A comprehensive hyperelastic model that precisely forecasts the mechanical characteristics of materials with rubber-like qualities is presented. This model relies on the well-established five-parameter Mooney-Rivlin model, which is then extended to incorporate strain rate dependent and temperature dependent term. To validate its accuracy, experimental data from ethylene propylene diene monomer (EPDM) rubber materials was utilized to compare with the model prediction. Hyperelastic stress-strain curves were collected from a variety of materials that were subjected to varying temperatures and strain rates to improve the model’s applicability. Its prediction results are compared against the collected experimental data, resulting in consistent and reliable outcomes. The simplified form of the model not only establishes an effective framework for characterizing and predicting the mechanical response of materials that resemble rubber under different working conditions but makes the coding and implementation of finite element analysis easier.
DalHAçıkgözKBadieniaY. On the performance of isotropic hyperelastic constitutive models for rubber-like materials: a state of the art review. Appl Mech Rev2021; 73(2): 020802.
2.
WangMCGuthE. Statistical theory of networks of non-Gaussian flexible chains. J Chem Phys1952; 20(7): 1144–1157.
3.
FloryPJRehnerJ. Statistical mechanics of cross-linked polymer networks II. Swelling. J Chem Phys1943; 11(11): 521–526.
4.
TreloarLRGRidingG. A non-Gaussian theory for rubber in biaxial strain. I. Mechanical properties. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences1979; 369(1737): 261–280.
5.
ArrudaEMBoyceMC. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J Mech Phys Solid1993; 41(2): 389–412.
6.
OgdenRW. Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences1972; 326(1567): 565–584.
7.
TreloarLRG. The elasticity of a network of long-chain molecules—II. Trans Faraday Soc1943; 39(0): 241–246.
8.
MooneyM. A theory of large elastic deformation. J Appl Phys1940; 11(9): 582–592.
9.
RivlinR. Large elastic deformations of isotropic materials IV. further developments of the general theory. Phil Trans Roy Soc Lond Math Phys Sci1948; 241(835): 379–397.
10.
RivlinR. Large elastic deformations of isotropic materials VI. Further results in the theory of torsion, shear and flexure. Phil Trans Roy Soc Lond Math Phys Sci1949; 242(845): 173–195.
11.
JohnsonARQuigleyCJ. A viscohyperelastic maxwell model for rubber viscoelasticity. Rubber Chem Technol1992; 65(1): 137–153.
12.
JohnsonARQuigleyCJFreeseCE. A viscohyperelastic finite element model for rubber. Comput Methods Appl Mech Eng1995; 127(1–4): 163–180.
13.
YangLMShimVPMLimCT. A visco-hyperelastic approach to modelling the constitutive behaviour of rubber. Int J Impact Eng2000; 24(6–7): 545–560.
14.
SuPYangYXiaoJ, et al.Corneal hyper-viscoelastic model: derivations, experiments, and simulations. Acta Bioeng Biomech2015; 17(2): 73–84.
15.
KhajehsaeidHNaghdabadiRArghavaniJ. A strain energy function for rubber-like materials. Constitutive Models for Rubber VIII. 2013; 8: 205–210.
16.
KhajehsaeidHArghavaniJNaghdabadiR, et al.A visco-hyperelastic constitutive model for rubber-like materials: a rate-dependent relaxation time scheme. Int J Eng Sci2014; 79: 44–58.
17.
WangHDengXWuH, et al.Investigating the dynamic mechanical behaviors of polyurea through experimentation and modeling. Defence Technology2019; 15(6): 875–884.
18.
SomarathnaHMCCRamanSNMohottiD, et al.Hyper-viscoelastic constitutive models for predicting the material behavior of polyurethane under varying strain rates and uniaxial tensile loading. Construct Build Mater2020; 236: 117417.
19.
LevYFayeAVolokhKY. Experimental study of the effect of temperature on strength and extensibility of rubberlike materials. Exp Mech2018; 58(5): 847–858.
20.
SaccomandiGOgdenRW. Mechanics and Thermomechanics of Rubberlike Solids. Berlin, Germany: Springer, 2004, Vol. 452.
21.
ShawJAJonesASWinemanAS. Chemorheological response of elastomers at elevated temperatures: experiments and simulations. J Mech Phys Solid2005; 53(12): 2758–2793.
22.
MaconDFarrisR. A new analytical and experimental approach to rubber thermodynamics. Macromolecules1999; 32: 5004–5016.
23.
FuXWangZMaL, et al.Temperature-Dependence of rubber hyperelasticity based on the eight-chain model. Polymers2020; 12(4): 932.
24.
FuXWangZMaL. Ability of constitutive models to characterize the temperature dependence of rubber hyperelasticity and to predict the stress-strain behavior of filled rubber under different defor mation states. Polymers2021; 13(3): 369.
25.
HuangYLiYZhaoH, et al.Research on constitutive models of hydrogenated nitrile butadiene rubber for packer at different temperatures. J Mech Sci Technol2020; 34(1): 155–164.
26.
