This research work aims at modeling the creep behavior of a material by a non-linear schapery’s viscoelastic model. We started with analytical part where three powerful methods of creep modeling have been developed and compared. That is the Heaviside, the Nordin and Varna and lastly our own proposed methods. From this preliminary study, it came out that our method is different to the two others because we took into account the loading time at the creep beginning. Besides we studied several loading programs and retained a five order non-linear polynomial which is the program that gave us satisfactory results. The other loading functions led to divergent results and wasn’t present here as consequence. In the second part of this work, we devoted ourselves to the determination of non-linear parameters in the schapery’s viscoelasticity equation, through a well developed and illustrated methodology. From this study, it is straight forward that non-linear parameters are stress dependent; confirming the results of several authors that preceded us in this studying field.
References
[1]
Talla, P.K., Foadieng, E., Fouotsa, W.C.M., Fogue, M., Bishweka, S., Ngarguededjim K.E., Alabeweh, F.S. and Foudjet, A. (2015) A Contribution to the Study of Entandrophragma Cylindricum Sprague and Lovoa Trichilioides Harms Long Term behaviour. Revue scientifique et Technique Forêt et Environnement du Bassin du Congo, X, 10-21.
[2]
Talla, P.K., Mabekou, J.S., Fogue, M., Fomethe, A., Bawe, G.N., Foadieng, E. and Foudjet, A. (2010) Non-Linear Creep Behavior of Raphia vinifera L. Arecacea under Flexural Load. International Journal of Mechanics and Solids, 5, 151-172.
[3]
Talla, P.K. (2008) Contribution à l’analyse mécanique de Raphia vinifera L. Arecacea. Thèse de Doctorat (Ph.D), Université de Dschang, Faculté des Sciences, Cameroun.
[4]
Talla, P.K., Pelab, F.B., Fogue, M., Fomethe, A., Bawe, G.N., Foadieng, E. and Foudjet, A. (2007) Non-Linear Creep Behavior of Raphia vinifera L. Arecacea. International Journal of Mechanics and Solids, 2, 1-11.
[5]
Foadieng, E., Fogue, M. and Talla, P.K. (2012) Effect of the Span Length on the Deflection and the Creep Behavior of Raffia Bamboo Vinifera L. Arecacea Beam. International Journal of Material Science, 7, 153-167.
[6]
Nordin, L.O. and Varna, J. (2006) Methodology for Parameter Identification in Non-Linear Viscoelastic Material Model. Mech. Time Matter, 9, 259-280.
[7]
Schapery, R.A. (1969) On the Characterization of Non-Linear Viscoelastic Materials. Polymer Engineering & Science, 9, 295-310.
https://doi.org/10.1002/pen.760090410
[8]
Lou, Y.C. and Schapery, R.A. (1971) Viscoelastic Characterization of a Non-Linear Fiber-Reinforced Plastic. Journal of Composite Materials, 5, 208-234.
https://doi.org/10.1177/002199837100500206
[9]
Kshitish, A.P. (2009) Linear and Non-Linear Viscoelastic Characterization of Proton Exchange Membranes and Stress Modeling for Fuel Cell Application. Doctor of Philosophy thesis, Virginia Polytechnic Institute and State University, USA.
[10]
Chien, W.H., Rashid, K.A., Eyad, A.M., Dallas, N.L. and Gordon, D.A. (2011) Numerical Implementation and Validation of a Non-Linear Viscoelastic and Viscoplastic Model for Asphalt Mixes. International Journal of Pavement Engineering, 12, 433-447. https://doi.org/10.1080/10298436.2011.574137
[11]
Zapas, L.J. and Philips, J.C. (1971) Simple Shearing Flows in Polyisobutylene Solutions. Journal of Research of the National Bureau of Standards, 75A, 33-41.
https://doi.org/10.6028/jres.075A.005
Rami, M.H.K. and Anastasia, H.M. (2003) Numerical Finite Element Formulation of the Schapery Non-Linear Viscoelastic Material Model. International Journal for Numerical Methods in Engineering, 59, 25-45.
[14]
Ahlberg, J.H., Nilson, E.N. and Walsh, J.L. (1967) The Theory of Splines and Their Applications. Academic Press, New York.
[15]
Benjamin, B. (2013) Interpolation Polynomiale. Agrégation de mathématiques, Option modélisation, Université de Rennes 1.
[16]
Ratchada, S. and Raffaella, D.V. (2011) A Mathematical Model for Creep, Relaxation and Strain Stiffening in Parallel-Fibered Collagenous Tissues. Journal of Medical Engineering and Physics, 33, 1056-1063.
https://doi.org/10.1016/j.medengphy.2011.04.012
[17]
Calgcagno, B., Lopez, G.M., Kuhns, M. and Lakes, R.S. (2008) On the Non-Linear Creep and Recovery of Open Cell Earplug Foams. Journal of Cellular Polymers, 27, 165-178.
[18]
Kaouther, B.A.A. (2010) Relations entre propriétés rhéologiques et structure microscopique de dispersions de particules d’argile dans des solutions de polymères. Thèse de Doctorat (Ph.D.), Université de Haute Alsace, France.
[19]
Ashish, O., Ray, V.J. and Roderic, S.L. (2003) Interralation of Creep and Relaxation for Non-Linearly Viscoelastic Materials: Application to Ligament and Metal. Rheologica Acta, 42, 557-568. https://doi.org/10.1007/s00397-003-0312-0
[20]
Tuttle, M.E. and Brinson, H.F. (1985) Prediction of the Long-Term Creep Compliance of General Composite Laminates. Experimental Mechanics, 26, 89-102.
https://doi.org/10.1007/BF02319961
[21]
Ever, J.B. (2007) Prediction of Long-Term Creep of Composites from Doubly-Shifted Polymer Creep Data. Journal of Composite Materials.
