R. Alicandro, M. Cicalese, and A. Gloria, Mathematical derivation of a rubber-like stored energy functional, Comptes Rendus Mathematique, vol.345, issue.8, pp.345479-482, 2007.
DOI : 10.1016/j.crma.2007.10.005
URL : https://hal.archives-ouvertes.fr/hal-00766739

R. Alicandro, M. Cicalese, and A. Gloria, Convergence analysis of the Böl-Reese discrete model for rubber, Proceedings of the 11th International Symposium on Continuum Models and Discrete Systems, 2008.

R. Alicandro, M. Cicalese, and A. Gloria, Integral Representation Results for Energies Defined on Stochastic Lattices and Application to Nonlinear Elasticity, Archive for Rational Mechanics and Analysis, vol.262, issue.1, pp.881-943, 2011.
DOI : 10.1007/s00205-010-0378-7
URL : https://hal.archives-ouvertes.fr/inria-00437765

E. M. Arruda and M. C. Boyce, A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials, Journal of the Mechanics and Physics of Solids, vol.41, issue.2, pp.389-412, 1993.
DOI : 10.1016/0022-5096(93)90013-6
URL : https://hal.archives-ouvertes.fr/hal-01390807

E. M. Arruda and M. C. Boyce, Constitutive models of rubber elasticity : a review, Rubber Chemistry and Technology, vol.72, pp.504-523, 2000.

J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Archive for Rational Mechanics and Analysis, vol.8, issue.4, pp.337-403, 1977.
DOI : 10.1007/BF00279992

M. Böl and S. Reese, Finite element modelling of rubber-like materials ??? a comparison between simulation and experiment, Journal of Materials Science, vol.40, issue.22, pp.5933-5939, 2005.
DOI : 10.1007/s10853-005-5058-x

M. Böl and S. Reese, Finite element modelling of rubber-like polymers based on chain statistics, International Journal of Solids and Structures, vol.43, issue.1, pp.2-26, 2006.
DOI : 10.1016/j.ijsolstr.2005.06.086

P. G. Ciarlet, Mathematical elasticity. Volume I: three-dimensional elasticity, of Studies in Mathematics and its Applications, 1988.
URL : https://hal.archives-ouvertes.fr/hal-01077424

B. N. Delone, N. P. Dolbilin, M. I. Stogrin, and R. V. Galiulin, A local test for the regularity of a system of points, Dokl. Akad. Nauk SSSR, vol.227, issue.1, pp.19-21, 1976.

P. J. Flory, Statistical mechanics of chain molecules, 1969.

P. J. Flory, Network topology and the theory of rubber elasticity, British Polymer Journal, vol.45, issue.2, pp.96-102, 1985.
DOI : 10.1002/pi.4980170202

G. Geymonat, S. Müller, and N. Triantafyllidis, Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity, Archive for Rational Mechanics and Analysis, vol.52, issue.3, pp.231-290, 1993.
DOI : 10.1007/BF00380256

A. Gloria, Strong ellipticity of nonlinear elastic materials and homogenization of periodic and stochastic discrete systems

A. Gloria, A direct approach to numerical homogenization in finite elasticity, Netw. Heterog. Media, vol.1, pp.109-141, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00070383

A. Gloria, Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.46, issue.1, pp.1-38, 2012.
DOI : 10.1051/m2an/2011018
URL : https://hal.archives-ouvertes.fr/inria-00510514

A. Gloria and F. Otto, An optimal variance estimate in stochastic homogenization of discrete elliptic equations, The Annals of Probability, vol.39, issue.3, pp.779-856, 2011.
DOI : 10.1214/10-AOP571
URL : https://hal.archives-ouvertes.fr/hal-00383953

A. Gloria and F. Otto, An optimal error estimate in stochastic homogenization of discrete elliptic equations, The Annals of Applied Probability, vol.22, issue.1, pp.1-28
DOI : 10.1214/10-AAP745
URL : https://hal.archives-ouvertes.fr/inria-00457020

A. Gloria and M. D. Penrose, Random Parking, Euclidean Functionals, and Rubber Elasticity, Communications in Mathematical Physics, vol.272, issue.1, 2012.
DOI : 10.1007/s00220-013-1725-y
URL : https://hal.archives-ouvertes.fr/hal-00675037

G. Heinrich and M. Kaliske, Theoretical and numerical formulation of a molecular based constitutive tube-model of rubber elasticity, Computational and Theoretical Polymer Science, vol.7, issue.3-4, pp.3-4227, 1997.
DOI : 10.1016/S1089-3156(98)00010-5

W. Kuhn and F. Grün, Beziehungen zwischen elastischen Konstanten und Dehnungsdoppelbrechung hochelastischer Stoffe, Kolloid-Zeitschrift, vol.101, issue.3, pp.248-271, 1942.
DOI : 10.1007/BF01793684

P. and L. Tallec, Numerical methods for nonlinear three-dimensional elasticity, Handbook of numerical analysis, pp.465-622, 1994.
DOI : 10.1016/S1570-8659(05)80018-3

P. and L. Tallec, Mécanique des Milieux Continus, 2006.

C. Miehe, S. Göktepe, and F. Lulei, A micro-macro approach to rubber-like materials?Part I: the non-affine micro-sphere model of rubber elasticity, Journal of the Mechanics and Physics of Solids, vol.52, issue.11, pp.2617-2660, 2004.
DOI : 10.1016/j.jmps.2004.03.011

M. D. Penrose, Random Parking, Sequential Adsorption,??and the Jamming Limit, Communications in Mathematical Physics, vol.218, issue.1, pp.153-176, 2001.
DOI : 10.1007/s002200100387

M. Rubinstein and S. Panyukov, Elasticity of Polymer Networks, Macromolecules, vol.35, issue.17, pp.6670-6686, 2002.
DOI : 10.1021/ma0203849

D. Ruelle, Statistical mechanics. Rigorous results, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00126389

M. Tkachuk and C. Linder, The maximal advance path constraint for the homogenization of materials with random network microstructure, Philosophical Magazine, vol.102, issue.22, 2012.
DOI : 10.1016/j.cma.2010.07.021

M. Vidrascu, Solution of non-linear elasticity problems using the continu software, Inria Report Research, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00072500

A. Gloria, Project-team SIMPAF, Inria Lille -Nord Europe, Villeneuve d'Ascq, France E-mail address: agloria@ulb.ac.be (Patrick Le Tallec) LMS, ´ Ecole polytechnique, E-mail address: patrick.letallec@polytechnique.edu (Marina Vidrascu) Project-team REO