A MULTISCALE MODEL FOR RUBBER VISCOELASTICITY UNDER SHEAR DEFORMATION

N. G. MEDHIN

Title	A MULTISCALE MODEL FOR RUBBER VISCOELASTICITY UNDER SHEAR DEFORMATION
Publication Type	Journal Article
Year of Publication	2008
Authors	MEDHIN, NG
Volume	12
Issue	2
Start Page	147
Pagination	14
Date Published	2008
ISSN	1083-2564
Abstract	A molecular based model for the viscoelasticity of rubber under shear deformation is developed using a stick-slip continuous molecular model. In our model cross-linked(CC)-system of molcules restrict the motion of entrapped or physically constrained(PC)-molecules. The dynamics of the PC-molecules is modeled by reptation in which the CC-molecules act as constraint boxes and the PC-molecules have to reptate in between the CC-molecules. We assume that a CC-unit cell is placed at each point of the rubber continuum with an entrapped PC-cell inside it. The deformation of the CC-cell causes a deformation of the PC-system which relaxes after removal of the deformation. In the relaxation process the PC-molecules act as internal variables affecting the relaxation process of the CC-system. The Rouse model for relaxing polymers is incorporated into the stick-slip model presented by Johnson and Stacer [13] for describing the dynamics of the entrapped molecule for a short time right after instantneous step-strain of the constraining CC-cell.
URL	http://www.acadsol.eu/en/articles/12/2/4.pdf
Refereed Designation	Refereed
Full Text	REFERENCES [1] H.T. Banks, J.B. Hood, and N.G. Medhin. A molecular based model for polymer viscoelasticity: Intra- and inter-molecular variability. Technical Report CRSC-TR04-39, NCSU, 2004. [2] H. T. Banks, and N.G. Medhin. A Molecular Based Model for Viscoelactic Responses of Rubber in Tensile Deformations, Communications on Applied Nonlinear Analysis 8(2001), No. 3, 1–18. [3] H.T. Banks, N.G. Medhin, G. Pinter. Multiscale Consideration in Modeling of Nonlinear Elastomers.(To appear: Journal of Computational Methods in Sciences and Engineering). [4] H.T. Banks, N.G. Medhin, G. Pinter. Nonlinear Reptation in Molecular Based Hysteresis Models for Polymers. (Quarterly of Applied Mathematics, 2004.) [5] H.T. Banks, N.G. Medhin, G. Pinter. Nonlinear Shear Deformations of Elastomers. (To be submitted) [6] H.T. Banks, G.A. Pinter and L.K. Potter. “Existence of Unique Weak Solutions to a Dynamical System for Nonlinear Elastomers with Hysteresis”, CRSC-TR98-43, NCSU, Nov. 1998; Differential and Integral Equations, 13 (2000). [7] H.T. Banks, G.A. Pinter, L.K. Potter, M.J. Gaitens and L.C. Yanyo. “Modeling of Nonlinear Hysteresis in Elastomers Under Uniaxial Tension”, CRSC-TR99-09, NCSU, Feb. 1999; J. Intelligent Materaial Systems and Structures 10 (1999) pp. 116–134. [8] M. Doi and S.F. Edwards. The Theory of Polymer Dynamics, Oxford, New York, 1986. [9] de Gennes, Scaling Concepts in Polymer Physics(Cornell Univ. Press, Ithaca (1991). [10] de Gennes, P. G. Molecular individualism, Science 276, 199 (1997). [11] S.F. Edwards, Proc. Phys. Soc. 92 (1967). [12] W.W. Graessly, Entangled linear, branched and Network Polymer Systems-Molecular Theories, Adv. Polym. Sci. 47 (1982) pp. 67–117. [13] A.R. Johnson and R.G. Stacer, Rubber Viscoelasticity Using the Physically constrained Systems Stretches as Internal Variables, Rubber Chemistry and Technology, 66 (1993), pp. 567– 577. [14] N.G. Medhin, Molecular-Based Model for Hysteresis with Random Forcing, Contemporary Problems in Mathematical Physics, ed. J. Gvaerts, M. Hounkonnou, A. Msezane, World Scientific Pub. Co. 2002, pp. 259–267. [15] L.R.G. Treloar, The Physics of Rubber Elasticity, Clarendon, Oxford 1975. [16] H.T. Banks and N. Lybeck, Modeling methodology for elastomer dynamic, in Systems and Control in the 21st Century, Birkhauser, Boston, 1996, pp. 37–50. [17] H.T. Banks, N.J. Lybeck, M.J. Gaitens, B.C. Munoz and L.C. Yanyo, Computational methods for estimation in the modeling of nonlinear elastomers, CRSU-TR95-40, NCSU, Kybernetika 32 (1996), pp. 526–542. [18] H.T. Banks, D.S. Gilliam and V.I. Shubov, Global solvability for damped abstract nonlinear hyperbolic systems, Differential and Integral Equations 10 (1997), pp. 309–332. [19] H.T. Banks and G. A. Pinter, Approximation results for parameter estimation in nonlinear elastomers, Control and Estimation of Distributed Parameter Systems, F. Kappel, et. al., eds., Birkhauser, Boston, 1997. [20] H.T. Banks, N.J. Lybeck, M.J. Gaitens, B.C. Munoz and L.C. Yanyo, Computational methods for estimation in the modeling of nonlinear elastomers, CRSU-TR95-40, NCSU, Kybernetika 32 (1996), pp. 526–542. [21] H.T. Banks, G.A. Pinter, and L.K. Potter, Modeling of Nonlinear Hysteresis in Elastomers Under Uniaxial Tension, J. Intelligent Material Systems and Structures 10 (1999), pp. 116–134. [22] H.T. Banks and G.A. Pinter, Damping: hysteretic damping and models. Encyclopedia of Vibrations, Academic Press, London, 2001, pp. 658–664. [23] M. Doi. Introduction to Polymer Physics. Clarendon Press, Oxford, 1996. [24] Jiro Doke. Grabit.m. The MathWorks MatLab Central Website, March 17, 2005. http://www.mathworks.com/matlabcentral/fileexchange (accessed April 13, 2005). [25] D.P. Fyhrie and J.R. Barone. Polymer dynamics as a mechanistic model for the flowindependent viscoelasticity of cartilage. J. Biomech. Eng., 125:578–584, 2003. [26] C.Y. Huang, V.C. Mow, and G.A. Ateshian. The role of flow-independent viscoelasticity in the biphasic tensile and compressive responses of articular cartilage. J. Biomech. Eng., 123:410– 417, 2001. [27] R.W. Ogden. Non-Linear Elastic Deformations. Ellis Horwood Limited, Chichester, 1984. [28] E. Riande, R. Diaz-Calleja, M.G.Prolongo, R.M. Masegosa, and C. Salom. Polymer Viscoelasticity - Stress and Strain in Practice. Marcel Dekker, Inc, New York, 2000.