C. Esveld, Modern Railway Track, Second Edition, 2001.

S. Becker and K. H. Lier, Bewertung und Varianten-vergleich von Bauarten der Festen Fahrbahn, Eisenbahn Ingenieur, issue.2, 1999.

G. Oberweiler, Die Feste Fahrbahn-Entwicklung und Beurteilung aus der Sicht des Anwenders, 1989.

J. Hillig, Erdbautechnische Anforderungen an eine schotterlose Fahrbahn, Eisenbahn Ingenieur, vol.5, 1994.

A. Pfleiderer, Rheda 2000-Die monolitische Feste Fahrbahn mit Direktafbau auf HGT

H. Widmann, Feste Fahrbahn Bauan Züblin, Feste Fahrbahn, 1997.

J. Eisenmann, Oberbauforschung-Oberbautechnik, Stand und Weiterentwicklung, p.10, 1985.

R. Lutz, Survey of the work by ORE about Railway Noise, Third International Workshop on Railway and Tracked Transit System Noise, 1981.

G. Paul and W. , Rail system noise and vibration control, Proceedings of ACOUSTICS, 2004.

M. Berg, A model for rubber springs in the dynamic analysis of rail vehicles, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, pp.95-108, 1997.

J. D. Ferry, Viscoelastic Properties of Polymers, 1980.

W. Battermann and R. Köhler, Elastomere Federung Elastische Lagerungen, 1982.

E. F. Göbel, Rubber Springs Design, 1974.

P. B. Lindley, Engineering Design with Natural Rubber, NR Technical Bulletin, 1992.

C. M. Harris, Shock and Vibration Handbook?Properties of Rubber, Ch, vol.35, 1988.

A. N. Gent, Engineering with Rubber-How to Design Rubber Components

H. Dal and M. Kaliske, Bergström?Boyce model for nonlinear finite rubber viscoelasticity: theoretical aspects and algorithmic treatment for the FE method, Computational Mechanics, pp.809-823, 2009.

M. Sasso, G. Palmieri, G. Chiappini, and D. Amodio, Characterization of hyperelastic rubber-like materials by biaxial and uniaxial stretching tests based on optical methods, Polymer Testing, vol.27, issue.8, pp.995-1004, 2008.
DOI : 10.1016/j.polymertesting.2008.09.001

A. S. Wineman and K. R. Rajagopal, Mechanical Response of Polymers, An Introduction, 2000.

H. T. Banks, S. Hu, and Z. R. Kenz, A brief review of elasticity and viscoelasticity, CRSC-TR10-08, Advances in Applied Mathematics and Mechanics, 2010.

M. Gurtin and E. Sternberg, On the linear theory of viscoelasticity, Archive for Rational Mechanics and Analysis, pp.291-365, 1965.

T. H. Shellhammer, T. R. Rumsey, and J. M. Krochta, Viscoelastic properties of edible lipids, Journal of Food Engineering, vol.33, issue.3-4, pp.305-320, 1997.
DOI : 10.1016/S0260-8774(97)00030-7

C. S. Drapaca, S. Sivaloganathan, and G. Tenti, Nonlinear Constitutive Laws in Viscoelasticity, Mathematics and Mechanics of Solids, vol.12, issue.5, pp.475-501, 2007.
DOI : 10.1177/1081286506062450

Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissue, 1993.

F. J. Lockett, Nonlinear Viscoelastic Solids, Academic, 1972.

K. N. Morman and J. , Rubber viscoelasticity ? a review of current understanding, Proceedings of the Second Symposium on Analysis and Design of Rubber Parts, pp.14-15, 1985.

R. A. Schapery, Nonlinear viscoelastic solids, International Journal of Solids and Structures, vol.37, issue.1-2, pp.359-366, 2000.
DOI : 10.1016/S0020-7683(99)00099-2

J. Smart and J. G. Williams, A comparison of single-integral non-linear viscoelasticity theories, Journal of the Mechanics and Physics of Solids, vol.20, issue.5, pp.313-324, 1972.
DOI : 10.1016/0022-5096(72)90027-0

A. E. Green and R. S. Rivlin, The mechanics of non-linear materials with memory, Archive for Rational Mechanics and Analysis, pp.1-21, 1957.