ChevalierLLuoYMMonteiroE, et al.On visco-elastic modelling of polyethylene terephthalate behaviour during multiaxial elongations slightly over the glass transition temperature. Mech Mater2012; 52: 103–116.
27.
ZhangJZhengJChenX, et al.A thermovisco-hyperelastic constitutive model of NEPE propellant over a large range of strain rates. J Eng Mater Technol2014; 136(3): 031002.
28.
SaccomandiGOgdenRW. Mechanics and thermomechanics of rubberlike solids. New York: Springer, 2004.
29.
AllenGKirkhamMPadgetJ, et al.Thermodynamics of rubber elasticity at constant volume. Trans Faraday Soc1971; 67: 1278–1292.
30.
SmithTL. Large deformation tensile properties of elastomers. I. Temperature dependence of c1 and c2 in the mooney-rivlin equation. In Journal of Polymer Science Part C: Polymer Symposia. : Wiley Online Library, 1967, pp. 841–858.
31.
ChadwickP. Thermo-mechanics of rubberlike materials. Phil Trans Roy Soc Lond Math Phys Sci1974; 276: 371–403.
LuSPisterK. Decomposition of deformation and representation of the free energy function for isotropic thermoelastic solids. Int J Solid Struct1975; 11: 927–934.
34.
HumphreyJRajagopalK. Finite thermoelasticity of constrained elastomers subject to biaxial loading. J Elasticity1997; 49: 189–200.
35.
OgdenR. Aspects of the phenomenological theory of rubber thermoelasticity. Polymer1987; 28: 379–385.
SimoJC. On a fully three-dimensional finite-strain viscoelastic damage model: formulation and computational aspects. Comput Methods Appl Mech Eng1987; 60: 153–173.
38.
HolzapfelGASimoJC. A new viscoelastic constitutive model for continuous media at finite thermomechanical changes. Int J Solid Struct1996; 33(20-22): 3019–3034.
39.
Abaqus analysis user’s manual, Version 6.14. Abaqus, Inc, 2014.
40.
MohottiDAliMNgoT, et al.Strain rate dependent constitutive model for predicting the material behaviour of polyurea under high strain rate tensile loading. Mater Des2014; 53: 830–837.
41.
WangJPengXHuangZ, et al.A temperature-dependent 3D anisotropic visco-hyperelastic constitutive model for jute woven fabric reinforced poly (butylene succinate) biocomposite in thermoforming. Compos B Eng2021; 208: 108584.
42.
LaiXWangZQinN. Comparative studies of the constitutive models for tungsten heavy alloy (95W-3.5Ni-1.5Fe) at high strain rates. Proc IME C J Mech Eng Sci2022; 236(7): 3636–3650.
43.
MirjaliliSMirjaliliSMLewisA. Grey wolf optimizer. Adv Eng Software2014; 69: 46–61.
44.
Institution BS. ISO 37. Rubber, vulcanized or thermoplastic. Determination of tensile stress-strain properties. Technical report, International Organization for Standardization. 2005.
45.
LongRMayumiKCretonC, et al.Time dependent behavior of a dual cross-link self-healing gel: theory and experiments. Macromolecules2014; 47(20): 7243–7250.
46.
LenhartJLColePJUnalB, et al.Development of nonaqueous polymer gels that exhibit broad temperature performance. Appl Phys Lett2007; 91(6).
47.
CasemDTDwivediAKMrozekRA, et al.Compression response of a thermoplastic elastomer gel tissue surrogate over a range of strain-rates. Int J Solid Struct2014; 51(11–12): 2037–2046.
48.
RolandCMTwiggJNVuY, et al.High strain rate mechanical behavior of polyurea. Polymer2007; 48(2): 574–578.
49.
WangLPengXLiuM. Development and application of hyperelastic model for diaphragm considering the influence of temperature. International Journal of Computational Materials Science and Engineering2019; 08(03): 1950010.
50.
LiXBaiTLiZ, et al.Influence of the temperature on the hyper-elastic mechanical behavior of carbon black filled natural rubbers. Mech Mater2016; 95: 136–145.
51.
TreloarL. The physics of rubber elasticity. 3rd ed.UK: Clarendon Press, 2005.
52.
ToaderGRusenETeodorescuM, et al.New polyurea MWCNTs nanocomposite films with enhanced mechanical properties. J Appl Polym Sci2017; 134(28): 45061.
53.
LiuQChenPZhangY, et al.Compressive behavior and constitutive model of polyurea at high strain rates and high temperatures. Mater Today Commun2020; 22: 100834.
54.
UngerRArashBExnerW, et al.Effect of temperature on the viscoelastic damage behaviour of nanoparticle/epoxy nanocomposites: constitutive modelling and experimental validation. Polymer2020; 191: 122265.
55.
BowerDI. An introduction to polymer physics: Cambridge University Press, 2002.
56.
ŞerbanDAWeberGMarşavinaL, et al.Tensile properties of semi-crystalline thermoplastic polymers: effects of temperature and strain rates. Polym Test2013; 32(2): 413–425.
