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Numerical study of the size of representative volume element for linear elasticity problem

Treść / Zawartość
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Warianty tytułu
Języki publikacji
PL
Abstrakty
EN
In the paper, a numerical study of the size of representative volume element for the linear elasticity problem is performed. The calculations are carried out for three different types of random microstructures: checkerboard, the Ising model microstructure and Debye microstructure. It is postulated and then verified that there exists a relation between the morphology of microstructure contained in the lineal-path function and the minimum RVE size. It is confirmed, on the basis of numerical examples, that for all the microstructures considered the largest lineal-path can be treated as the size of RVE.
Wydawca
Rocznik
Strony
67--81
Opis fizyczny
Bibliogr. 24 poz., tab., rys.
Twórcy
  • Institute of Geotechnics and Hydrotechnics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław
autor
  • Institute of Geotechnics and Hydrotechnics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław
  • 5th year student of Wrocław University of Technology Faculty of Civil Engineering
Bibliografia
  • [1] BERAN M.J., Statistical Continuum Theories, Monographs in Statistical Physics, Interscience Publishers, 1968.
  • [2] FELLER W., An Introduction to Probability Theory and its Applications, Vol. I, 2nd Edition, John Wiley and Sons, N.Y., 1961.
  • [3] GITMAN I.M., ASKES H., SLUYS L.J., Representative volume: existence and size determination, Eng. Fract. Mech., Vol. 74, 2007, 2518–2534.
  • [4] GRAHAM S., YANG N., Representative volumes of materials based on microstructural statistics, Scripta Materialia, Vol. 48, 2003, 269–274.
  • [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.
  • [6] GUSEV A., Representative volume element size for elastic composites: a numerical study, J. Mech. Phys. Solids, Vol. 45, 1997, 1449–1459.
  • [7] JANKE W., Pseudo random number: generation and quality checks, Lecture Notes John von Neumann Institute for Computing, Vol. 10, 2002, 447.
  • [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] KIRKPATRICK S., GELATT C.D., VECCHI M.P., Optimization by simulated annealing, Science, Vol. 220, 1983, 671–680.
  • [10] LU B., TORQUATO S., Lineal-path function for random heterogeneous materials, Phys. Rev. A, 1992, Vol. 45 (2), 922–929.
  • [11] Mathematica: Wolfram Mathematica Tutorial Collection, 2008.
  • [12] POVIRK G.L., Incorporation of microstructural information into model of two-phase materials, Acta Metal. Mater., Vol. 43 (8), 1995, 3199–3206.
  • [13] QUINTANILLA J., TORQUATO S., Lineal measures of clustering in overlapping particle systems, Phys. Rev. E, Vol. 54 (4), 1996, 4027–4036.
  • [14] RÓŻAŃSKI A., Random composites: representativity, minimum RVE size, effective transport properties, PhD dissertation, USTL, LML (UMR CNRS 8107), No. 40444, 2010.
  • [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] 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] 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] 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] SEJNOHA M., ZEMAN J., Micromechanical Analysis of Random Composites, Czech Technical Univ., 2000.
  • [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.
  • [21] TORQUATO S., Random Heterogeneous Materials. Microstructure and Macroscopic Properties, Springer-Verlag, New York, 2002.
  • [22] YEONG C.L.Y., TORQUATO S., Reconstructing random media, Phys. Rev. E, Vol. 587, 1998, 495.
  • [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.
  • [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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-3c25f908-71a6-4854-9c7e-f91d401c5abd
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