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

Różański, Adrian; Łydżba, Dariusz; Jabłoński, Piotr

doi:10.2478/sgem-2013-0024

Abstract

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

References

[1] BERAN M.J., Statistical Continuum Theories, Monographs in Statistical Physics, Interscience Publishers, 1968.10.1119/1.1974326
Search in Google Scholar
[2] FELLER W., An Introduction to Probability Theory and its Applications, Vol. I, 2nd Edition, John Wiley and Sons, N.Y., 1961.
Search in Google Scholar
[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
Search in Google Scholar
[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
Search in Google Scholar
[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
Search in Google Scholar
[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
Search in Google Scholar
[7] JANKE W., Pseudo random number: generation and quality checks, Lecture Notes John von Neumann Institute for Computing, Vol. 10, 2002, 447.
Search in Google Scholar
[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.
Search in Google Scholar
[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
Search in Google Scholar
[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
Search in Google Scholar
[11] Mathematica: Wolfram Mathematica Tutorial Collection, 2008.
Search in Google Scholar
[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
Search in Google Scholar
[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
Search in Google Scholar
[14] RÓŻAŃSKI A., Random composites: representativity, minimum RVE size, effective transport properties, PhD dissertation, USTL, LML (UMR CNRS 8107), No. 40444, 2010.
Search in Google Scholar
[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.
Search in Google Scholar
[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.
Search in Google Scholar
[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.
Search in Google Scholar
[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).
Search in Google Scholar
[19] SEJNOHA M., ZEMAN J., Micromechanical Analysis of Random Composites, Czech Technical Univ., 2000.
Search in Google Scholar
[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
Search in Google Scholar
[21] TORQUATO S., Random Heterogeneous Materials. Microstructure and Macroscopic Properties, Springer-Verlag, New York, 2002.10.1115/1.1483342
Search in Google Scholar
[22] YEONG C.L.Y., TORQUATO S., Reconstructing random media, Phys. Rev. E, Vol. 587, 1998, 495.10.1103/PhysRevE.57.495
Search in Google Scholar
[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
Search in Google Scholar
[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
Search in Google Scholar

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

Abstract

Paradigm

My account