DE Constitutive equation

Doi and Edwards noted that since % = 2 is expected to be much smaller than the reptation time Tj, then for flows that are fast compared to the rate of reptation 1/Tj, but slow compared to the rate of retraction 1 /t, one can assume that the chains remain completely retracted during flow i.e., there is no chain stretch. Under this assumption, Doi and Edwards, in a seminal series of papers [12-15] derived the famous constitutive equation that bears their name. The Doi-Edwards (DE) constitutive equation, introduced in Section 10.3.4, is written as ... 

The simplest nonlinear tube model is the classical Doi-Edwards (DE) constitutive equation for linear polymers, which accounts for reptation and affine rotation of tube segments. The Doi-Edwards equation predicts thinning in both shear and extension, because it accounts for orientation of tube segments, but it is unable to predict extension thickening because it neglects the stretching of tube segments. Inclusion of tube stretch leads to the Doi-Edwards-Marrucci-... 

The DE Constitutive Equations. The DE model (52-56) made a major breakthrough in polymer viscoelasticity in that it provided an important new molecular physics based constitutive relation (between the stress and the applied deformation history). This section outlines the DE approach that built on the reptation-tube model developed above and gave a nonlinear constitutive equation, which in one simplified form gives the K-BKZ equation (70,71). The model also inspired a significant amount of experimental work. One should begin by... 

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