K. Alderson, A. Alderson, N. Ravirala, V. Simkins, and P. Davies, Manufacture and characterisation of thin flat and curved auxetic foam sheets, physica status solidi (b), vol.249, issue.7, pp.1315-1321, 2012.

G. Aletti, E. G. Bongiorno, and V. Capasso, Statistical aspects of fuzzy monotone set-valued stochastic processes. Application to birth-and-growth processes, Fuzzy Sets and Systems, vol.160, issue.21, pp.3140-3151, 2009.

G. Aletti, E. G. Bongiorno, and V. Capasso, Integration in a dynamical stochastic geometric framework, ESAIM: Probability and Statistics, vol.15, pp.402-416, 2011.

G. Allaire, Homogenization and Two-Scale Convergence, SIAM Journal on Mathematical Analysis, vol.23, issue.6, pp.1482-1518, 1992.
URL : https://hal.archives-ouvertes.fr/hal-01111805

E. Andreassen and C. S. Andreasen, How to determine composite material properties using numerical homogenization, Computational Materials Science, vol.83, pp.488-495, 2014.

X. Blanc, C. Le-bris, and F. Legoll, Some variance reduction methods for numerical stochastic homogenization, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.374, issue.2066, p.20150168, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01196499

A. Bourgeat and A. Piatnitski, Approximations of effective coefficients in stochastic homogenization, Annales de l?Institut Henri Poincare (B) Probability and Statistics, vol.40, issue.2, pp.153-165, 2004.

B. D. Caddock and K. E. Evans, Microporous materials with negative Poisson's ratios. I. Microstructure and mechanical properties, Journal of Physics D: Applied Physics, vol.22, issue.12, pp.1877-1882, 1989.

N. Chan and K. E. Evans, Fabrication methods for auxetic foams, Journal of Materials Science, vol.32, issue.22, pp.5945-5953, 1997.

S. N. Chiu, D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and its Applications, 2013.

J. Dagdelen, J. Montoya, M. De-jong, and K. Persson, Computational prediction of new auxetic materials, Nature Communications, vol.8, issue.1, pp.1-8, 2017.

S. Domaschke, A. Morel, G. Fortunato, and A. E. Ehret, Random auxetics from buckling fibre networks, Nature Communications, vol.10, issue.1, pp.1-8, 2019.

S. Forte and M. Vianello, Symmetry classes for elasticity tensors, Journal of Elasticity, vol.43, issue.2, pp.81-108, 1996.

R. Gao, D. Li, L. Dong, and X. Wang, Numerical Analysis of the Mechanical Properties of 3D Random Voronoi Structures With Negative Poisson's Ratio, physica status solidi (b), vol.256, issue.7, p.1800539, 2019.

E. Garner, H. M. Kolken, C. C. Wang, A. A. Zadpoor, and J. Wu, Compatibility in microstructural optimization for additive manufacturing, Additive Manufacturing, vol.26, pp.65-75, 2019.

J. Lorna, M. Gibson, and . Ashby, Cellular solids: structure and properties, 1999.

N. Joseph, L. Grima, . Mizzi, M. Keith, R. Azzopardi et al., Auxetic perforated mechanical metamaterials with randomly oriented cuts, Advanced materials, vol.28, issue.2, pp.385-389, 2016.

F. Varda, M. F. Hagh, and . Thorpe, Disordered auxetic networks with no reentrant polygons, Physical Review B, vol.98, issue.10, p.100101, 2018.

F. Han, G. Seiffert, Y. Zhao, and B. Gibbs, Acoustic absorption behaviour of an open-celled aluminium foam, Journal of Physics D: Applied Physics, vol.36, issue.3, pp.294-302, 2003.

J. Hu, M. Li, X. Yang, and S. Gao, Cellular structure design based on free material optimization under connectivity control, Computer-Aided Design, vol.127, p.102854, 2020.

T. Kanit, S. Forest, I. Galliet, V. Mounoury, and D. Jeulin, 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.

H. . Kolken and A. A. Zadpoor, Auxetic mechanical metamaterials, RSC Advances, vol.7, issue.9, pp.5111-5129, 2017.

A. G. Kolpakov, Determination of the average characteristics of elastic frameworks, Journal of Applied Mathematics and Mechanics, vol.49, issue.6, pp.739-745, 1985.

A. Jagdish, . Krishnaswamy, C. Federico, R. Buroni, L. Melnik et al., Design of polymeric auxetic matrices for improved mechanical coupling in lead-free piezocomposites, Smart Materials and Structures, vol.29, issue.5, p.54002, 2020.

S. Kumar, S. Tan, L. Zheng, and D. M. Kochmann, Inverse-designed spinodoid metamaterials, npj Computational Materials, vol.6, issue.1, pp.1-10, 2020.

R. Lakes, Foam Structures with a Negative Poisson's Ratio, Science, vol.235, issue.4792, pp.1038-1040, 1987.

S. Roderic and . Lakes, Negative-Poisson's-ratio materials: auxetic solids. Annual review of materials research, vol.47, pp.63-81, 2017.

R. Lanza, R. Langer, J. Vacanti, and A. Atala, Preface, Principles of Tissue Engineering, p.xli, 2020.

D. Li, L. Dong, J. Yin, and R. S. Lakes, Negative Poisson?s ratio in 2D Voronoi cellular solids by biaxial compression: a numerical study, Journal of Materials Science, vol.51, issue.14, pp.7029-7037, 2016.

