This article aims at proposing various estimates of the size of the Representative Volume Element (RVE) of random linear elastic matrix–inclusion composites. These estimates are derived from the computation of the apparent behavior of finite size volume elements (VE) by a new procedure presented in [18] by Salmi et al. (2012) and briefly recalled. Two different points of view to define an RVE are considered: the RVE is defined as being the smallest VE required either to evaluate numerically the considered effective property of the composite by appropriate statistical averaging of apparent ones, or to be allowed to replace any instance of the heterogeneous material by a unique homogeneous equivalent one in structural mechanics problems. In order to introduce the fluctuations of the apparent properties within such definitions of the RVE size, we first study the statistics of the apparent properties. Then, relying on the results of this statistical study, several proposals of RVE criteria are presented and applied to random linear elastic fiber–matrix composites for several contrasts and inclusion (or pore) volume fractions.
@article{CRMECA_2012__340_4-5_230_0,
author = {Moncef Salmi and Fran\c{c}ois Auslender and Michel Bornert and Michel Fogli},
title = {Various estimates of {Representative} {Volume} {Element} sizes based on a statistical analysis of the apparent behavior of random linear composites},
journal = {Comptes Rendus. M\'ecanique},
pages = {230--246},
publisher = {Elsevier},
volume = {340},
number = {4-5},
year = {2012},
doi = {10.1016/j.crme.2012.02.007},
language = {en},
}
TY - JOUR AU - Moncef Salmi AU - François Auslender AU - Michel Bornert AU - Michel Fogli TI - Various estimates of Representative Volume Element sizes based on a statistical analysis of the apparent behavior of random linear composites JO - Comptes Rendus. Mécanique PY - 2012 SP - 230 EP - 246 VL - 340 IS - 4-5 PB - Elsevier DO - 10.1016/j.crme.2012.02.007 LA - en ID - CRMECA_2012__340_4-5_230_0 ER -
%0 Journal Article %A Moncef Salmi %A François Auslender %A Michel Bornert %A Michel Fogli %T Various estimates of Representative Volume Element sizes based on a statistical analysis of the apparent behavior of random linear composites %J Comptes Rendus. Mécanique %D 2012 %P 230-246 %V 340 %N 4-5 %I Elsevier %R 10.1016/j.crme.2012.02.007 %G en %F CRMECA_2012__340_4-5_230_0
Moncef Salmi; François Auslender; Michel Bornert; Michel Fogli. Various estimates of Representative Volume Element sizes based on a statistical analysis of the apparent behavior of random linear composites. Comptes Rendus. Mécanique, Volume 340 (2012) no. 4-5, pp. 230-246. doi : 10.1016/j.crme.2012.02.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.02.007/
[1] Elastic properties of reinforced solids: Some theoretical principles, Journal of the Mechanics and Physics of Solids, Volume 11 (1963), pp. 357-372
[2] Analysis of composite materials, Journal of Applied Mechanics, Volume 50 (1983), pp. 481-505
[3] Material spatial randomness: From statistical to representative volume element, Probabilistic Engineering Mechanics, Volume 21 (2006), pp. 112-132
[4] Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics, vol. 127, Springer Verlag, Berlin–New York, 1980
[5] Rigorous results in statistical mechanics in quantum field theory (J. Fritz; J.L. Lebowitz; D. Szasz, eds.), Colloquia Mathematica Societatis Janos Bolyai, North-Holland, Amsterdam, 1978, pp. 835-873
[6] On the homogenization and the simulation of random materials, European Journal of Mechanics A/Solids, Volume 11 (1992), pp. 585-607
[7] A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites, Journal of the Mechanics and Physics of Solids, Volume 44 (1996), pp. 497-524
[8] A micromechanics-based nonlocal constitutive equation for elastic composites containing randomly oriented spheroidal heterogeneities, Journal of the Mechanics and Physics of Solids, Volume 52 (2004), pp. 359-393