A. C. Pipkin and T. G. Rogers, A non-linear integral representation for viscoelastic behaviour, Journal of the Mechanics and Physics of Solids, vol.16, issue.1, pp.59-72, 1968.
DOI : 10.1016/0022-5096(68)90016-1

A. Wineman, Nonlinear Viscoelastic Solids--A Review, Mathematics and Mechanics of Solids, vol.14, issue.3, pp.300-366, 2009.
DOI : 10.1177/1081286509103660

J. G. Oakley, A. J. Giacomin, and J. A. Yosick, Molecular origins of nonlinear viscoelasticity, Mikrochimica Acta, vol.34, issue.4, pp.1-28, 1998.
DOI : 10.1007/BF01254586

M. Liu and M. , A constitutive equation for filled rubber under cyclic loading, International Journal of Non-Linear Mechanics, vol.46, issue.2, pp.446-456, 2011.
DOI : 10.1016/j.ijnonlinmec.2010.11.006

H. T. Banks and N. Luke, Modelling of propagating shear waves in biotissue employing an internal variable approach to dissipation, Communication in Computational Physics, vol.3, pp.603-640, 2008.

H. T. Banks, N. G. Medhin, and G. A. Pinter, Nonlinear reptation in molecular based hysteresis models for polymers, Quarterly of Applied Mathematics, vol.62, issue.4, pp.767-779, 2004.
DOI : 10.1090/qam/2104273

J. E. Soussou, F. Moavenzadeh, and M. H. Gradowczyk, Application of Prony Series to Linear Viscoelasticity, Transactions of the Society of Rheology, vol.14, issue.4, pp.573-584, 1970.
DOI : 10.1122/1.549179

P. Haupt and A. , Lion, on finite linear viscoelasticity of incompressible isotropic materials Acta Mech, pp.87-124, 2002.

J. S. Bergström and M. C. Boyce, Constitutive modelling of the large strain time-dependent behaviour of elastomers, J. Mech. Phys. Solids, pp.46-931, 1998.

J. S. Bergström and M. C. Boyce, Constitutive modeling of the time-dependent and cyclic loading of elastomers and application to soft biological tissues, Mechanics of Materials, vol.33, issue.9, pp.523-530, 2001.
DOI : 10.1016/S0167-6636(01)00070-9

Y. Tomita, K. Azuma, and M. Naito, Computational evaluation of strain-rate-dependent deformation behavior of rubber and carbon-black-filled rubber under monotonic and cyclic straining, International Journal of Mechanical Sciences, vol.50, issue.5, pp.856-868, 2008.
DOI : 10.1016/j.ijmecsci.2007.09.010

A. Lion, A constitutive model for carbon black filled rubber: Experimental investigations and mathematical representation, Continuum Mechanics and Thermodynamics, vol.16, issue.1, pp.153-169, 1996.
DOI : 10.1007/BF01181853

A. Lion, A physically based method to represent the thermo-mechanical behaviour of elastomers, Acta Mechanica, vol.75, issue.7, pp.1-25, 1997.
DOI : 10.1007/BF01178397

S. Reese and S. Govindjee, A theory of finite viscoelasticity and numerical aspects, International Journal of Solids and Structures, vol.35, issue.26-27, pp.3455-3482, 1998.
DOI : 10.1016/S0020-7683(97)00217-5

N. Huber and C. Tsakmakis, Finite deformation viscoelasticity laws, Mechanics of Materials, vol.32, issue.1, pp.1-18, 2000.
DOI : 10.1016/S0167-6636(99)00045-9

A. F. Amin, A. Lion, S. Sekita, and Y. Okui, Non-linear dependence of viscosity in modelling the rate-dependent response of natural and high damping rubbers in compression and shear: experimental identification and numerical verification, Int. J. Plast, pp.22-1610, 2006.

J. Simo and C. Miehe, Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation, Computer Methods in Applied Mechanics and Engineering, vol.98, issue.1, pp.41-104, 1992.
DOI : 10.1016/0045-7825(92)90170-O

J. Simo, Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory, Computer Methods in Applied Mechanics and Engineering, vol.99, issue.1, pp.61-112, 1992.
DOI : 10.1016/0045-7825(92)90123-2

G. Weber and L. Anand, Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids, Computer Methods in Applied Mechanics and Engineering, vol.79, issue.2, pp.173-202, 1990.
DOI : 10.1016/0045-7825(90)90131-5

A. Cuitino and M. Ortiz, A MATERIAL???INDEPENDENT METHOD FOR EXTENDING STRESS UPDATE ALGORITHMS FROM SMALL???STRAIN PLASTICITY TO FINITE PLASTICITY WITH MULTIPLICATIVE KINEMATICS, Engineering Computations, vol.9, issue.4, pp.437-451, 1992.
DOI : 10.1108/eb023876

H. T. Banks, N. G. Medhin, and G. A. Pinter, Multiscale considerations in modelling of nonlinear elastomers, J. Comp. Meth. Engr. Sci. and Mech, vol.8, pp.53-62, 2003.

