Constitutive Model of High-Damping Rubber Materials
Publication: Journal of Engineering Mechanics
Volume 130, Issue 2
Abstract
A mathematical model of high-damping rubber materials is developed. First the material experiments necessary for modeling are systematically conducted. Then, on the basis of the results of the material experiments, a constitutive model for rubber materials is proposed. The model is decomposed into two parts. The first part consists of an elastoplastic body with a strain-dependent isotropic hardening law and it represents the energy dissipation of the material, while the second part consists of a hyperelastic body with a damage model and it expresses the evolutional direction of the stress tensor. By comparing the experimental results with the simulation by the model, the model is found to well approximate the behaviors of high-damping rubber materials. Finally, a hybrid analysis method is proposed. In this method, the strain field of laminated rubber bearings measured by image processing is combined with the numerical analysis to confirm the applicability of the proposed model to the bearing. In addition, by this hybrid analysis method, the bulk modulus of rubber material is also computed.
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References
Abe, M., Yoshida, J., and Fujino, Y. (2004). “Multi-axial behaviors of laminated rubber bearings and their modeling: I. Experimental study.” J. Struct. Eng., in press.
Aiken, I. D., Kelly, J. M., Clark, W. P., Tamura, K., Kikuchi, M., and Itoh, T. (1992). “Experimental studies of the mechanical characteristics of three types of seismic isolation bearings.” Proc., 3rd World Conf. on Earthquake Engineering, Madrid, Spain, 4, 2281–2286.
Alexander, H.(1968). “A constitutive relation for rubber-like material.” Int. J. Eng. Sci., 6, 549–563.
Bathe, K. J. (1996). Finite element procedures, Prentice-Hall, Englewood Cliffs, N.J.
Crisfield, M. A. (1997). Non-linear finite element analysis of solid and structures Vol. 2: Advanced topics, Wiley, Chichester, England.
Govindjee, S., and Simo, J. C.(1991). “A micro-mechanically based continuum damage model for carbon black-filled rubbers incorporating Mullins’ effect.” J. Mech. Phys. Solids, 39, 87–112.
Govindjee, S., and Simo, J. C.(1992a). “Transition from micromechanics to computationally efficient phenomenology: Carbon black filled rubbers incorporating Mullins’ effect.” J. Mech. Phys. Solids, 40, 213–233.
Govindjee, S., and Simo, J. C.(1992b). “Mullins’ effect and the strain amplitude dependence of the storage modulus.” Int. J. Solids Struct., 29(14/15), 1737–1751.
Graesser, E. J., and Cozzarelli, F. A. (1991). “A multidimensional hysteretic model for energy absorbing devices.” Technical Rep. No. NCEER-91-0006, State University of New York at Buffalo, N.Y.
Holzapfel, G. A. (2001). Nonlinear solid mechanics—A continuum approach for engineering, Wiley, New York.
Hosam-Eddin, M. A., and Abdel-Ghaffar, A. M.(1995). “Modeling of rubber and lead passive-control bearings for seismic analysis.” J. Struct. Eng., 121(7), 1134–1144.
Hwang, J. S., and Ku, S. W.(1997). “Analytical modeling of high damping rubber bearings.” J. Struct. Eng., 128(8), 1029–1036.
Kelly, J. M. (1991). “Dynamic and failure characteristics of Bridgestone isolation bearings.” EERC Rep. No. 515/K34, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif.
Khan, A. S., and Huang, S. (1995). Continuum theory of plasticity, Wiley, New York.
Kikuchi, M., and Aiken, I. D.(1997). “An analytical hysteresis model for elastomeric seismic isolation bearings.” Earthquake Eng. Struct. Dyn., 26, 215–231.
Matsuda, A. (2001). “Evaluation for mechanical properties of laminated rubber bearings using nonlinear finite element analysis with hyperelasticity.” PhD dissertation, Department of System & Information Engineering, Tsukuba Univ., Japan (in Japanese).
Morman, K. N.(1986). “The generalized strain measure with application to nonhomogeneous deformation in rubber-like solids.” J. Appl. Mech., 53, 726–728.
Ogden, R. W. (1984). Non-linear elastic deformation, Ellis Horwood, Chichester, England.
Press, H. W., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1988). Numerical recipes in C, Cambridge University Press, New York.
Reese, S., and Govindjee, S.(1998). “Theoretical and numerical aspects in the thermo-viscoelastic material behaviour of rubber-like polymer.” Mech. Time-Depend. Mater., 1, 357–396.
Salomon, O., Oller, S., and Barbat, A.(1999). “Finite element analysis of base isolated buildings subjected to earthquake loads.” Int. J. Numer. Methods Eng., 46, 1741–1761.
Seki, W., Fukahori, Y., Iseda, Y., and Matsunaga, T. (1987). “A large deformation finite element analysis for multilayer elastomeric bearings.” Trans. Meeting of the Rubber Division, American Chemical Society, 856–870.
Simo, J. C.(1987). “On a fully three-dimensional finiexperimentrain viscoelastic damage model: Formulation and computational aspect.” Comput. Methods Appl. Mech. Eng., 60, 153–173.
Simo, J. C., and Hughes, T. J. R. (1997). Interdisciplinary applied mathematics volume 7: Computational inelasticity, Springer, New York.
Skinner, R. I., Robinson, H. W., and McVerry, H. G. (1993). An introduction to seismic isolation, Wiley, Chichester, England.
Takayama, M., Tada, H., and Tanaka, R. (1990). “Finite element analysis of laminated rubber bearing used in base-isolation system.” Proc., Meeting of the Rubber Division, American Chemical Society, Washington, D.C., 46–62.
Treloar, L. (1975). Physics of rubber elasticity, 3rd Ed., Oxford University Press, London.
Watanabe, H., and Hisada, T.(1996). “Mixed finite element analysis of incompressible hyperelastic materials.” Theor. Appl. Mech., 45, 3–8.
Yamashita, Y., and Kawabata, S.(1992). “Strain energy density approximation formula for carbon-filled rubber.” Jpn. Rubber Assoc., 65(9), 517–527 (in Japanese).
Yoshida, J., Abe, M., Fujino, Y., and Lewangamage, C. S. (2004a). “Measurement method for continua by image processing.” J. Struct. Eng., in press.
Yoshida, J., Abe, M., Fujino, Y., and Watanabe, H. (2004b). “Three-dimensional finite element analysis of high damping rubber bearings.” J. Eng. Mech., in press.
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Published In
Journal of Engineering Mechanics
Volume 130 • Issue 2 • February 2004
Pages: 129 - 141
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Sep 25, 2002
Accepted: Feb 21, 2003
Published online: Jan 16, 2004
Published in print: Feb 2004
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