In this paper we will show how the recently introduced deformation field method (Peters et al. 1999 and van Heel et al. 1999) can be generalized to complex flow simulations of nontime strain separable integral constitutive models. To illustrate this generalization we start with the time strain separable Doi Edwards model and we show how the approach can be generalized to nontime strain separable models. As an example of such a model we consider the reptation model which was recently introduced by Mead et al. (Mead et al. 1998). In this reptation model also tube-stretch and convective constraint release are taken into account. We use both models to simulate startup of two-dimensional flow past a cylinder positioned between two parallel plates.
Peters, E. A. J. F., van Heel, A. P. G., Hulsen, M. A., & Brule, van den, B. H. A. A. (2000). Generalization of the deformation field method to simulate advanced reptation models in complex flows. Journal of Rheology, 44(4), 811-829. https://doi.org/10.1122/1.551125