Citation: Cheng SHI, Heng-Wei ZHOU, Ming-Ming DING, Feng YE, Tong-Fei SHI. A Hyperelastic Mixed Constitutive Model for Rubber Based on Molecular Chain Statistical Theory[J]. Chinese Journal of Applied Chemistry, ;2021, 38(2): 228-235. doi: 10.19894/j.issn.1000-0518.200325 shu

A Hyperelastic Mixed Constitutive Model for Rubber Based on Molecular Chain Statistical Theory

Cheng SHI ^{1, 2} ,
Heng-Wei ZHOU ¹ ,
Ming-Ming DING ^{1, 2,,} ,
Feng YE ^2,, ,
Tong-Fei SHI ^{1, 2}

1.
Xinjiang Laboratory of Phase Transitions and Microstructures in Condensed Matter Physics, College of Physical Science and Technology, Yili Normal University, Yining 835000, China
2.
State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China

Corresponding author: Ming-Ming DING, mmding@ciac.ac.cn Feng YE, yefeng@ciac.ac.cn
Received Date: 30 October 2020
Accepted Date: 31 December 2020

Figures(4)

Rubber materials are widely used in practice because of their unique hyperelasticity. The analysis of the stress-strain relationship can provide theoretical guidance for the engineering application of rubber mechanical properties. In order to describe the mechanical properties of rubber materials more accurately, a hybrid hyperelastic constitutive model was proposed in this paper. The new model is based on the Gaussian model and 8-chain model, which are coupled by the weight function related to the stretching ratio. When the stretching ratio is small, the new model degenerates into Gaussian form; When the stretching ratio is large, the new model can improve the deficiency of 8-chain model in small deformation by regulating of the weight function. We select experiment data from three aspects to verify the applicability of the new model: Stress-strain curve of orientation hardening, stress-strain curve of non-oriented hardening, stress-strain curve of different stretch ratios. We carry on the fitting verification from uniaxial tension, biaxial tension and pure shear experiments, respectively. The results show that the new model retains the advantages of Gaussian model in small deformation range and 8-chain model in large deformation range at the same time and has no dependence on stretching ratios and stress-strain curve forms. It breaks through the limitation of Gaussian model and 8-chain model, and provides a new idea for prediction of rubber hyperelastic mechanical properties.
- Rubber,
- Hyperelasticity,
- Molecular statistical theory,
- Constitutive model
1. [1]
  DING F, ZHANG H, DING M M. Theoretical models for stress-strain curves of elastomer materials[J]. Acta Polym Sin, 2019,50(12):1357-1366.
2. [2]
  PENG X F, LI L X. State of the art of constitutive relations of hyperelastic materials[J]. Chinese J Theor Appl Mech, 2020,52(5):1221-1232.
3. [3]
  DESTRADE M, SACCOMANDI G, SGURA I. Methodical fitting for mathematical models of rubber-like materials[J]. Proc Roy Soc A, 2017,473(2198)20160811. doi: 10.1098/rspa.2016.0811
4. [4]
  PUGLISI G, SACCOMANDI G. Multiscale modelling of rubber-like materials and soft tissues: an appraisal[J]. Proc Roy Soc A, 2016,472(2187)20160060. doi: 10.1098/rspa.2016.0060
5. [5]
  MOONEY M A. Theory of large elastic deformation[J]. J Appl Phys, 1940,11(9):582-592. doi: 10.1063/1.1712836
6. [6]
  TRELOAR L R G. The elasticity of a network of long-chain molecules. I[J]. Trans Faraday Soc, 1946,42.
7. [7]
  RIVLIN R S. Large elastic deformations of isotropic materials. iv. further developments of the general theory[J]. Philos Trans Roy Soc Lond Ser A, 1948,241(835):379-397. doi: 10.1098/rsta.1948.0024
8. [8]
  OGDEN R. Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids[J]. Proc Ror Soc A, 1972,326(1567):565-584.
9. [9]
  WAENER H R. Theory and rheology of dilute suspensions of finitely extendible dumbbells[J]. Ind Eng Chem Fundam, 1972,11(3):379-387. doi: 10.1021/i160043a017
10. [10]
  KILIAN H G. Equation of state of real networks[J]. Polymer, 1981,22(2):209-217. doi: 10.1016/0032-3861(81)90200-7
11. [11]
  YEOH O H. Some forms of the strain energy function for rubber[J]. Rubber Chem Technol, 1993,66(5):754-771. doi: 10.5254/1.3538343
12. [12]
  GENT A N. A new constitutive relation for rubber[J]. Rubber Chem Technol, 1996,69(1):59-61. doi: 10.5254/1.3538357
13. [13]
  SHARIFF M. Strain energy function for filled and unfilled rubberlike material[J]. Rubber Chem Technol, 2000,73(1):1-18. doi: 10.5254/1.3547576
14. [14]
  CARROLL M M. A strain energy function for vulcanized rubbers[J]. J Elast, 2011,103(2):173-187. doi: 10.1007/s10659-010-9279-0
15. [15]
  JAMES H M, GUTH E. Theory of the elastic properties of rubber[J]. J Chem Phys, 1943,11(10):455-481. doi: 10.1063/1.1723785
16. [16]
  FLORY P J, REHNER J. Statistical mechanics of cross-linked polymer networks I. rubberlike elasticity[J]. J Chem Phys, 1943,11(11):512-520. doi: 10.1063/1.1723791
17. [17]
  FLORY P J. Network structure and the elastic properties of vulcanized rubber[J]. Chem Rev, 1944,35(1):51-75. doi: 10.1021/cr60110a002
18. [18]
  ARRUDA E M, BOYCE M C. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials[J]. J Mech Phys Solids, 1993,41(2):389-412. doi: 10.1016/0022-5096(93)90013-6
19. [19]
  WU P D, GIESSEN E V D. On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers[J]. J Mech Phys Solids, 1993,41(3):427-456. doi: 10.1016/0022-5096(93)90043-F
20. [20]
  MARCKMANN G, VERRON E. Comparison of hyperelastic models for rubber-like materials[J]. Rubber Chem Technol, 2006,79(5):835-858. doi: 10.5254/1.3547969
21. [21]
  KUHN W, GRUN F. Relations between elastic constants and the strain birefringence of high-elastic substances[J]. Colloid Polym Sci, 1942,101(3):248-271.
22. [22]
  TRELOAR L R G, RIDING G. A non-gaussian theory for rubber in biaxial strain. I. mechanical properties[J]. Proc Roy Soc A, 1979,369(1737):261-280.
23. [23]
  MANSOURI M R, DARIJANI H. Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach[J]. Int J Solids Struct, 2014,51(25/26):4316-4326.
24. [24]
  TRELOAR L R G. Stress-strain data for vulcanised rubber under various types of deformation[J]. Trans Faraday Soc, 1944,40:59-69. doi: 10.1039/tf9444000059
25. [25]
  ATTARD M M, HUNT G W. Hyperelastic constitutive modeling under finite strain[J]. Int J Eng Sci, 2004,41(18/19):5327-5350.
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