H. T. Banks, N. G. Medhin, and G. A. Pinter, Modelling of viscoelastic shear: A nonlinear stick-slip formulation, pp.17-383, 2006.

H. T. Banks and G. A. Pinter, Damping: hysteretic damping and models, CRSC-TR99-36, NCSU, pp.658-664, 1999.

P. Höfer and . Lion, Modelling of frequency- and amplitude-dependent material properties of filler-reinforced rubber, Journal of the Mechanics and Physics of Solids, vol.57, issue.3, pp.500-520, 2009.
DOI : 10.1016/j.jmps.2008.11.004

Y. C. Fung, Foundation of Solid Mechanics, Journal of Applied Mechanics, vol.33, issue.1, 1965.
DOI : 10.1115/1.3625018

Y. C. Fung, A First Course in Continuum Mechanics, 1994.

H. T. Banks and G. A. Pinter, A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue, Multiscale Modelling and Simulation, pp.395-412, 2005.

H. T. Banks, G. A. Pinter, L. K. Potter, M. J. Gaitens, and L. C. Yanyo, Modelling of quasistatic and dynamic load responses of filled viscoelastic materials, CRSC-TR98-48, NCSU, Mathematical Modelling: Case Studies from Industry (E. Cumberbatch and A. Fitt, pp.229-252, 1998.

H. T. Banks, G. A. Pinter, L. K. Potter, B. C. Munoz, and L. C. Yanyo, Estimation and control related issues in smart material structures and fluids, CRSC-TR98-02, NCSU, pp.19-34, 1998.

B. Häggblad, Finite element techniques for engineering rubber problems, Int. J. Numer. Methods in Engng

A. C. Pipkin, Lectures on Viscoelasticity Theory, 1986.
DOI : 10.1007/978-1-4615-9970-8

J. Nicolin and T. Dellmann, Über die modellhafte Nachbildung der dynamischen Eigenschaften einer Gummifeder , ZEV-Glasers Annalen, pp.169-175, 1985.

M. Berg, A Non-Linear Rubber Spring Model for Rail Vehicle Dynamics Analysis, Vehicle System Dynamics, International Journal of Vehicle Mechanics and Mobility, vol.29, 1998.

M. Sjöberg, On Dynamic Properties of Rubber Isolators, 2002.

P. Austrell, A. Olsson, and M. J¨onsson, A method to analyse the nonlinear dynamic behaviour of carbon-black-filled rubber components using standard FE codes

E. Betz, Spring and dashpot models and their applications in the study of the dynamic properties of rubber. Mechanical and Chemical Engineering Transactions, pp.15-24, 1969.

B. Lodhia and I. Esat, Vibration simulation of systems incorporating linear viscoelastic mounts using prony series formulation, Proceedings of Engineering Systems Design and Analysis Conference, pp.171-176, 1996.

A. Olsson and P. Austrell, A fitting procedure for a viscoelastic-elastoplastic material model, Constitutive Models for Rubber II. Swets and Zeitlinger, pp.205-211, 2001.

S. Park, Analytical modelling of viscoelastic dampers for structural and vibration control, International Journal of Solids and Structures, vol.36, pp.939-970, 2001.

