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Entangled polymers are an important class of materials for their toughness, processability, and functionalizability. During processing, deformation introduces elastic stresses due to a combination of polymer orientation and polymer stretching. For many flows, however, the elastic contribution from chain stretching is not significant, and so-called “nonstretching” approximations have been developed to help explain and interpret experimental observations. Unfortunately, these nonstretching models tend to be limited to simple polymer formulations (linear and monodisperse) and are not useful for understanding any effects from marginal chain stretching that may be present. In this paper, we show that nonstretching approximations can be formally constructed as a perturbation expansion starting from a fully stretching constitutive equation. We apply this framework to the Rolie-Poly model, deriving the existing nonstretching variation and expanding to the second order. The second-order continuation provides quantitatively improved accuracy for both steady and unsteady flows and prevents a pathological/nonphysical blowup that can occur when effects from marginal chain stretching are ignored. We also derive and discuss leading order nonstretching approximations for more complex models of entangled polymers, accounting for disentanglement dynamics, polydispersity, and reversible scission reactions. Alternatives to the formal perturbation framework are also discussed, with potential trade-offs between accuracy, versatility, and computational cost. 

We review a selection of models for wormlike micelles undergoing reptation and chain sequence rearrangement (e.g. reversible scission) and show that many different assumptions and approximations all produce similar predictions for linear rheology. Therefore, the inverse problem of extracting quantitative microscopic information from linear rheology data alone may be ill-posed without additional supporting data to specify the sequence rearrangement pathway. At the same time, qualitative parameter estimates can be obtained equally well from any of the models in question. Through our study, we also show that the Poisson renewal model can be reformulated as a differential constitutive equation on the tube survival prob- ability distribution function. Using this reformulation, we identify two previously overlooked inconsistencies with Poisson renewal and discuss how these can be resolved by re-interpreting what the model calls a `breaking time'.