Abstract
Visco-elastic properties of polymers and elastomers are of fundamental importance to understand their mechanical behavior, especially dealing with dynamic and vibration problems. In this paper experimental results of a series of compression and tension tests on specimens of styrene-butadiene rubber and polypropylene plastic are presented; tests consist in cyclic loading at different frequencies, relaxation tests and creep tests. Experimental data are used to calibrate some linear viscoelastic models; besides the classical approach based on a combination in series or parallel of standard mechanical elements (springs and dashpots), a new method based on differential equations of fractional order (Fractional Derivative Model) is investigated. The two approaches are compared analyzing their capability to reproduce the experimental data.
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References
Chunyu Li, Jim Lua, “A hyper-viscoelastic constitutive model for polyurea”, Materials letters, 63, 877–880, 2009.
N. Huber, C. Tsakmakis, “Finite deformation viscoelasticity laws”, Mechanics of materials, 32, 1–18, 2000.
S.W. Park, “Analytical modeling of viscoelastic dampers for structural and vibration control”, International Journal of Solids and Structures, 38, 8065–8092, 2001.
A.F.M.S. Amin, M.S. Alam, 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, 34, 75–95, 2002.
V.L. Popov, T. Geike, “A new constitutive model of rubber”, Tribology International, 40, 1012–1016, 2007.
A.R. Bhuiyan, Y. Okui, H. Mitamura, T. Imai, “A rheology model of high damping rubber bearings for seismic analysis: identification of nonlinear viscosity”, International Journal of Solids and Structures, 46
1778–1792, 2009.
K.B. Oldham, J. Spanier, “The fractional calculus”, New York: academic press, 1974.
R.L. Bagley, P.J. Torvik, “On the fractional calculus model of viscoelastic behavior”, Journal of Rheology, 30, 133–155, 1986.
T.M. Atanackovic, “A modified Zener model of a viscoelastic body”, Continuum Mech. Thermodyn., 14, 137–148, 2002.
T.M. Atanackovic, B. Stankovic, “Dynamics of viscoelastic rod of fractional derivative type”, ZAMM –Journal of Applied Mathematics and Mechanics, 82, 377–386, 2002.
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Sasso, M., Palmieri, G., Amodio, D. (2011). Application of Fractional Derivatives Models to Time-dependent Materials. In: Proulx, T. (eds) Time Dependent Constitutive Behavior and Fracture/Failure Processes, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9794-4_31
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DOI: https://doi.org/10.1007/978-1-4419-9794-4_31
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