DOI QR코드

DOI QR Code

Dynamic visco-hyperelastic behavior of elastomeric hollow cylinder by developing a constitutive equation

  • Asgari, Masoud (Faculty of Mechanical Engineering, K. N. Toosi University of Technology) ;
  • Hashemi, Sanaz S. (Faculty of Mechanical Engineering, K. N. Toosi University of Technology)
  • Received : 2015.12.07
  • Accepted : 2016.04.15
  • Published : 2016.08.25

Abstract

In this study, developments of an efficient visco-hyperelastic constitutive equation for describing the time dependent material behavior accurately in dynamic and impact loading and finding related materials constants are considered. Based on proposed constitutive model, behaviour of a hollow cylinder elastomer bushing under different dynamic and impact loading conditions is studied. By implementing the developed visco-hyperelastic constitutive equation to LS-DYNA explicit dynamic finite element software a three dimensional model of the bushing is developed and dynamic behaviour of that in axial and torsional dynamic deformation modes are studied. Dynamic response and induced stress under different impact loadings which is rarely studied in previous researches have been also investigated. Effects of hyperelastic and visco-hyperelastic parameters on deformation and induced stresses as well as strain rate are considered.

Keywords

References

  1. Adkins, J.E. and, A.N. (1954), "Gent load-deflexion relations of rubber bush mountings", Brit. J. Appl. Phys., 5, 340-354. https://doi.org/10.1088/0508-3443/5/9/108
  2. Amin, A.F., Alam, M.S. and Okui, Y. (2002), "An improved hyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification", Mech. Mater., 34, 75-95. https://doi.org/10.1016/S0167-6636(01)00102-8
  3. Aniskevich, K., Starkova, O., Jansons, J. and Aniskevich, A. (2010), "Viscoelastic properties of a silicafilled styrene-butadiene rubber under uniaxial tension", Mech. Compos. Mater., 46, 375-386. https://doi.org/10.1007/s11029-010-9154-x
  4. Bechir, H., Chevalier, L., Chaouche, M. and Boufala, K. (2006), "Hyperelastic constitutive model for rubber-like materials based on the first Seth strain measures invariant", Eur. J. Mech. A/Solid., 25, 110-124.
  5. Bergstrom, J.S. and Boyce, M.C. (1998), "Constitutive modeling of the large strain time-dependent behavior of elastomers", J. Mech. Phys. Solid., 46, 931-954. https://doi.org/10.1016/S0022-5096(97)00075-6
  6. Bjornsson, P. and Danielsson, H. (2005), "Strength and creep analysis of glued rubber foil timber joints", 1, 145-158.
  7. Busfield, J.C. and Davies, C.K.L. (2001), "Stiffness of simple bonded elastomer bushes, Part 1-Initial behavior", Plast. Rub. Compos., 30, 243-257. https://doi.org/10.1179/146580101101541679
  8. Centeno, O. (2009), Finite element modeling of a rubber bushing for crash simulation experimental tests and validation, Structural Mechanics Journal, Sweden.
  9. Chen, J.S. and Wu, C.T. (1997), "On computational issues in large deformation analysis of rubber bushings", Mech. Struct. Mach., 33(5), 327-349.
  10. Diani, J., Brieu, M. and Gilormini, P. (2006), "Observation and modeling of the anisotropic viscohyperelasticbehavior of a rubberlike material", Int. J. Solid. Struct., 43(10), 3044-3056. https://doi.org/10.1016/j.ijsolstr.2005.06.045
  11. Fung, Y.C. (1965), Foundations of solid mechanics, Upper Saddle River, New Jersey, USA.
  12. Gavin, H. (2011). "The Levenberg-Marquardt method for nonlinear least squares curve-fitting problems", Department of Civil and Environmental Engineering, Duke University, 1-15.
  13. Gent, A. (1996), "A new constitutive relation for rubber", Rub. Chem. Technol., 69, 59-61. https://doi.org/10.5254/1.3538357
  14. Goh, S.M., Charalambides, M.N. and Williams, J.G. (2004), "Determination of the constitutive constants of non-linear viscoelastic materials", Mech. Time-Depend. Mater., 8, 255-268. https://doi.org/10.1023/B:MTDM.0000046750.65395.fe
  15. Hakansson, P. (2000), "Finite element modeling of a rubber block exposed to shock loading", Diss. Master's Dissertation, Lund University, Lund, Sweden.
  16. Hallquist, J.O. (2006), LS-DYNA Theory Manual, Livermore Software Technology Corporation.
