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

Z. P. Bazant and B. H. Oh, Efficient Numerical Integration on the Surface of a Sphere, ZAMM - Journal of Applied Mathematics and Mechanics, vol.146, issue.1, pp.37-49, 1986.
DOI : 10.1002/zamm.19860660108

D. Besdo and J. Ihlemann, Directional sensitivity of Mullins effect constitutive models for rubber, Contitutive Models for Rubber IV. ECCMR05, pp.229-235, 2005.

R. Bonart, X-ray investigations concerning the physical structure of cross-linking in segmented urethane elastomers, Journal of Macromolecular Science, Part B, vol.2, issue.1, pp.115-138, 1968.
DOI : 10.1080/00222346808212867

G. Chagnon, Modélisation de l'effet Mullins dans les élastomères, Thèse de doctorat. Ecole Centrale de Nantes, 2003.

G. Chagnon, E. Verron, L. Gornet, G. Marckmann, and P. Charrier, On the relevance of Continuum Damage Mechanics as applied to the Mullins effect in elastomers, Journal of the Mechanics and Physics of Solids, vol.52, issue.7, pp.1627-1650, 2004.
DOI : 10.1016/j.jmps.2003.12.006

URL : https://hal.archives-ouvertes.fr/hal-01007152

G. Chagnon, E. Verron, G. Marckmann, and L. Gornet, Development of new constitutive equations for the Mullins effect in rubber using the network alteration theory, International Journal of Solids and Structures, vol.43, issue.22-23, pp.6817-6831, 2006.
DOI : 10.1016/j.ijsolstr.2006.02.011

URL : https://hal.archives-ouvertes.fr/hal-01006742

R. Dargazany and M. Itskov, A network evolution model for the anisotropic Mullins effect in carbon black filled rubbers, International Journal of Solids and Structures, vol.46, issue.16, pp.2967-2977, 2009.
DOI : 10.1016/j.ijsolstr.2009.03.022

J. Diani, M. Brieu, and P. Gilormini, Observation and modeling of the anisotropic visco-hyperelastic behavior of a rubberlike material, International Journal of Solids and Structures, vol.43, issue.10, 2006.
DOI : 10.1016/j.ijsolstr.2005.06.045

URL : https://hal.archives-ouvertes.fr/hal-00124139

J. Diani, M. Brieu, and J. M. Vacherand, A damage directional constitutive model for Mullins effect with permanent set and induced anisotropy, European Journal of Mechanics - A/Solids, vol.25, issue.3, pp.483-496, 2006.
DOI : 10.1016/j.euromechsol.2005.09.011

URL : https://hal.archives-ouvertes.fr/hal-00086217

J. Diani, B. Fayolle, and P. Gilormini, A review on the Mullins effect, European Polymer Journal, vol.45, issue.3, pp.601-612, 2009.
DOI : 10.1016/j.eurpolymj.2008.11.017

URL : https://hal.archives-ouvertes.fr/hal-00773015

L. Dorfmann and R. W. Ogden, A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber, International Journal of Solids and Structures, vol.41, issue.7, pp.1855-1878, 2004.
DOI : 10.1016/j.ijsolstr.2003.11.014

L. Dorfmann and F. Pancheri, A constitutive model for the Mullins effect with changes in material symmetry, International Journal of Non-Linear Mechanics, vol.47, issue.8, pp.874-887, 2012.
DOI : 10.1016/j.ijnonlinmec.2012.05.004

J. Gillibert, M. Brieu, and J. Diani, Anisotropy of direction-based constitutive models for rubber-like materials, International Journal of Solids and Structures, vol.47, issue.5, pp.640-646, 2010.
DOI : 10.1016/j.ijsolstr.2009.11.002

URL : https://hal.archives-ouvertes.fr/hal-00444336

S. Göktepe and C. Miehe, A micro-macro approach to rubber-like materials. Part III: The micro-sphere model of anisotropic Mullins-type damage, Journal of the Mechanics and Physics of Solids, vol.53, issue.10, 2005.
DOI : 10.1016/j.jmps.2005.04.010

S. Govindjee and J. C. Simo, A micro-mechanically based continuum damage model for carbon black-filled rubbers incorporating Mullins' effect, Journal of the Mechanics and Physics of Solids, vol.39, issue.1, pp.87-112, 1991.
DOI : 10.1016/0022-5096(91)90032-J

G. A. Holzapfel, M. Stadler, and R. W. Ogden, Aspects of stress softening in filled rubbers incorporating residual strains. Constitutive models for rubber, 1999.

M. Itskov, A. Ehret, R. Kazakeviciute-makovska, and G. Weinhold, A thermodynamically consistent phenomenological model of the anisotropic Mullins effect, ZAMM, vol.9, issue.3, pp.370-386, 2010.
DOI : 10.1002/zamm.200900279

H. M. James and A. Green, Strain energy functions of rubber. II. The characterization of filled vulcanizates, Journal of Applied Polymer Science, vol.19, issue.8, pp.2319-2330, 1975.
DOI : 10.1002/app.1975.070190822

H. M. James and E. Guth, Theory of the Elastic Properties of Rubber, The Journal of Chemical Physics, vol.11, issue.10, pp.455-481, 1943.
DOI : 10.1063/1.1723785

M. A. Johnson and M. F. Beatty, The mullins effect in uniaxial extension and its influence on the transverse vibration of a rubber string, Continuum Mechanics and Thermodynamics, vol.69, issue.2, pp.83-115, 1993.
DOI : 10.1007/BF01141446

M. A. Johnson and M. F. Beatty, The Mullins effect in equibiaxial extension and its influence on the inflation of a balloon, International Journal of Engineering Science, vol.33, issue.2, pp.223-245, 1995.
DOI : 10.1016/0020-7225(94)E0052-K

W. Kuhn and F. Grün, Beziehunger zwichen elastischen konstanten und dehnungsdoppelbrechung hochelastischerstoffe, Kolloideitschrift, vol.101, pp.248-271, 1942.