[9] A micromechanics-based nonlocal constitutive equation and minimum RVE size estimates for random elastic composites containing aligned spheroidal heterogeneities, Journal of the Mechanics and Physics of Solids, Volume 57 (2009), pp. 1578-1595
[10] Representative volume element size for elastic composites: A numerical study, Journal of the Mechanics and Physics of Solids, Volume 45 (1997), pp. 1449-1459
[11] Random field models of heterogeneous materials, International Journal of Solids and Structures, Volume 35 (1998), pp. 2429-2455
[12] A numerical approximation to the elastic properties of sphere-reinforced composites, Journal of the Mechanics and Physics of Solids, Volume 50 (2002), pp. 2107-2121
[13] Determination of the size of the representative volume element for random composites: statistical and numerical, International Journal of Solids and Structures, Volume 40 (2003), pp. 3647-3679
[14] Quantification of stochastically stable representative volumes for random heterogeneous materials, Archive of Applied Mechanics, Volume 75 (2006), pp. 79-92
[15] Determination of the size of the representative volume element for random quasi-brittle composites, International Journal of Solids and Structures, Volume 46 (2009), pp. 2842-2855
[16] Estimation of local stresses and elastic properties of a mortar sample by FFT computation of fields on a 3D image, Cement and Concrete Research, Volume 41 (2011), pp. 542-556
[17] Representative volume: Existence and size determination, Engineering Fracture Mechanics, Volume 74 (1996), pp. 2518-2534
[18] M. Salmi, F. Auslender, M. Bornert, M. Fogli, Apparent and effective mechanical properties of linear matrix–inclusion random composites: improved bounds for the effective behavior, International Journal of Solids and Structures (2012), in press, . | DOI
[19] Application of variational concepts to size effects in elastic heterogeneous bodies, Journal of the Mechanics and Physics of Solids, Volume 38 (1990), pp. 813-841
[20] Micromechanics, macromechanics and constitutive modeling of the elasto-viscoplastic deformation rubber-toughened glassy polymers, Journal of the Mechanics and Physics of Solids, Volume 55 (2007), pp. 533-561
[21] Spring network models in elasticity and fracture of composites and polycrystals, Computational Materials Science, Volume 7 (1996), pp. 82-93
[22] Effect of nonuniform distribution of voids on the plastic response of voided materials: a computational and statistical analysis, International Journal of Solids and Structures, Volume 42 (2005), pp. 517-538
[23] Analyse morphologique et approches variationnelles du comportement dʼun milieu élastique hétérogène, Comptes Rendus de lʼAcadémie des Sciences II, Volume 312 (1991), pp. 143-150
[24] Morphologically representative pattern-based bounding in elasticity, Journal of the Mechanics and Physics of Solids, Volume 44 (1996), pp. 307-331
[25] Reconstruction of the structure of dispersions, Journal of Colloid and Interface Science, Volume 186 (1997), pp. 467-476
[26] Localization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: Exact solutions and dilute expansions, Journal of the Mechanics and Physics of Solids, Volume 56 (2008), pp. 1245-1268
[27] The determination of the elastic field of an ellipsoidal inclusion and related problems, Proceeding of the Royal Society A, Volume 421 (1957), pp. 376-396
[28] Elastic behavior of composites containing Boolean random sets of inhomogeneities, International Journal of Engineering Science, Volume 47 (2009), pp. 313-324
[29] Statistical Inference, Duxbury Press, United States, 2001
[30] V. Blanc, Modélisation du comportement thermomécanique des combustibles à particules par une approche multi-échelle, PhD thesis, Université de Provence, 11 décembre 2009.
[31] Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume, Journal of the Mechanics and Physics of Solids, Volume 42 (1994), pp. 1995-2011
[32] Stochastic Finite Elements: A Spectral Approach, Dover Publications, 1991
Cité par Sources :
Commentaires - Politique
Closed hypersurfaces of with constant mean curvature and zero Gauß–Kronecker curvature
Tsasa Lusala; André Gomes de Oliveira
C. R. Math (2005)