Use of classical variational principles to determine bounds for the effective bulk modulus in heterogeneous media, Quarterly of Applied Mathematics, vol.24, issue.2 ,
DOI : 10.1090/qam/99925
Statistical Continuum Theories, 1968. ,
DOI : 10.1119/1.1974326
Variational bounds on elastic constants for the penetrable sphere model, Journal of Physics D: Applied Physics, vol.18, issue.4, pp.585-597, 1985. ,
DOI : 10.1088/0022-3727/18/4/003
The effective elastic moduli of composite materials containing spherical inclusions at non-dilute concentrations, Int. J. Solids Structures, vol.14, pp.349-364, 1978. ,
Prévision du comportementélectromagnétiquecomportementélectromagnétique de matériaux compositesàposites`positesà partir de leur mode d'´ elaboration et de leur morphologie, Thesis, Paris School of Mines, 2001. ,
Critical Properties of the Void Percolation Problem for Spheres, Physical Review Letters, vol.52, issue.17, pp.1516-1519, 1984. ,
DOI : 10.1103/PhysRevLett.52.1516
The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. Lond. A 241, pp.376-396, 1957. ,
A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials, Journal of Applied Physics, vol.33, issue.10, pp.3125-3131, 1962. ,
DOI : 10.1063/1.1728579
A variational approach to the theory of the elastic behaviour of multiphase materials, Journal of the Mechanics and Physics of Solids, vol.11, issue.2, pp.127-140, 1963. ,
DOI : 10.1016/0022-5096(63)90060-7
Rubber with carbon black fillers: parameters identification of a multiscale nanostructure model, Proc. Eur. Conf. on Constitutive Models for Rubber ECCMR2007, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00183046
Random structure analysis and modelling by Mathematical Morphology, Proc. CMDS5, pp.217-226, 1987. ,
Modèles morphologiques de structures aléatoires et de changement d'´ echelle, Thèse de Doctorat d' ´ Etat, 1991. ,
Morphological modeling of random composites, Proc. CMDS8 Conference, pp.11-16, 1995. ,
Modeling heterogeneous materials by random structures, Invited lecture , European Workshop on Application of Statistics and Probabilities in Wood Mechanics, MM, vol.96, 1996. ,
Bounds of physical properties of some random structure, Proceedings of the CMDS9 Conference, pp.147-154, 1998. ,
Random Structure Models for Homogenization and Fracture Statistics, CISM Lecture Notes N ?, vol.430, pp.33-91, 2001. ,
DOI : 10.1007/978-3-7091-2780-3_2
Space, Structure and Randomness, Contributions in Honor of Georges Matheron in the Fields of Geostatistics, pp.183-222, 2005. ,
Multi-scale simulation of random spheres aggregates-Application to nanocomposites, Proc. of the 9th European Congress for Stereology, 2005. ,
Percolation d'agrégats multi-´ echelles de sphères et de fibres : Application aux nanocomposites, pp.13-17, 2006. ,
Statistical representative volume element for predicting the dielectric permittivity of random media, Proc. CMDS 11, pp.429-436, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00834780
Morphological models of random structures ,
Determination of the size of the representative volume element for random composites: statistical and numerical approach, International Journal of Solids and Structures, vol.40, issue.13-14, pp.3647-3679, 2003. ,
DOI : 10.1016/S0020-7683(03)00143-4
Apparent and effective physical properties of heterogeneous materials: Representativity of samples of two materials from food industry, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.33-36, pp.195-3960, 2006. ,
DOI : 10.1016/j.cma.2005.07.022
URL : https://hal.archives-ouvertes.fr/hal-00139164
Statistical Continuum Mechanics, 1971. ,
DOI : 10.1007/978-3-7091-2862-6
