Use of classical variational principles to determine bounds for the effective bulk modulus in heterogeneous media, Quarterly of Applied Mathematics, vol.24, issue.2, pp.107-118, 1966. ,
DOI : 10.1090/qam/99925
The dielectric constant of a composite material???A problem in classical physics, Physics Reports, vol.43, issue.9, pp.377-407, 1978. ,
DOI : 10.1016/0370-1573(78)90009-1
Clausius-Mossotti-type approximation for elastic moduli of a cubic array of spheres, Physical Review B, vol.68, issue.2, p.24104, 2003. ,
DOI : 10.1103/PhysRevB.68.024104
Simple algebraic approximations for the effective elastic moduli of cubic arrays of spheres, J. of Mech. and Phys. of Sol, vol.52, p.9, 2004. ,
Prévision du comportementélectromagnétiquecomportementélectromagnétique de matériaux compositesàcompositesà partir de leur mode d'´ elaboration et de leur morphologie, Thesis, Paris School of Mines, 2001. ,
Measurement of elasticity and conductivity of a three-dimensional percolation system, Physical Review Letters, vol.54, issue.9, p.913, 1985. ,
DOI : 10.1103/PhysRevLett.54.913
Critical Properties of the Void Percolation Problem for Spheres, Physical Review Letters, vol.52, issue.17, pp.17-1516, 1984. ,
DOI : 10.1103/PhysRevLett.52.1516
A fast numerical scheme for computing the response of composites using grid refinement, Eur. Phys, J. AP, vol.6, issue.1, 1999. ,
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
Ostoja-Starzewski (eds) Mechanics of Random and Multiscale Microstructures, CISM Lecture Notes N ?, vol.430, 2001. ,
Random Structures in Physics, Contributions in Honor of Georges Matheron in the Fields of Geostatistics, Random Sets, and Mathematical Morphology. strongly anisotropic, [12] D. Jeulin, M. Moreaud, pp.183-222, 2005. ,
DOI : 10.1007/0-387-29115-6_9
Moreaud Statistical representative volume element for predicting the dielectric permittivity of random media, Proc. CMDS 11, D ,
Jeulin, Determination of the size of the representative volume element for random composites: statistical and numerical approach, Int. J. of Sol. and Str, vol.40, 2003. ,
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, 1972. ,
DOI : 10.1007/978-3-7091-2862-6
The theory of regionalized variables and its applications, Paris School of Mines publications, 1971. ,
Random sets and integral geometry, 1975. ,
Estimating and Choosing, 1989. ,
DOI : 10.1007/978-3-642-48817-7
A computational scheme for linear and non???linear composites with arbitrary phase contrast, International Journal for Numerical Methods in Engineering, vol.58, issue.12, 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
1417. [23] for most volume fractions H. Moulinec, P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Acad. Sci. Paris II Comp. Methods in Appl. Mech. and Engrg, vol.318, issue.157, pp.1-2, 1994. ,
Comparison of FFT-based methods for computing the response of composites with highly contrasted mechanical properties, Physica B: Condensed Matter, vol.338, issue.1-4, p.338, 2003. ,
DOI : 10.1016/S0921-4526(03)00459-9
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, p.30, 1997. ,
DOI : 10.1088/0305-4470/30/16/005
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
Ponte Castañeda, Localization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: Exact solutions and dilute expansions, J. of the Mech. and Phys. of Sol, vol.56, issue.4, 2008. ,