  17. Holzapfel, G. (1996), "On large strain viscoelasticity: continuum formulation and finite element applications to elastomeric structures", Int. J. Numer. Meth. Eng., 39, 3903-3926. https://doi.org/10.1002/(SICI)1097-0207(19961130)39:22<3903::AID-NME34>3.0.CO;2-C
  18. Hopkinton, Simple Bushings_VAD-Lit: www.barrycontrols.com
  19. Horton, J.M., Gover, M.J. and Tupholme, G.E. (2000), "Stiffness of rubber bush mountings subjected to radial loading", Rub. Chem. Technol., 73, 253-264. https://doi.org/10.5254/1.3547589
  20. Huber, N. and Tsakmakis, Ch. (2000), "Finite deformation viscoelasticity laws", Mech. Mater., 32, 1-18 https://doi.org/10.1016/S0167-6636(99)00045-9
  21. James, J.H. and Guth, E. (1943), "Theory of the elastic properties of rubber", J. Chem. Phys., 11, 455-481. https://doi.org/10.1063/1.1723785
  22. Kadlowec, J., Gerrard, D. and Pearlman, H. (2009), "Coupled axial-torsional behavior of cylindrical elastomer bushings", Polym. Test., 28, 139-144. https://doi.org/10.1016/j.polymertesting.2008.10.003
  23. Kadlowec, J., Wineman, A. and Hulbert, G. (2001), "Coupled response model for elastomeric bushing", Rub. Chem. Technol., 74(2), 338-352. https://doi.org/10.5254/1.3544955
  24. Kadlowec, J., Wineman, A. and Hulbert, G. (2003), "Elastomer bushing response: experiments and finite element modelling", Acta Mechanica, 163, 25-38.
  25. Khajehsaeid, H., Baghani, M. and Naghdabadi, R. (2013), "Finite strain numerical analysis of elastomeric bushings under multi-axial loadings: a compressible visco-hyperelastic approach", Int. J. Mech. Mater. Des., 9, 385-399. https://doi.org/10.1007/s10999-013-9228-8
  26. Kim, J., Lee, S. and Min, K.W. (2014), "Design of MR dampers to prevent progressive collapse of moment frames", Struct. Eng. Mech., 52(2), 291-306. https://doi.org/10.12989/sem.2014.52.2.291
  27. Macosko, C.W. and Larson, R.G. (1994), "Rheology: principles, measurements, and applications", 1, 145-158.
  28. Martinez, J.M.M. (2006), "Natural rubber by a rubber man", Mater. Today, 9(3), 55-68.
  29. MATLAB Release (2012b), The MathWorks, Inc., Natick, Massachusetts, United States.
  30. More, J. (1978), The Levenberg-Marquardt algorithm: implementation and theory, Numerical analysis, Springer, Berlin Heidelberg.
  31. Naghdabadi, R., Baghani, M. and Arghavani, J. (2012), "A viscoelastic constitutive model for compressible polymers based on logarithmic strain and its finite element implementation", Finite Elem. Anal. Des., 62, 18-27. https://doi.org/10.1016/j.finel.2012.05.001
  32. Nilesh, D. and Adivi, K.P. (2011), Modelling of Engine Suspension Components for Crash Simulations.
  33. Ogden, R.W. (1972), "Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids", Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences., 326(67), The Royal Society.
  34. Okwu, U.N. and Okieimen, F.E. (2011), "Preparation and properties of thioglycollic acid modified epoxidised natural rubber and its blends with natural rubber", Eur. Polym. J., 37, 2253-2258.
  35. Ouyang, X. (2006), "Constitutive equations of rubber under large tensile strain and high strain rates", Diss. The University of Akron.
  36. Rivlin, R.S., Barenblatt, G.I. and Joseph, D.D. (1997), Collected papers of RS Rivlin, Springer Science & Business Media.
  37. Suarez, L.E. and Gaviria, C.A. (2015), "Dynamic properties of a building with viscous dampers in nonproportional arrangement", Struct. Eng. Mech., 55(6), 1241-1260. https://doi.org/10.12989/sem.2015.55.6.1241
  38. Treloar, L.R. (2005), The Physics of Rubber Elasticity, Oxford University Press, New York.
  39. Yang, L.M. and Shim, V.P. (2004), "A visco-hyperelastic constitutive description of elastomeric foam", Int. J. Impact Eng., 30, 1099-1110.
  40. Yang, L.M., Shim, V.P.W. and Lim, C.T. (2002), "A visco-hyperelastic approach to modelling the constitutive behaviour of rubber", Int. J. Impact Eng., 24, 545-560.
  41. Yeoh, O.H. and Fleming, P.D. (1997), "A new attempt to reconcile the statistical and phenomenological theories of rubber elasticity", J. Polym. Sci. B Polym. Phys. Edit., 35, 1919-1932. https://doi.org/10.1002/(SICI)1099-0488(19970915)35:12<1919::AID-POLB7>3.0.CO;2-K