Determination of the size of the representative volume element for random composites: statistical and numerical approach
Tóm tắt
Từ khóa
Tài liệu tham khảo
Barbe, 2001, Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: FE model, Int. J. Plasticity, 17, 513, 10.1016/S0749-6419(00)00061-9
Barbe, 2001, Intergranular and intragranular behavior of polycrystalline aggregates. Part 2: Results, Int. J. Plasticity, 17, 537, 10.1016/S0749-6419(00)00062-0
Beran, 1968
Besson, J., Cailletaud, G., Chaboche, J.L., Forest, S., 2001. Mécanique non linéaire des matériaux. Hermès Science
Bornert, M., Bretheau, T., Gilormini, P., 2001. Homogénéisation en mécanique des matériaux. Hermès
Cailletaud, 1994, Size effect on elastic properties of random composites, Engng. Computat., 11, 99, 10.1108/02644409410799227
Colworth, U.R., 2000. Unilever Laboratory Progress Report
Coster, M., Chermant, J.L., 1989. Précis d’Analyse d’Images. Presses du CNRS
Decker, 2000, Simulation 3D de matériaux aléatoires polycristallins, La Revue de Métallurgie-CIT/Science et Génie des Matériaux, 271, 10.1051/metal/200097020271
Drugan, 1996, A micromechanics-based nonlocal constitutive equations and estimates of representative volume element size for elastic composites, J. Mech. Phys. Solids, 44, 497, 10.1016/0022-5096(96)00007-5
Fahrat, 1994, Implicit parallel processing in structural mechanics, Comput. Mech. Adv., 2, 47
Feyel, F., 1998. Application du calcul parallèle aux modèles à grand nombre de variables internes, Thèse de Doctorat. Ecole des Mines de Paris
Feyel, F., Cailletaud, G., Kruch, S., Roux, F.X., 1997. Application du calcul parallèle aux modèles à grand nombre de variables internes. Colloque national en calcul de structures, May 20–23, Giens, France, pp. 309–314
Forest, 2000, Cosserat modelling of size effects in the mechanical behavior of polycrystals and multi-phase materials, Int. J. Solids Struct., 37, 7105, 10.1016/S0020-7683(99)00330-3
Forest, 2002, Introduction au calcul de microstructures, Mécanique et Industries, 3, 439
Ghosh, 1995, Elastic–plastic analysis of arbitrary heterogeneous materials with the Voronoi Cell finite element method, Comput. Methods Appl. Mech. Engng., 121, 373, 10.1016/0045-7825(94)00687-I
Gilbert, 1962, Random subdivisions of space into crystals, Ann. Math. Stat., 33, 958, 10.1214/aoms/1177704464
Gusev, 1997, Representative volume element size for elastic composites: a numerical study, J. Mech. Phys. Solids, 45, 1449, 10.1016/S0022-5096(97)00016-1
Hashin, 1963, A variational approach to the theory of elastic behavior of multiphase materials, J. Mech. Phys. Solids, 11, 127, 10.1016/0022-5096(63)90060-7
Hazanov, 1994, Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume, J. Mech. Phys. Solids, 42, 1995, 10.1016/0022-5096(94)90022-1
Hershey, 1954, The elasticity of an isotropic aggregate of anisotropic cubic crystals, J. Appl. Mech., 21, 236, 10.1115/1.4010899
Huet, 1990, Application of variational concepts to size effects in elastic heterogeneous bodies, J. Mech. Phys. Solids, 38, 813, 10.1016/0022-5096(90)90041-2
Jeulin, D., 1981. Mathematical morphology and multiphase materials. In: Proceedings of 3rd European Symposium of Stereology, vol. 3, suppl. 1. Streol. Iugosl., pp. 265–286
Jeulin, D., 2001. Caractérisation Morphologique et Modèles de Structures Aléatoires, Extrait de: Homogénéisation en mécanique des matériaux (tome1). Hermès, France
Jeulin, D., Ostoja-Starzewski, M., 2001. Mechanics of Random and Multiscale Microstructures, vol. 430. CISM Lecture Notes, Springer-Verlag