L. Gaul, The influence of damping on waves and vibrations, Mechanical Systems and Signal Processing, vol.13, issue.1, pp.1-30, 1999.
DOI : 10.1006/mssp.1997.0185

Y. Rossikhin and M. Shitikova, Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids, Applied Mechanics Reviews, vol.50, issue.1, 1997.
DOI : 10.1115/1.3101682

N. Shimizu and W. Zhang, Fractional Calculus Approach to Dynamic Problems of Viscoelastic Materials., JSME International Journal Series C, vol.42, issue.4, 1999.
DOI : 10.1299/jsmec.42.825

R. Koeller, Applications of Fractional Calculus to the Theory of Viscoelasticity, Journal of Applied Mechanics, vol.51, issue.2, pp.299-307, 1984.
DOI : 10.1115/1.3167616

P. Cosson and J. Michon, Identification by a non-integer order model of the mechanical behaviour of an elastomer, Chaos, Solitons & Fractals, vol.7, issue.11, pp.1807-1824, 1996.
DOI : 10.1016/S0960-0779(96)00044-6

A. Horr and L. Schmidt, A fractional-spectral method for vibration of damped space structures, Engineering Structures, vol.18, issue.12, pp.947-956, 1996.
DOI : 10.1016/0141-0296(95)00220-0

R. Bagley and P. Torvik, Fractional calculus - A different approach to the analysis of viscoelastically damped structures, AIAA Journal, vol.21, issue.5, pp.741-748, 1983.
DOI : 10.2514/3.8142

X. Moreau, ?. Ramus, C. Serment, and A. Oustaloup, Fractional differentiation in passive vibration control, Nonlinear Dynamics, vol.29, issue.1/4, pp.343-362, 2002.
DOI : 10.1023/A:1016518118007

K. Papoulia and J. Kelly, Visco-Hyperelastic Model for Filled Rubbers Used in Vibration Isolation, Journal of Engineering Materials and Technology, vol.119, issue.3, pp.292-297, 1997.
DOI : 10.1115/1.2812259

L. Kari, P. Eriksson, and B. Stenberg, Dynamic stiffness of natural rubber cylinders in the audible frequency range using wave guides, Kautschuk Gummi Kunststoffe, vol.543, pp.106-113, 2001.

L. Yuan and O. Agrawal, A Numerical Scheme for Dynamic Systems Containing Fractional Derivatives, Journal of Vibration and Acoustics, vol.124, issue.2, pp.321-324, 2002.
DOI : 10.1115/1.1448322

J. Hwang and T. Hsu, A fractional derivative model to include effect of ambient temperature on HDR bearings, Engineering Structures, vol.23, issue.5, pp.484-490, 2001.
DOI : 10.1016/S0141-0296(00)00063-8

L. Eldred, W. Baker, and A. Palazotto, Numerical application of fractional derivative model constitutive relations for viscoelastic materials, Computers & Structures, vol.60, issue.6, pp.875-882, 1996.
DOI : 10.1016/0045-7949(95)00447-5

T. Atanackovic and B. Stankovic, Dynamics of a Viscoelastic Rod of Fractional Derivative Type, Zeitschrift für Angewandte Mathematik und Mechanik, pp.377-386, 2002.
DOI : 10.1002/1521-4001(200206)82:6<377::AID-ZAMM377>3.0.CO;2-M

A. Schmidt and L. Gaul, Finite element formulation of viscoelastic constitutive equations using fractional time derivatives, Nonlinear Dynamics, vol.29, issue.1/4, pp.37-55, 2002.
DOI : 10.1023/A:1016552503411

A. Fenander, Modal synthesis when modelling damping by use of fractional derivatives, 36th Structures, Structural Dynamics and Materials Conference, pp.1051-1058, 1996.
DOI : 10.2514/6.1995-1182

M. Enelund and P. Olsson, Damping described by fading memory???analysis and application to fractional derivative models, International Journal of Solids and Structures, vol.36, issue.7, pp.939-970, 1999.
DOI : 10.1016/S0020-7683(97)00339-9

M. Enelund, L. M¨ahler, K. Runesson, and B. Josefson, Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws, International Journal of Solids and Structures, vol.36, issue.16, pp.2417-2442, 1999.
DOI : 10.1016/S0020-7683(98)00111-5

M. Sjöberg and . Kari, Nonlinear Isolator Dynamics at Finite Deformations: An Effective Hyperelastic, Fractional Derivative, Generalized Friction Model, pp.323-336, 2003.

