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A rheology model of high damping rubber bearings for seismic analysis: identification of nonlinear viscosity. (English) Zbl 1217.74022
Summary: The mechanical behavior of high damping rubber bearings (HDRBs) is investigated under horizontal cyclic shear deformation with a constant vertical compressive load. On the basis of experimental observations, an elasto-viscoplastic rheology model of HDRBs for seismic analysis is developed. In this model, the Maxwell model is extended by adding a nonlinear elastic spring and an elasto-plastic model (spring-slider) in parallel. In order to identify constitutive relations of each element in the rheology model, an experimental scheme comprised of three types of tests, namely a cyclic shear test, a multi-step relaxation test, and a simple relaxation test, are carried out at room temperature. HDRB specimens with the standard ISO geometry and three different high damping rubber materials are employed in these tests. A nonlinear viscosity law of the dashpot in the Maxwell model is deduced from the experimental scheme, and incorporated into the rheology model to reproduce the nonlinear rate dependent behavior of HDRBs. Finally, numerical simulation results for sinusoidal loading are presented to illustrate capability of the proposed rheology model in reproducing the mechanical behavior of HDRBs.

##### MSC:
 74C20 Large-strain, rate-dependent theories of plasticity 74-05 Experimental work for problems pertaining to mechanics of deformable solids
Mathematica
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##### References:
 [1] Abe, M.; Yoshida, J.; Fujino, Y.: Multiaxial behaviors of laminated rubber bearings and their modeling. I: experimental study, Journal of structural engineering 130, 1119-1132 (2004) [2] Abe, M.; Yoshida, J.; Fujino, Y.: Multiaxial behaviors of laminated rubber bearings and their modeling. I: modeling, Journal of structural engineering 130, 1133-1144 (2004) [3] American Association of State Highways and Transportation Officials (AASHTO), 2000. Guide Specification for Seismic Isolation Design, 2/e. [4] Amin, A. F. M.S.; Alam, M. S.; Okui, Y.: 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) [5] Amin, A. F. M.S.; Lion, A.; Sekita, S.; Okui, Y.: Nonlinear dependence of viscosity in modeling the rate-dependent response of natural and high damping rubbers in compression and shear: experimental identification and numerical verification, International journal of plasticity 22, 1610-1657 (2006) · Zbl 1146.74310 [6] Bergstrom, J. S.; Boyce, M. C.: Constitutive modeling of the large strain time-dependent behavior of elastomers, Journal of the mechanics and physics of solids 46, 931-954 (1998) · Zbl 1056.74500 [7] Bergstrom, J. S.; Boyce, M. C.: Large strain time-dependent behavior of filled elastomers, Mechanics of materials 32, 627-644 (2000) [8] Besdo, D.; Ihlemann, J.: Properties of rubber like materials under large deformations explained by self-organizing linkage patterns, International journal of plasticity 19, 1001-1018 (2003) · Zbl 1090.74525 [9] Bueche, F.: Molecular basis for the Mullins effect, Journal of applied polymer science 4, 107-114 (1960) [10] Dall’asta, A.; Ragni, L.: Experimental tests and analytical model of high damping rubber dissipating devices, Engineering structures 28, 1874-1884 (2006) [11] Hwang, J. S.; Ku, S. W.: Analytical modeling of high damping rubber bearings, Journal of structural engineering 123, 1029-1036 (1997) [12] Hwang, J. S.; Wang, J. C.: Seismic response prediction of HDR bearings using fractional derivatives Maxwell model, Engineering structures 20, 849-856 (1998) [13] Hwang, J. S.; Wu, J. D.; Pan, C. T.; Yang, G.: A mathematical hysteretic model for elastomeric isolation bearings, Earthquake engineering and structural dynamics 31, 771-789 (2002) [14] International Organization of Standardization (ISO), 2005. Elastomeric seismic-protection isolators. Part 1: test methods. [15] Ihlemann, J., 1999. Modeling of inelastic rubber behavior under large deformations based on self-organizing linkage patterns. In: Proceedings of the First European Conference on Constitutive Models for Rubber. Vienna, Austria. A.A. Bulkema Publishers, London, UK. [16] Japan Road Association, 1996. Specifications for highway bridges. Part V: seismic design. [17] Japan Road Association, 2002. Specifications for highway bridges. Part V: seismic design. [18] Kilian, H. G.; Strauss, M.; Hamm, W.: Universal properties in filler-loaded rubbers, Rubber chemistry and technology 67, 1-16 (1994) [19] Kikuchi, M.; Aiken, I. D.: An analytical hysteresis model for elastomeric seismic isolation bearings, Earthquake engineering and structural dynamics 26, 215-231 (1997) [20] Koh, C. G.; Kelly, J. M.: Application of fractional derivatives to seismic analysis of base isolated models, Earthquake engineering and structural dynamics 19, 229-241 (1990) [21] Lion, A.: A constitutive model for carbon black filled rubber: experimental investigations and mathematical representation, Continuum mechanics and thermodynamics 8, 153-169 (1996) [22] Lion, A.: A physically based method to represent the thermo-mechanical behavior of elastomers, Acta mechanica 123, 1-25 (1997) · Zbl 0910.73019 [23] Mullins, L.: Softening of rubber by deformation, Rubber chemistry and technology 42, 339-362 (1969) [24] Sano, T.; Di Pasquale, G.: A constitutive model for high damping rubber bearings, Journal of pressure vessel technology 117, 53-57 (1995) [25] Salomon, O.; Oller, S.; Barbat, A.: Finite element analysis of base isolated buildings subjected to earthquake loads, International journal for numerical methods in engineering 46, 1741-1761 (1999) · Zbl 0962.74070 [26] Skinner, R.I., Robinson, W.H., McVerry, G.H., 1993. An introduction to seismic isolation. DSIR Physical Science. Wellington, New Zealand. [27] Spathis, G.; Kontou, E.: Modeling of nonlinear viscoelasticity at large deformations, Journal of material science 43, 2046-2052 (2008) [28] Treloar, L R.G., 1975. The Physics of Rubber Elasticity, 3/e. Oxford Univ. Press. [29] Tsai, C. S.; Chiang, Tsu-Cheng; Chen, Bo-Jen; Lin, Shih-Bin: An advanced analytical model for high damping rubber bearings, Earthquake engineering and structural dynamics 32, 1373-1387 (2003) [30] Venkataraman, P.: Applied optimization with Matlab programming, (2002) [31] Wen, Y. K.: Method for random vibration of hysteretic systems, Journal of engineering mechanics 102, 249-263 (1976) [32] Wolfram Research Inc., 2005. Mathematica Version 5.2. USA.
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