L. Cam, J. B. Huneau, B. Verron, E. Gornet, and L. , Mechanism of Fatigue Crack Growth in Carbon Black Filled Natural Rubber, Macromolecules, vol.37, issue.13, pp.5011-5017, 2004.
DOI : 10.1021/ma0495386

URL : https://hal.archives-ouvertes.fr/hal-01492140

G. Machado, G. Chagnon, and D. Favier, Induced anisotropy by the Mullins effect in filled silicone rubber, Mechanics of Materials, vol.50, pp.70-80, 2012.
DOI : 10.1016/j.mechmat.2012.03.006

G. Machado, G. Chagnon, and D. Favier, Theory and identification of a constitutive model of induced anisotropy by the Mullins effect, Journal of the Mechanics and Physics of Solids, vol.63, pp.29-39, 2014.
DOI : 10.1016/j.jmps.2013.10.008

URL : https://hal.archives-ouvertes.fr/hal-00958608

G. Marckmann, E. Verron, L. Gornet, G. Chagnon, P. Charrier et al., A theory of network alteration for the Mullins effect, Journal of the Mechanics and Physics of Solids, vol.50, issue.9, pp.2011-2028, 2002.
DOI : 10.1016/S0022-5096(01)00136-3

URL : https://hal.archives-ouvertes.fr/hal-01004954

Y. Merckel, M. Brieu, J. Diani, and J. Caillard, A Mullins softening criterion for general loading conditions, Journal of the Mechanics and Physics of Solids, vol.60, issue.7, pp.1257-1264, 2012.
DOI : 10.1016/j.jmps.2012.04.001

URL : https://hal.archives-ouvertes.fr/hal-00696158

Y. Merckel, J. Diani, M. Brieu, and J. Caillard, Constitutive modeling of the anisotropic behavior of Mullins softened filled rubbers, Mechanics of Materials, vol.57, pp.30-41, 2013.
DOI : 10.1016/j.mechmat.2012.10.010

URL : https://hal.archives-ouvertes.fr/hal-00992343

C. Miehe, Discontinuous and continuous damage evolution in Ogden type large strain elastic materials, Eur. J. Mech, vol.14, issue.5, pp.697-720, 1995.

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

A. H. Muhr, J. Gough, and I. H. Gregory, Experimental determination of model for liquid silicone rubber: Hyperelasticity and Mullins effect, Proceedings of the First European Conference on Constitutive Models for Rubber, pp.181-187, 1999.

L. Mullins, Effect of Stretching on the Properties of Rubber, Rubber Chemistry and Technology, vol.21, issue.2, pp.275-289, 1947.
DOI : 10.5254/1.3546914

L. Mullins, Softening of Rubber by Deformation, Rubber Chemistry and Technology, vol.42, issue.1, pp.339-362, 1969.
DOI : 10.5254/1.3539210

R. W. Ogden and D. G. Roxburgh, A pseudo-elastic model for the Mullins effect in filled rubber, Proc. R. Soc. Lond. A 455, pp.2861-2877, 1999.
DOI : 10.1098/rspa.1999.0431

H. Pawelski, Softening behaviour of elastomeric media after loading in changing directions. Constitutive models for rubber, pp.27-34, 2001.

M. Rebouah and G. Chagnon, Permanent set and stress-softening constitutive equation applied to rubber-like materials and soft tissues, Acta Mechanica, vol.61, issue.6, pp.1685-1698, 2014.
DOI : 10.1007/s00707-013-1023-y

URL : https://hal.archives-ouvertes.fr/hal-00963802

M. Rebouah, G. Machado, G. Chagnon, and D. Favier, Anisotropic Mullins stress softening of a deformed silicone holey plate, Mechanics Research Communications, vol.49, pp.36-43, 2013.
DOI : 10.1016/j.mechrescom.2013.02.002

A. Robisson, Comportement mécanique d'unélastomèreunélastomère chargé en silice. Etude de l'influence des charges et modélisation par une loi viscohyperélastique endommageable, 2000.

M. H. Shariff, An anisotropic model of the Mullins effect, Journal of Engineering Mathematics, vol.42, issue.4, pp.415-435, 2006.
DOI : 10.1007/s10665-006-9051-4

A. L. Svistkov and L. A. Komar, Modeling of relaxation processes in filled elastomeric materials, Polym. Sci. Ser. A, vol.47, issue.4, pp.370-375, 2005.

L. R. Treloar, Stress-strain data for vulcanised rubber under various types of deformation, Transactions of the Faraday Society, vol.40, pp.59-70, 1944.
DOI : 10.1039/tf9444000059

K. C. Valanis and R. F. Landel, The Strain-Energy Function of a Hyperelastic Material in Terms of the Extension Ratios, Journal of Applied Physics, vol.38, issue.7, pp.2997-3002, 1967.
DOI : 10.1063/1.1710039