J. Harris and A. Stevenson, On the Role of Nonlinearity in the Dynamic Behavior of Rubber Components, Rubber Chemistry and Technology, vol.59, issue.5, pp.740-764, 1986.
DOI : 10.5254/1.3538231

B. Ravindra and A. K. Mallik, Hard duffing-type vibration isolator with combined Coulomb and viscous damping, International Journal of Non-Linear Mechanics, vol.28, issue.4, pp.427-440, 1993.
DOI : 10.1016/0020-7462(93)90017-F

B. Ravindra and A. K. Mallik, Performance of Non-linear Vibration Isolators Under Harmonic Excitation, Journal of Sound and Vibration, vol.170, issue.3, pp.325-337, 1994.
DOI : 10.1006/jsvi.1994.1066

B. Ravindra and A. K. Mallik, Chaotic response of a harmonically excited mass on an isolator with non-linear stiffness and damping characteristics, Journal of Sound and Vibration, vol.182, issue.3, pp.345-353, 1995.
DOI : 10.1006/jsvi.1995.0203

S. Natsiavas and P. Tratskas, ON VIBRATION ISOLATION OF MECHANICAL SYSTEMS WITH NON-LINEAR FOUNDATIONS, Journal of Sound and Vibration, vol.194, issue.2, pp.173-185, 1996.
DOI : 10.1006/jsvi.1996.0351

K. Gjika, R. Dufour, and G. Ferraris, TRANSIENT RESPONSE OF STRUCTURES ON VISCOELASTIC OR ELASTOPLASTIC MOUNTS: PREDICTION AND EXPERIMENT, Journal of Sound and Vibration, vol.198, issue.3, pp.361-278, 1996.
DOI : 10.1006/jsvi.1996.0575

N. C. Shekhar, H. Hatwal, and A. K. Mallik, RESPONSE OF NON-LINEAR DISSIPATIVE SHOCK ISOLATORS, Journal of Sound and Vibration, vol.214, issue.4, pp.589-603, 1998.
DOI : 10.1006/jsvi.1997.1468

A. K. Mallik, V. Kher, M. Puri, and H. Hatwal, ON THE MODELLING OF NON-LINEAR ELASTOMERIC VIBRATION ISOLATORS, Journal of Sound and Vibration, vol.219, issue.2, pp.239-253, 1999.
DOI : 10.1006/jsvi.1998.1883

N. C. Shekhar, H. Hatwal, and A. K. Mallik, PERFORMANCE OF NON-LINEAR ISOLATORS AND ABSORBERS TO SHOCK EXCITATIONS, Journal of Sound and Vibration, vol.227, issue.2, pp.293-307, 1999.
DOI : 10.1006/jsvi.1999.2346

C. M. Richards and R. Singh, CHARACTERIZATION OF RUBBER ISOLATOR NONLINEARITIES IN THE CONTEXT OF SINGLE- AND MULTI-DEGREE-OF-FREEDOM EXPERIMENTAL SYSTEMS, Journal of Sound and Vibration, vol.247, issue.5, pp.807-834, 2001.
DOI : 10.1006/jsvi.2001.3759

V. Coveney, D. Johnson, and D. Turner, A Triboelastic Model for the Cyclic Mechanical Behavior of Filled Vulcanizates, Rubber Chemistry and Technology, vol.68, issue.4, pp.660-670, 1995.
DOI : 10.5254/1.3538765

V. Coveney, S. Jamil, D. Johnson, M. Keavey, and H. Williams, Rate dependent triboelastic and other models for elastomers and prospects for implementation in finite element analysis Finite Element Analysis of Elastomers, 1999.

M. Gregory, Dynamic properties of rubber in automotive engineering, Elastomerics, vol.117, issue.11, pp.19-24, 1985.

V. Coveney, S. Jamil, D. Johnson, M. Keavey, C. Menger et al., Implementation in finite element analysis of a triboelastic law for dynamic behaviour of filled elastomers Finite Element Analysis of Elastomers, 1999.

S. Bruni and A. Collina, Modelling the Viscoelastic Behaviour of Elastomeric Components: An Application to the Simulation of Train-Track Interaction, Vehicle System Dynamics, vol.34, issue.4, pp.283-301, 2000.
DOI : 10.1076/vesd.34.4.283.2061

C. Brackbill, G. Lesieutre, E. Smith, and L. Ruhl, Characterization and Modeling of the Low Strain Amplitude and Frequency Dependent Behavior of Elastomeric Damper Materials, Journal of the American Helicopter Society, vol.45, issue.1, pp.34-42, 2000.
DOI : 10.4050/JAHS.45.34

A. Mallik, V. Kher, M. Puri, and H. Hatwal, ON THE MODELLING OF NON-LINEAR ELASTOMERIC VIBRATION ISOLATORS, Journal of Sound and Vibration, vol.219, issue.2, pp.239-253, 1999.
DOI : 10.1006/jsvi.1998.1883

A. Barber, Accurate models for complex vehicle components using empirical methods. SAE Paper No, 1625.

M. Berg, A Three-dimensional airspring model with friction and orifice damping, Vehicle System Dynamics, vol.33, pp.528-539, 1999.

