zbMATH — the first resource for mathematics

A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. (English) Zbl 1355.74020
Summary: A constitutive model is proposed for the deformation of rubber materials which is shown to represent successfully the response of these materials in uniaxial extension, biaxial extension, uniaxial compression, plane strain compression and pure shear. The developed constitutive relation is based on an eight chain representation of the underlying macromolecular network structure of the rubber and the non-Gaussian behavior of the individual chains in the proposed network. The eight chain model accurately captures the cooperative nature of network deformation while requiring only two material parameters, an initial modulus and a limiting chain extensibility. Since these two parameters are mechanistically linked to the physics of molecular chain orientation involved in the deformation of rubber, the proposed model represents a simple and accurate constitutive model of rubber deformation. The chain extension in this network model reduces to a function of the root-mean-square of the principal applied stretches as a result of effectively sampling eight orientations of principal stretch space. The results of the proposed eight chain model as well as those of several prominent models are compared with experimental data of Treloar illustrating the superiority, simplicity and predictive ability of the proposed model. Additionally, a new set of experiments which captures the state of deformation dependence of rubber is described and conducted on three rubber materials. The eight chain model is found to model and predict accurately the behavior of the three tested materials further confirming its superiority and effectiveness over earlier models.

74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
PDF BibTeX Cite
Full Text: DOI
[1] Arruda, E.M.; Boyce, M.C., Anisotropy and localization of plastic deformation, (), 483
[2] Fardshisheh, F.; Onat, E.T., Problems in plasticity, (), 89 · Zbl 0273.73025
[3] Flory, P.J.; Erman, B., Macromol., 15, 800, (1982)
[4] Flory, P.J.; Rehner, J., J. chem. phys., 11, 512, (1943)
[5] Jones, D.F.; Treloar, L.R.G., J. phys. D: appl. phys., 8, 1285, (1975)
[6] Kuhn, W.; Grün, F., Kolloid Z., 101, 248, (1942)
[7] Mark, J.E.; Erman, B., Rubberlike elasticity A molecular primer, (1988), John Wiley New York
[8] Mooney, M., J. appl. phys., 11, 582, (1940)
[9] Ogden, R.W., (), 565
[10] Rivlin, R.S., Phil. trans. R. soc. lond. A., 241, 479, (1948)
[11] Treloar, L.R.G., Trans. Faraday soc., 40, 59, (1944)
[12] Treloar, L.R.G., Trans. Faraday soc., 42, 83, (1946)
[13] Treloar, L.R.G., Trans. Faraday soc., 50, 881, (1954)
[14] Treloar, L.R.G., The physics of rubber elasticity, (1975), Oxford University Press Oxford · Zbl 0347.73042
[15] Treloar, L.R.G., (), 301
[16] Treloar, L.R.G.; riding, G., (), 261
[17] Valanis, K.C.; Landel, R.F., J. appl. phys., 38, 2997, (1967)
[18] Wang, M.C.; Guth, E., J. chem. phys., 20, 1144, (1952)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.