Finite Deformation and Viscoelasticity Modeling and Test
Tibi Beda, Yvon Chevalier, Kokou-Esso Atcholi, Essole Padayodi, Jean-Claude Sagot
DOI: 10.4236/eng.2011.38098   PDF    HTML     5,497 Downloads   10,049 Views   Citations


A model is considered as a representation of compressive and incompressive elastomeric materials in nonlinear behavior. Applications are done on one hand by the characterisation of polyurethane 60 - 65 shore A (a compressive material), and on the other hand by the characterisation of polyurethane 95 shore A and fluorosilicone, both incompressive materials. The Rivlin energy expression is used for incompressive materials. Linear vibrations superposed on static large deformation, which is most often the real using state of elastomeric materials, are studied. Relative experimental and numerical results presented show good predictions.

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T. Beda, Y. Chevalier, K. Atcholi, E. Padayodi and J. Sagot, "Finite Deformation and Viscoelasticity Modeling and Test," Engineering, Vol. 3 No. 8, 2011, pp. 810-814. doi: 10.4236/eng.2011.38098.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. Salencon, “Mécanique des Milieux Continus,” Editions El-lispe, Paris, 1988.
[2] J. S. Lai and N. W. Findley, “Stress Relaxation of Nonlinear Viscoelastic Material under Uniaxial Strain,” Transactions of the Society of Rheolog, Vol. 12, No. 2, 1968, pp. 259-280. doi:10.1122/1.549108
[3] F. J. Locket, “Nonlinear Viscoelastic Solids,” Academic Press, San Diego, 1972.
[4] A. Molinari, “Sur la Relaxation Entre Fluage et Relaxation en Viscoélasticité non Linéaire,” Comptes Rendus, Académie des Sciences, Tome 277, Série A, 1973, pp. 621-623.
[5] C. Huet, “Relations between Creep and Relaxa-tion Function in Nonlinear Viscoelasticity with or without Aging,” Journal of Rheology, Vol. 29, No. 3, 1985, pp. 245-257. doi:10.1122/1.549789
[6] B. D. Coleman and W. Noll, “Foundation of Linear Viscoelasticity,” Reviews of Modern Physics, Vol. 33, No. 2, 1961, pp. 239-249. doi:10.1103/RevModPhys.33.239
[7] R. A. Schapery, “On the Characterization of Nonlinear Viscoelastic Materials,” Polymer Engineering Science, Vol. 9, No. 4, 1969, pp. 295-310. doi:10.1002/pen.760090410
[8] N. P. O’Dowd and W. G. Knauss, “Time Dependent Large Principal Deformation of Polymers,” Journal of the Mechanics and Physics of Solids, Vol. 43, No. 5, 1996, pp. 771-792.
[9] K. C. Valanis and R. F. Landel, “Large Axial Deformation Behavior of Filled Rubber,” Trans. of the Soc. of Rheo., Vol. 11, 1967, pp. 213-256. doi:10.1122/1.549080
[10] T. Beda and Y. Chevalier, “Sur le Comportement Statique et Dynamique des élastomères en Grandes Déformations,” Mécanique Industrielle et Matériaux, Vol. 50, No. 5, 1997, pp. 228-231.
[11] R. W. Ogden, “Nonlinear Elastic Deformation,” Ellis Horwood Edition, Robson, 1984.
[12] T. Beda, Y. Chevalier, H. Gacem and P. Mbarga, “Domain of Validity and Fit of Gent-Thomas and Flory-Erman Rubber Models to Data,” Express Polymer Letters, Vol. 2, No. 9, 2008, pp. 615-622. doi:10.3144/expresspolymlett.2008.74
[13] T. Beda, “Com-bining Approach in Stages with Least Squares for Fits of Data in Hyperelasticity,” Comptes Rendus Mecanique, Académie des Sciences, Elsevier, Paris, Vol. 334, No. 10, 2006, pp. 628-633.
[14] H. Bechir, “Comportement Viscoélastique des élas-tomères de Polyuréthane en Grandes Déformations— Modéli-sation—Validation,” PhD Thesis in Mechanics, CNAM, Paris, 1996.
[15] M. Soula, T. Ving, Y. Chevalier, T. Beda and C. Esteoule, “Measurements of Isothermal Complex Moduli of Viscoelastic Materials over a Large Range of Frequencies,” Journal of Sound and Vibration, Vol. 205, No. 2, 1997, pp. 167-184. doi:10.1006/jsvi.1997.0978
[16] M. Soula, T. Ving and Y. Chevalier, “Transient Responses of Polymers and Elastomers Deduced from Harmonic Responses,” Journal of Sound and Vibration, Vol. 205, No. 2, 1997, pp. 185-203. doi:10.1006/jsvi.1997.0979
[17] Y. Chevalier, T. Beda and J. Merdrignac, “Détermination de Modules d’Young Complexes par Identification,” Mécanique Matériaux, Electricité, GAMI, No. 431, 1989, pp. 55-60.
[18] T. Beda and Y. Chevalier, “Identification of Viscoelastic Fractional Complex Modulus,” American Institute of Aeronautics and Astronautics Journal, AIAA, Vol. 42, No. 7, 2004, pp. 1450-1456.
[19] Y. Chevalier and T. Beda, “Fractional Derivative in Materials and Structures Vibratory Behaviour: Identification Methods,” Journal Eu-ropéen des Systèmes Automatisés, Hermès Lavoisier, Vol. 42, No. 6-7-8, 2008, pp. 863-877.
[20] M. Soula and Y. Chevalier, “La Dérivée Fractionnaire en Rhéologie des Po-lymères—Application aux Comportements éLastiques et Vis-coélastiques Linéaires et non Linéaires des élastomères,” ESAIM Proceeding, Vol. 5, 1998, pp. 193-204. doi:10.1051/proc:1998007
[21] A. D. Nashif, D. I. J. Jones and J. P. Henderson, “Vibration Damping,” Wiley, New York, 1984.

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