Abstract
The implementation of the deformation fields method for integral models within a finite element context [1,2] has been updated with various techniques to have a numerical stability that is comparable to state-of-the-art implementations of differential models. In particular, the time-dependent stability in shear flow, decoupled schemes for zero or small solvent viscosities and the log-conformation representation now have counterparts in the numerical implementation of integral models leading to similar numerical stability. The new techniques have been tested in transient shear flow and the flow around a cylinder confined between two plates for the integral version of upper-convected Maxwell model and for integral models having a non-constant damping function.
Highlights
Integral models are frequently used for modelling the constitutive behaviour of polymer liquids
The implementation of the deformation fields method for integral models within a finite element context [1, 2] has been updated with various techniques to have a numerical stability that is comparable to state-of-the-art implementations of differential models
The time-dependent stability in shear flow, decoupled schemes for zero or small solvent viscosities and the log-conformation representation have counterparts in the numerical implementation of integral models leading to similar numerical stability
Summary
Integral models are frequently used for modelling the constitutive behaviour of polymer liquids. In particular the factorable K-BKZ equation, where the linear rheology is specified by the memory function and the non-linear rheology Preprint submitted to Journal of Non-Newtonian Fluid Mechanics is given by the damping function, is very popular. For an extensive review of the various damping functions that have been used see [3]. New constitutive models based on molecular considerations are often formulated in terms of memory integrals, see for example [4]. Recent developments in modelling complex fluids with a broad power-law relaxation spectrum are of the integral type [5]
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