Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Non Linear Viscoelastic Constitutive Relation of Elastomers for Hysteresis Behavior

히스테리시스 거동을 하는 탄성체의 비선형 점탄성 구성방정식

  • Yoo, Sairom (Dept. of Aerospace Engineering, Korea Aerospace Univ.) ;
  • Ju, Jaehyung (Dept. of Mechanical Engineering, Univ. of North Texas) ;
  • Choi, Seok-Ju (R&D Center, Hnakook Tire Co. Ltd.) ;
  • Kim, Dooman (Dept. of Aerospace Engineering, Korea Aerospace Univ.)
  • Received : 2015.10.05
  • Accepted : 2016.02.10
  • Published : 2016.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

An accurate hysteresis model of an elastomer is important for quantifying viscoelastic energy loss. We suggest a highly nonlinear hyper-viscoelastic constitutive model of elastomers. The model captures a nonlinear viscoelastic characteristic by combining Yeoh's hyperelastic model and Hoofatt's hysteresis model used Neo-Hookean hyperelastic model. Analytical and numerical models were generated from uniaxial cyclic tests of an elastomer under a sinusoidal load with a mean strain of 150%, amplitudes of 20~80%, and frequencies of 0.02~0.2Hz. The viscoelastic model can highly capture the viscoelastic energy loss up to a strain of 230%.

정확한 점탄성 재료의 히스테리시스 모델은 에너지 손실을 정량화 하는데 매우 중요하다. 우리는 본 논문에서 대변형 상태의 탄성체에 대한 비선형 초-점탄성 지배방정식 모델을 제시하고자 한다. 본 연구는 Hoofatt의 모델에서 Neo-Hookean 초탄성 모델 대신 Yeoh 초탄성 모델로 지배 방정식을 유도하여 탄성체의 점탄성 거동을 모델링하였다. 또한 폴리우레탄 시편을 사용하여, 평균 변형률 ${\varepsilon}_m=1.5$, 진폭 변형률 ${\varepsilon}_a=0.2{\sim}0.8$, 주파수 f=0.02~0.2의 조건에서 단축 사인형 반복 하중 실험과 제시한 점탄성 모델을 Matlab으로 비교하였다. 본 연구의 점탄성 모델은 변형률이 230% 이상의 대변형 상태의 에너지 손실도 계산할 수 있다.

Keywords

References

  1. Buckley, Mc C. and Bucknell, 2003, Principles of Polymer Engineering, pp. 117-176.
  2. Wiechert, E., 1889, Ueber Elastische Nachwirkung, Dissertation, Konigsberg University, Germany.
  3. Wiechert, E., 1893, Gesetze der elastischen Nachwirkung fur constante Temperatur, Annalen der Physik, pp. 286, 335-348, 546-570.
  4. Soussou, J. E., Moavenzadeh, F. and Gradowczyk, M. H., 1970, "Application of Prony Series to Linear Viscoelasticity," Trans. Soc. Rheol. Vol. 14, pp. 573-584. https://doi.org/10.1122/1.549179
  5. Haupt, P. and Lion, A., 2002, "On Finite Linear Viscoelasticity of Incompressible Isotropic Materials," Acta Mech. Vol. 159, pp. 87-124. https://doi.org/10.1007/BF01171450
  6. Bergstrom, J. S. and Boyce, M. C., 1998, "Constitutive Modeling of the Large Strain Time-dependent Behavior of Elastomers," J. Mech. Phys. Solids, Vol. 46, pp. 931-954. https://doi.org/10.1016/S0022-5096(97)00075-6
  7. Bergstrom, J. S. and Boyce, M. C., 2001, "Constitutive Modeling of the Time-dependent and Cyclic Loading of Elastomers and Application to Soft Biological Tissues," Mech. Mater, Vol. 33, pp. 523-530. https://doi.org/10.1016/S0167-6636(01)00070-9
  8. Lion, A., 1996, "A Constitutive Model for Carbon Black Filled Rubber: Experimental Investigations and Mathematical Representation," Continuum Mech. Thermo-dyna, Vol. 8 pp. 153-169. https://doi.org/10.1007/BF01181853
  9. Lion, A., 1997, "A Physically Based Method to Represent the Thermo-mechanical Behavior of Elastomers," Acta Mech. Vol. 123, pp. 1-25. https://doi.org/10.1007/BF01178397
  10. Tomita, Y., Lu, W., Naito, M. and Furutani, Y., 2006, "Numerical Evaluation of Micro - to Macroscopic Mechanical Behavior of Carbon-black-filled Rubber," International Journal of Mechanical Sciences, Vol. 48, pp. 108-116. https://doi.org/10.1016/j.ijmecsci.2005.08.009
  11. Tomita, Y., Azuma, K. and Naito, M., 2008, "Computational Evaluation of Strain-rate-dependent Deformation Behavior of Rubber and Carbon-blackfilled Rubber Under Monotonic and Cyclic Straining," Int. J. Mech. Sci, Vol. 50 pp. 856-868. https://doi.org/10.1016/j.ijmecsci.2007.09.010
  12. Liu, M. and HooFatt, Michelle S., 2011, "A Constitutive Equation for Filled Under Cyclic Loading," International Journal of Non-Linear Mechanics, Vol. 46, pp. 446-456. https://doi.org/10.1016/j.ijnonlinmec.2010.11.006
  13. Liu, F., Sutcliffe, M.P.F. and Graham, W.R., 2010, "Prediction of Tread Block Forces for a Free-rolling Tyre in Contact with a Smooth Road," Wear, Vol. 269, pp. 672-683. https://doi.org/10.1016/j.wear.2010.07.006
  14. Lee, E.H. and Liu, D.H., 1967, "Finite-strain Elastic-plastic Theory with Application to Plane-wave Analysis," J. Appl. Phys., Vol. 38 pp. 19-27. https://doi.org/10.1063/1.1708953
  15. Huber, N., Tsakmakis, C., 2000, "Finite Deformation Viscoelasticity Laws," Mech. Mater., Vol. 32 pp. 1-18. https://doi.org/10.1016/S0167-6636(99)00045-9
  16. Robertson, C. G. and Wang, X., 2006, "Spectral Hole Burning to Probe the Nature of Unjamming (Payne effect) in Particulate-filled Elastomers," Europhys. Lett, Vol. 76, pp. 278-284. https://doi.org/10.1209/epl/i2006-10256-8
  17. Payne, A.R., 1967, "Dynamic properties of PBNA-natural Rubber Vulcanizates," J. Appl. Polym. Sci. Vol. 11, pp. 383-387. https://doi.org/10.1002/app.1967.070110306

Cited by

  1. Optimal Design for the Rear-Glass Joint of an Automobile for Squeak and Rattle Noise Reduction vol.19, pp.5, 2018, https://doi.org/10.1007/s12239-018-0083-3