Z. Chen, . Shin, J. Andrawes, and . Edwards, Parametric study on damage and load demand of prestressed concrete crosstie and fastening systems, Engineering Failure Analysis, vol.46, pp.49-61, 2014.
DOI : 10.1016/j.engfailanal.2014.08.002

R. D. Frohling, Low Frequency Dynamic Vehicle/Track Interaction: Modelling and Simulation, Vehicle System Dynamics, vol.24, issue.sup1, pp.30-46, 1998.
DOI : 10.1080/00423119808969550

C. González-nicieza, M. I. Álvarez-fernández, A. Menéndez-díaz, A. E. Álvarez-vigil, and F. , Ariznavarreta-Fernández, Failure analysis of concrete sleepers in heavy haul railway tracks, Eng Fail Anal, pp.15-90, 2008.

F. Rezaie, M. R. Shiri, and S. M. Farnam, Experimental and numerical studies of longitudinal crack control for pre-stressed concrete sleepers, Engineering Failure Analysis, vol.26, pp.21-30, 2012.
DOI : 10.1016/j.engfailanal.2012.07.001

S. Kaewunruen and A. M. Remennikov, NONLINEAR TRANSIENT ANALYSIS OF A RAILWAY CONCRETE SLEEPER IN A TRACK SYSTEM, International Journal of Structural Stability and Dynamics, vol.08, issue.03, pp.505-520, 2008.
DOI : 10.1142/S0219455408002776

H. Yu and D. Jeong, Finite element modelling of railroad concrete crossties ? a preliminary study, ICRE2010 ? International Conference on Railway Engineering, 2010.

H. Yu, D. Jeong, J. Choros, and T. Sussmann, Finite element modelling of prestressed concrete crosstie with ballast and subgrade support, ASME 2011 international design engineering technical conference & computers and information in engineering conference, 2011.

T. Dahlberg and A. Lundqvist, Load impact on railway track due to unsupported sleepers, Proc Inst Mech Eng, Part F: J Rail Rapid Transit, vol.219, pp.67-77129, 2003.

S. Tariq, A. Giacomin, and S. Gunasekaran, Nonlinear viscoelasticity of cheese, Biorheology, vol.35, issue.3, pp.171-191, 1998.
DOI : 10.1016/S0006-355X(99)80006-7

S. Onogi and T. Matsumoto, Rheological properties of polymer solutions and melts containing suspended particles, Polymer Engineering Reviews, vol.1, pp.45-87, 1981.

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

L. Mullins, Mechanical behaviour of polymers ? Accomplishments and problems

M. Sjöberg, Dynamic behaviour of a rubber component in the low frequency range- Measurements and modelling, Proceedings of the 7 th International Conference of Sound and Vibration, Garmisch-Partenkirchen, pp.2955-2962, 2000.

A. Medalia, Effect of Carbon Black on Dynamic Properties of Rubber Vulcanizates, Rubber Chemistry and Technology, vol.51, issue.3, pp.437-523, 1978.
DOI : 10.5254/1.3535748

A. Payne and R. Whittaker, Low Strain Dynamic Properties of Filled Rubbers, Rubber Chemistry and Technology, vol.44, issue.2, pp.440-478, 1971.
DOI : 10.5254/1.3547375

G. Dean, J. Duncan, and A. Johnson, Determination of non-linear dynamic properties of carbon-filled rubbers, Polymer Testing, vol.4, issue.2-4, pp.225-249, 1984.
DOI : 10.1016/0142-9418(84)90014-X

F. Jurado, A. Matero, N. Gil-negrete, J. Vinolas, and L. Kari, Testing and FE modelling of the dynamic properties of carbon black filled rubber, Proceedings of EAEC 99, 1999.