On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations, Acta Materialia, vol.52, issue.18, pp.5347-5361, 2004. ,
DOI : 10.1016/j.actamat.2004.07.040
Eléments pour une théorie des milieux poreux, 1967. ,
Composition des perméabilités en milieu poreux hétérogène: critique de la r` egle de pondération géométrique, Rev. IFP, vol.23, pp.201-218, 1968. ,
The theory of regionalized variables and its applications, 1971. ,
Random sets and integral geometry, 1975. ,
Estimating and Choosing, 1989. ,
DOI : 10.1007/978-3-642-48817-7
On the deplacement field in an elastic medium with random variations of material properties, Recent Advances in Engineering Sciences, vol.5, pp.235-254, 1970. ,
A computational scheme for linear and non???linear composites with arbitrary phase contrast, International Journal for Numerical Methods in Engineering, vol.58, issue.12, pp.139-158, 2001. ,
DOI : 10.1002/nme.275
Bounds on the elastic and transport properties of two-component composites, Journal of the Mechanics and Physics of Solids, vol.30, issue.3, pp.177-191, 1982. ,
DOI : 10.1016/0022-5096(82)90022-9
A fast numerical method for computing the linear and nonlinear properties of composites, C. R. Acad. Sci. Paris II, vol.318, pp.1417-1423, 1994. ,
A numerical method for computing the overall response of nonlinear composites with complex microstructure, Computer Methods in Applied Mechanics and Engineering, vol.157, issue.1-2 ,
DOI : 10.1016/S0045-7825(97)00218-1
URL : https://hal.archives-ouvertes.fr/hal-01282728
Intraphase strain heterogeneity in nonlinear composites: a??computational approach, European Journal of Mechanics - A/Solids, vol.22, issue.5, pp.751-770, 2003. ,
DOI : 10.1016/S0997-7538(03)00079-2
Homogenization for Nonlinear Composites in the Light of Numerical Simulations, Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials, pp.193-223, 2004. ,
DOI : 10.1007/1-4020-2623-4_8
Electrical conductivity of a mixture of conducting and insulating spheres: an application of some percolation concepts, Journal of Physics C: Solid State Physics, vol.11, issue.7, pp.11-1311, 1978. ,
DOI : 10.1088/0022-3719/11/7/021
Application of percolation concepts to electrical conductivity of polyaniline???inorganic salt composites, Journal of Materials Chemistry, vol.9, issue.10, pp.2425-2428, 1999. ,
DOI : 10.1039/a904687i
Precise determination of the critical threshold and exponents in a three-dimensional continuum percolation model, Journal of Physics A: Mathematical and General, vol.30, issue.16, pp.585-592, 1997. ,
DOI : 10.1088/0305-4470/30/16/005
Morphological analysis of carbonpolymer composite materials from thick sections, Acta Stereologica, vol.18, issue.3, pp.297-303, 1999. ,
???point matrix probability functions for fully penetrable spheres, The Journal of Chemical Physics, vol.79, issue.3, pp.79-1505, 1983. ,
DOI : 10.1063/1.445941
Effective properties of two-phase disordered composite media: II. Evaluation of bounds on the conductivity and bulk modulus of dispersions of impenetrable spheres, Physical Review B, vol.33, issue.9, pp.6428-6434, 1986. ,
DOI : 10.1103/PhysRevB.33.6428
Random Heterogeneous Media: Microstructure and Improved Bounds on Effective Properties, Applied Mechanics Reviews, vol.44, issue.2, pp.37-76, 1991. ,
DOI : 10.1115/1.3119494
THE OVERALL ELASTIC MODULI OF A DILUTE SUSPENSION OF SPHERES, The Quarterly Journal of Mechanics and Applied Mathematics, vol.29, issue.2, pp.163-177, 1976. ,
DOI : 10.1093/qjmam/29.2.163
Elastic behavior of composites containing Boolean random sets of inhomogeneities, International Journal of Engineering Science, vol.47, issue.2, pp.313-324, 2009. ,
DOI : 10.1016/j.ijengsci.2008.09.016
URL : https://hal.archives-ouvertes.fr/hal-00426398