Kanit, T., Forest, S., Mounoury, V., Jeulin, D., in preparation. Large-scale computations of two-phase microstructures from confocal 3D images: elastic and thermal properties
Kröner, 1958, Berechnung der elastischen Konstanten des Vielkristalls aus des Konstanten des Einkristalls, Z. Physik, 151, 504, 10.1007/BF01337948
Kröner, E., 1980. Linear properties of random media––the systematic theory. Comportements rhéologiques et structure des matériaux-CR 15ème Coll. GFR. Paris
Lantuéjoul, 1991, Ergodicity and integral range, J. Microsc., 161, 387, 10.1111/j.1365-2818.1991.tb03099.x
Lippmann, 1997, 3d-finite-element-modelling of microstructures with the method of multiphase elements, Comput. Mater. Sci., 9, 28, 10.1016/S0927-0256(97)00055-4
Matheron, 1971
Matheron, 1975
Matheron, 1989
Meille, 2001, Linear elastic properties of 2-d and 3-d models of porous materials made from elongated objects, Mod. Sim. Mater. Sci. Engng., 9, 1
Miller, 1969, Bounds for the effective electrical, thermal and magnetic properties of heterogeneous materials, J. Math. Phys., 10, 1988, 10.1063/1.1664794
Milton, 1982, Bounds on the elastic and transport properties of two component composites, J. Mech. Phys. Solids, 30, 177, 10.1016/0022-5096(82)90022-9
Milton, 1985, The coherent potential approximation is a realizable effective medium scheme, Commun. Math. Phys., 99, 453, 10.1007/BF01215906
Nemat-Nasser, 1993
Ostoja-Starzewski, 1998, Random field models of heterogeneous materials, Int. J. Solids Struct., 35, 2429, 10.1016/S0020-7683(97)00144-3
Ponte Castañeda, 1987, Nonlinear composites, Adv. Appl. Mech., 34
Povirk, 1994, Incorporation of microstructural information into models of two-phase materials, Acta Metall. Mater., 43, 3199, 10.1016/0956-7151(94)00487-3
Roberts, 1999, Elastic properties of a tungste-silver composite by reconstruction and computation, J. Mech. Phys. Solids, 47, 2029, 10.1016/S0022-5096(99)00016-2
Roberts, 2000, Elastic properties of model porous ceramics, J. Am. Ceram. Soc., 83, 3041, 10.1111/j.1151-2916.2000.tb01680.x
Roberts, 2001, Elastic moduli of model random three-dimensional closed-cell cellular solids, Acta Mater., 49, 189, 10.1016/S1359-6454(00)00314-1
Sab, 1992, On the homogenization and the simulation of random materials, Eur. J. Mech. Solids, 11, 585
Sanchez-Palencia, E., Zaoui, A., 1987. Homogenization techniques for composite media. Lecture Notes in Physics No. 272, Springer-Verlag, Berlin
Serra, 1982
Suquet, P., 1997. Continuum micromechanics. CISM Courses and Lectures No. 377, Springer-Verlag, Berlin
Terada, 1998, Characterization of the mechanical behaviors of solid-fluid mixture by the homogenization method, Comput. Methods Appl. Engng., 153, 223, 10.1016/S0045-7825(97)00071-6
Thompson, 1999
Torquato, 1991, Random heterogeneous media: microstructure and improved bounds on effective properties, Appl. Mech. Rev., 44, 37, 10.1115/1.3119494
Torquato, 1986, Effective properties of two phase disordered composite media: ii evaluation of bounds on the conductivity and bulk modulus of dispersions of impenetrable spheres, Phys. Rev. B, 33, 6428, 10.1103/PhysRevB.33.6428
Torquato, 1983, Microstructure of two-phase random media iii. the n-point matrix probability functions for fully penetrable spheres, J. Chem. Phys., 79, 1505, 10.1063/1.445941
Willis, 1981, Variational and related methods for the overall properties of composites, Adv. Appl. Mech., 21, 1, 10.1016/S0065-2156(08)70330-2