J. Sommer and D. Meyer, Factors controlling the dynamic properties of elastomeric products, 1973.

M. Sjöberg and L. Kari, Testing of nonlinear interaction effects of sinusoidal and noise excitation on rubber isolator stiffness, Polymer Testing, vol.22, issue.3, pp.347-355, 2003.
DOI : 10.1016/S0142-9418(02)00110-1

W. Luo, X. Hu, C. Wang, and Q. Li, Frequency- and strain-amplitude-dependent dynamical mechanical properties and hysteresis loss of CB-filled vulcanized natural rubber, International Journal of Mechanical Sciences, vol.52, issue.2, pp.168-174, 2010.
DOI : 10.1016/j.ijmecsci.2009.09.001

Y. Liu, Y. Luo, and H. P. Yin, Dynamic characteristic analysis of rubber absorber in rail fastening, Journal of Central South University (Science and Technology), vol.42, issue.9, 2011.

Y. Luo, Y. Liu, and H. P. Yin, Numerical investigation of nonlinear properties of a rubber absorber in rail fastening systems, International Journal of Mechanical Sciences, vol.69, pp.107-113, 2013.
DOI : 10.1016/j.ijmecsci.2013.01.034

F. Dinzart and P. Lipinski, Improved five-parameter fractional derivative model for elastomers, Arch. Mech, vol.61, issue.6, pp.459-474, 2009.

R. L. Bagley and P. J. Torvik, Fractional calculus - A different approach to the analysis of viscoelastically damped structures, AIAA Journal, vol.21, issue.5, pp.741-748, 1983.
DOI : 10.2514/3.8142

R. L. Bagley and P. J. Torvik, On the Fractional Calculus Model of Viscoelastic Behavior, Journal of Rheology, vol.30, issue.1, pp.133-135, 1986.
DOI : 10.1122/1.549887

C. Friedrich, Relaxation and retardation functions of the Maxwell model with fractional derivatives, Rheologica Acta, vol.29, issue.2, pp.89-93, 1991.
DOI : 10.1007/BF01134604

T. F. Nonnenmacher and W. G. Glöckle, A fractional model for mechanical stress relaxation, Philosophical Magazine Letters, vol.21, issue.2, pp.89-93, 1991.
DOI : 10.1039/tf9706600080

N. Heymans and J. C. Bauwens, Fractal rheological models and fractional differential equations for viscoelastic behavior, Rheologica Acta, vol.27, issue.3, pp.210-219, 1994.
DOI : 10.1007/BF00437306

H. Schiessel, R. Metzler, A. Blumen, and T. F. Nonnenmacher, Generalized viscolastic models: their fractional equations with solutions, J. Phys. A, issue.23, pp.28-6567, 1995.

A. Rossikhin and M. V. Shitikova, Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids, Applied Mechanics Reviews, vol.50, issue.1, pp.15-67, 1997.
DOI : 10.1115/1.3101682

R. Metzler and T. F. Nonnenmacher, Fractional relaxation processes and fractional rheological models for the description of a class of viscoelastic materials, International Journal of Plasticity, vol.19, issue.7, pp.941-959, 2003.
DOI : 10.1016/S0749-6419(02)00087-6

K. B. Oldham and J. Spanier, The fractional calculus, 1974.

L. Kari, Extended fractional-order derivative viscoelastic material model for structureborn sound analysis, Trita-FKT, p.18, 1997.

S. Jörgen and . Bergström, Dynamic finite element modelling of elastomers, Proceedings of Abaqus Users' Conference, 2008.

D. J. Charlton and J. Yang, A review of methods to characterize rubber elastic behaviour for use in finite element analysis, AIRBOSS LTD

T. Dalrymple, J. Choi, and K. Miller, Elastomer rate-dependence: a testing and material modelling methodology. Fall 172 nd Technical Meeting of the Rubber Division of the

K. Miller, Testing Elastomers for Hyperelastic Material Models in Finite Element Analysis

J. R. Day and K. A. Miller, Equiiaxial Stretching of Elastomeric Sheets, An Analytical Verification of Experimental Technique, Conference Proceedings, 2000.

S. P. Timoshenko, Theory of Elasticity. 3 rd Ed, 1970.

B. Duncan, L. Maxwell, R. Crocker, and . Hunt, Verification of hyperelastic test methods, NPL Report No. CMMT (A), vol.226, 1999.

