li W. Comparisons of the size of representative volume element in elastic, plastic, thermoelastic, and permeable random microstructures. Int. J. Multiscale Comput. Eng. 5 2 (2007) 73-82
13. Ren Z.Y., and Zheng Q.S. A quantitative study of minimum sizes of representative volume elements of cubic polycrystals - numerical experiments. J. Mech. Phys. Solids 50 (2002) 881-893
14. Xu X.F. A multiscale stochastic finite element method on elliptic problems involving uncertainties. Comput. Methods Appl. Mech. Eng. 196 (2007) 2723-2736
15. Xu, X.F., submitted for publication. Generalized variational principles for uncertainty quantification of boundary value problems of random heterogeneous materials.
16. Xu, X.F., 2008, unpublished.
17. Xu X.F., and Graham-Brady L. A stochastic computation method for evaluation of global and local behavior of random elastic media. Comput. Methods Appl. Mech. Eng. 194 (2005) 4362-4385
18. Xu X.F., and Graham-Brady L. Computational stochastic homogenization of random media elliptic problems using Fourier Galerkin method. Finite Elements Anal. Design (Special issue on 17th Melosh Competition) 42 7 (2006) 613-622