Wh. Han et al., Mechanical and swelling behaviors of rubber: A comparison of some molecular models with experiment, MATH MECH S, 4(2), 1999, pp. 139-167
A review is given of several current network models (constrained chain mode
l, localization model, liquidlike model, and eight-chain model) that have b
een developed to explain nonideal rubbery behavior. The stress-strain relat
ionships for both dry and swollen networks are discussed. It is shown that
the constrained chain model of Flory, Erman, and Monnerie provides the best
description of the considered models for the stress-strain response of bot
h the dry state and swollen state properties of cross-linked rubber network
s. The localization model of Gaylord and Douglas fits the dry-state stress-
strain data very well, but the predictions of the mechanical response in th
e swollen state are not as good as those obtained with the constrained chai
n model. The liquidlike model of DiMarzio yields reasonable description of
extension behavior, but it does not explain the observed modest decrease of
the elastic modulus (reduced stress) with increasing compression; nor does
the liquidlike model predict the decreasing modulus with increasing swelli
ng correctly. The eight-chain model of Arruda and Boyce puts forward a stre
ss-strain relation that includes the finite extensibility of the network ch
ains. It is shown that at moderate deformation ratios, the eight-chain mode
l does not provide even qualitative agreement with the experimental stress-
strain data for both the dry and swollen states.