F. Nassiri, New Approach in characterizing accessory drive belts for finite element applications, 2010.

M. Sasso and G. Palmieri, Characterization of hyperelastic rubber-like materials by biaxial and uniaxial stretching tests based on optical methods, Polymer Testing, vol.27, issue.8, pp.955-1004, 2008.
DOI : 10.1016/j.polymertesting.2008.09.001

K. Miller, Testing elastomers for ANSYS. Axel Products Inc. The Focus, publication for ANSYS users, 2002.

K. Miller, Measuring material properties to build material models in FEA

M. W. Gagnon, P. Hubert, M. P. Paidoussis, C. Semler, and D. Lavoie, Hyperelastic modelling of rubber in commercial finite element software (ANSYS), 51 ST Sample International Symposium, 2006.

J. D. Marshall and . Development, Analysis and Testing of a hybrid Passive Control Deice for Seismic Protection of Framed Structures, 2008.

K. P. Menard, Dynamic mechanical analysis. A practical Introduction

A. Goldman, Prediction of the properties of polymeric and composite materials, ACS, 1994.

P. F. Turnbull, N. C. Perkins, and W. W. Schultz, Contact-Induced Nonlinearity in Oscillating Belts and Webs, Journal of Vibration and Control, vol.1, issue.4, pp.459-479, 1995.
DOI : 10.1177/107754639500100404

A. Hellman, Simulation of complete vehicle dynamics using FE code Abaqus, 2008.

M. Olivero, V. Pulero, M. Barbi, F. Urbinati, B. Peyron et al., Static and dynamic simulations for automotive interiors components using ABAQUS, SIMULIA Community Conference, 2012.

A. N. Gent and P. B. Lindley, The compression of bonded rubber blocks, Proceedings of the institution of mechanicalEngineers, pp.111-122
DOI : 10.1243/PIME_PROC_1959_173_022_02

J. G. Williams and C. Gamonpilas, Using the simple compression test to determine young's modulus, Poisson's ratio and coulomb frictioin coefficient, International Journal of Solids and Structures, issue.16, pp.45-4448

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity

C. O. Horgan and G. Saccomandi, Phenomenological hyperelastic strainstiffening constitutive models for rubber

P. A. Martins, R. M. Jorge, and A. J. Ferreira, A Comparative Study of Several Material Models for Prediction of Hyperelastic Properties: Application to Silicone-Rubber and Soft Tissues, Strain, vol.34, issue.3, pp.135-147, 2006.
DOI : 10.1111/j.1475-1305.2006.00257.x

M. Mooney, A Theory of Large Elastic Deformation, Journal of Applied Physics, vol.11, issue.9, pp.582-592, 1940.
DOI : 10.1063/1.1712836

R. S. Rivlin, Large elastic deformations of isoltropic materials. IV: Further developments of the general theory, Philos. Trans. R. Soc. Lond, pp.241-379, 1948.

R. W. Ogden, Nonlinear Elastic Deformations, Journal of Applied Mechanics, vol.52, issue.3
DOI : 10.1115/1.3169137
URL : https://hal.archives-ouvertes.fr/hal-01303324

G. A. Holzapfel, Nonlinear solid mechanics, 2000.

W. M. Lai, D. Rubin, and E. Krempl, Introduction to continuum mechanics, 3 rd end

J. Shim and D. Mohr, Rate dependent finite strain constitutive model of polyurea, International Journal of Plasticity, vol.27, issue.6, pp.868-886, 2011.
DOI : 10.1016/j.ijplas.2010.10.001

A. F. Amin, M. S. Alam, and Y. Okui, An improved hyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification, Mechanics of Materials, vol.34, issue.2, pp.75-95, 2002.
DOI : 10.1016/S0167-6636(01)00102-8

N. Huber and C. Tsakmakis, Finite deformation viscoelasticity laws, Mechanics of Materials, vol.32, issue.1, pp.1-18, 2000.
DOI : 10.1016/S0167-6636(99)00045-9

J. Lubliner, A model of rubber viscoelasticity, Mechanics Research Communications, vol.12, issue.2, pp.93-99, 1985.
DOI : 10.1016/0093-6413(85)90075-8

P. Letallac, C. Rahier, and A. Kaiss, Three-dimensional incompressible viscoelasticity in large strains: Formulation and numerical approximation, Computer Methods in Applied Mechanics and Engineering, vol.109, issue.3-4, pp.233-258, 1993.
DOI : 10.1016/0045-7825(93)90080-H