J. Liu, Y. Nie, H. Tong, and N. Xu, Realizing negative Poisson's ratio in spring networks with close-packed lattice geometries, Physical Review Materials, vol.3, issue.5, p.55607, 2019.

J. Martínez, J. Dumas, and S. Lefebvre, Procedural voronoi foams for additive manufacturing, ACM Transactions on Graphics, vol.35, issue.4, pp.1-12, 2016.

J. Martínez, M. Skouras, C. Schumacher, S. Hornus, S. Lefebvre et al., Star-shaped metrics for mechanical metamaterial design, ACM Transactions on Graphics, vol.38, issue.4, pp.1-13, 2019.

M. J. Mirzaali, H. A. Pahlavani, and A. A. Zadpoor, Auxeticity and stiffness of random networks: Lessons for the rational design of 3D printed mechanical metamaterials, Applied Physics Letters, vol.115, issue.2, p.021901, 2019.

M. Moakher and A. N. Norris, The Closest Elastic Tensor of Arbitrary Symmetry to an Elasticity Tensor of Lower Symmetry, Journal of Elasticity, vol.85, issue.3, pp.215-263, 2006.

J. Mo?kus, On Bayesian Methods for Seeking the Extremum, Optimization Techniques IFIP Technical Conference, pp.400-404, 1975.

A. Norris, The isotropic material closest to a given anisotropic material, Journal of Mechanics of Materials and Structures, vol.1, issue.2, pp.223-238, 2006.

A. Okabe, B. Boots, K. Sugihara, and S. N. Chiu, Spatial Tessellations, 2000.

N. Pashine, D. Hexner, A. J. Liu, and S. R. Nagel, Directed aging, memory, and nature?s greed, Science Advances, vol.5, issue.12, p.eaax4215, 2019.

. Carlos-m-portela, S. Vidyasagar, T. Krödel, D. W. Weissenbach, J. R. Yee et al., Extreme mechanical resilience of self-assembled nanolabyrinthine materials, Proceedings of the National Academy of Sciences, vol.117, issue.11, pp.5686-5693, 2020.

G. Qin and Z. Qin, Negative Poisson?s ratio in two-dimensional honeycomb structures, npj Computational Materials, vol.6, issue.1, pp.1-6, 2020.

D. Rayneau-kirkhope, S. Bonfanti, and S. Zapperi, Density scaling in the mechanics of a disordered mechanical meta-material, Applied Physics Letters, vol.114, issue.11, p.111902, 2019.

N. Daniel-r-reid, A. S. Pashine, S. R. Bowen, J. Nagel, and . Pablo, Ideal isotropic auxetic networks from random networks, Soft Matter, vol.15, issue.40, pp.8084-8091, 2019.

N. Daniel-r-reid, J. M. Pashine, . Wozniak, M. Heinrich, A. J. Jaeger et al., Auxetic metamaterials from disordered networks, Proceedings of the National Academy of Sciences, vol.115, issue.7, pp.1384-1390, 2018.

X. Ren, R. Das, P. Tran, T. D. Ngo, and Y. M. Xie, Auxetic metamaterials and structures: a review, Smart Materials and Structures, vol.27, issue.2, p.023001, 2018.

H. Ronellenfitsch, N. Stoop, J. Yu, A. Forrow, and J. Dunkel, Inverse design of discrete mechanical metamaterials, Physical Review Materials, vol.3, issue.9, p.95201, 2019.

K. K. Saxena, R. Das, and E. P. Calius, Three Decades of Auxetics Research ? Materials with Negative Poisson's Ratio: A Review, Advanced Engineering Materials, vol.18, issue.11, pp.1847-1870, 2016.

C. Schroeder, W. C. Regli, A. Shokoufandeh, and W. Sun, Computer-aided design of porous artifacts, Computer-Aided Design, vol.37, issue.3, pp.339-353, 2005.

D. Stoyan and M. Schlather, Random sequential adsorption: relationship to dead leaves and characterization of variability, Journal of Statistical Physics, vol.100, issue.5/6, pp.969-979, 2000.

M. Stroeven, H. J. Askes, and L. J. Sluys, Numerical determination of representative volumes for granular materials, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.30-32, pp.3221-3238, 2004.

L. Head-tim, S. Gilles, and . Iaroslav,

. Vp-tran, S. Guilleminot, K. Brisard, and . Sab, Stochastic modeling of mesoscopic elasticity random field, Mechanics of Materials, vol.93, pp.1-12, 2016.

P. Vogiatzis, S. Chen, X. Wang, T. Li, and L. Wang, Topology optimization of multi-material negative Poisson?s ratio metamaterials using a reconciled level set method, Computer-Aided Design, vol.83, pp.15-32, 2017.

W. Voigt, Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik). By Woldemar Voigt. Pp. xxiv + 964, with 213 text-figures and 1 table. (Leipzig and Berlin: B. G. Teubner. 1910. Price 30 marks.), Mineralogical Magazine and Journal of the Mineralogical Society, vol.16, issue.75, pp.253-253, 1912.

B. Widom, Random Sequential Addition of Hard Spheres to a Volume, The Journal of Chemical Physics, vol.44, issue.10, pp.3888-3894, 1966.

W. Yang, Z. Li, W. Shi, B. Xie, and M. Yang, Review on auxetic materials, Journal of Materials Science, vol.39, issue.10, pp.3269-3279, 2004.

O. Zerhouni, M. G. Tarantino, and K. Danas, Numerically-aided 3D printed random isotropic porous materials approaching the Hashin-Shtrikman bounds, Composites Part B: Engineering, vol.156, pp.344-354, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01875669