Abstract
Several constitutive equations, including the differential models of Phan-Thien and Tanner, Giesekus, Leonov, Acierno et al., and of Larson, and examples of superposition integral models, are reviewed to determine which are best able at least qualitatively to match data for polymer melts in a wide range of deformations. It is found that the superposition integral models are not able to describe accurately reversing deformations, such as elastic recovery or reversing double step strains. The differential models show more promise in this respect, but for most of those proposed thus far, the stress relaxation after a step strain has little or no dependence on the second invariant of the Finger strain tensor. This characteristic can prevent these equations from simultaneously predicting stresses in deformations that strongly align molecules along a single axis, such as uniaxial extension, and those, such as biaxial extension, that do not.
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