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NUMERICAL STUDY OF THE SIZE OF REPRESENTATIVE VOLUME ELEMENT FOR LINEAR ELASTICITY PROBLEM Cover

NUMERICAL STUDY OF THE SIZE OF REPRESENTATIVE VOLUME ELEMENT FOR LINEAR ELASTICITY PROBLEM

Open Access
|Feb 2014

References

  1. [1] BERAN M.J., Statistical Continuum Theories, Monographs in Statistical Physics, Interscience Publishers, 1968.10.1119/1.1974326
  2. [2] FELLER W., An Introduction to Probability Theory and its Applications, Vol. I, 2nd Edition, John Wiley and Sons, N.Y., 1961.
  3. [3] GITMAN I.M., ASKES H., SLUYS L.J., Representative volume: existence and size determination, Eng. Fract. Mech., Vol. 74, 2007, 2518-2534.10.1016/j.engfracmech.2006.12.021
  4. [4] GRAHAM S., YANG N., Representative volumes of materials based on microstructural statistics, Scripta Materialia, Vol. 48, 2003, 269-274.10.1016/S1359-6462(02)00362-7
  5. [5] GRUFMAN C., FERNAND E., Determining a representative volume element capturing the morphology of fibre reinforced polymer composites, Compos. Sci. Technol., Vol. 67, 2007, 766-775.10.1016/j.compscitech.2006.04.004
  6. [6] GUSEV A., Representative volume element size for elastic composites: a numerical study, J. Mech.Phys. Solids, Vol. 45, 1997, 1449-1459.10.1016/S0022-5096(97)00016-1
  7. [7] JANKE W., Pseudo random number: generation and quality checks, Lecture Notes John von Neumann Institute for Computing, Vol. 10, 2002, 447.
  8. [8] KANIT T., FOREST S., GALLIET I., MOUNOURY V., JEULIN D., Determination of the size of the representative volume element for random composites: statistical and numerical approach, Int. J. Solids.Struct., Vol. 40, 2003, 3647.
  9. [9] KIRKPATRICK S., GELATT C.D., VECCHI M.P., Optimization by simulated annealing, Science, Vol. 220, 1983, 671-680.10.1126/science.220.4598.671
  10. [10] LU B., TORQUATO S., Lineal-path function for random heterogeneous materials, Phys. Rev. A, 1992, Vol. 45 (2), 922-929.10.1103/PhysRevA.45.922
  11. [11] Mathematica: Wolfram Mathematica Tutorial Collection, 2008.
  12. [12] POVIRK G.L., Incorporation of microstructural information into model of two-phase materials, Acta Metal. Mater., Vol. 43 (8), 1995, 3199-3206.10.1016/0956-7151(94)00487-3
  13. [13] QUINTANILLA J., TORQUATO S., Lineal measures of clustering in overlapping particle systems, Phys.Rev. E, Vol. 54 (4), 1996, 4027-4036.10.1103/PhysRevE.54.4027
  14. [14] RÓŻAŃSKI A., Random composites: representativity, minimum RVE size, effective transport properties, PhD dissertation, USTL, LML (UMR CNRS 8107), No. 40444, 2010.
  15. [15] RÓŻAŃSKI A., ŁYDŻBA D., RVE determination from a digital image of microstructure, Proceedings of the 2nd Int. Symp. on Comput. Geomech., COMGEO II, S. Pietruszczak et al. (eds.), Rhodes: IC2E International Centre for Computational Engineering, 2011.
  16. [16] RÓŻAŃSKI A., ŁYDŻBA D., From digital image of microstructure to the size of representative volume element: B4C/Al composite, Studia Geotechnica et Mechanica, Vol. XXXIII, No. 1, 2011, 55-68.
  17. [17] RÓŻAŃSKI A., ŁYDŻBA D., SHAO J.F., Numerical determination of minimum size of RVE for random composite materials: two-point probability approach, Proceedings of the 1st Int. Symp. on Comput.Geomech., COMGEO I, Juan les Pins, 2009.
  18. [18] RÓŻAŃSKI A., ŁYDŻBA D., SOBÓTKA M., Numerical determination of effective transport proeprties on the basis of microstructure digital images, AGH Journal of Mining and Geoengineering, Vol. 34 (2), 2010, 537-552 (in Polish).
  19. [19] SEJNOHA M., ZEMAN J., Micromechanical Analysis of Random Composites, Czech Technical Univ., 2000.
  20. [20] STROEVEN M., ASKES H., SLUYS L.J., Numerical determination of representative volumes for granular materials, Comput. Methods Appl. Mech. Eng., Vol. 193, 2004, 3221-3238.10.1016/j.cma.2003.09.023
  21. [21] TORQUATO S., Random Heterogeneous Materials. Microstructure and Macroscopic Properties, Springer-Verlag, New York, 2002.10.1115/1.1483342
  22. [22] YEONG C.L.Y., TORQUATO S., Reconstructing random media, Phys. Rev. E, Vol. 587, 1998, 495.10.1103/PhysRevE.57.495
  23. [23] YEONG C.L.Y., TORQUATO S., Reconstructing random media. II. Three-dimensional media form two-dimensional cuts, Phys. Rev. E, Vol. 58, 1998, 224.10.1103/PhysRevE.58.224
  24. [24] ZEMAN J., SEJNOHA M., Numerical evaluation of effective elastic properties of graphite fiber tow impregnated by polymer matrix, J. Mech. Phys. Solids, Vol. 49, 2001, 69. 10.1016/S0022-5096(00)00027-2
DOI: https://doi.org/10.2478/sgem-2013-0024 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365
Language: English
Page range: 67 - 81
Published on: Feb 14, 2014
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2014 Adrian Różański, Dariusz Łydżba, Piotr Jabłoński, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons License.