Nonlinear Generalized Maxwell-Type Models for Time-Dependent Rheology of Glass-Forming Fluids

Kurzfassung

The rheology of viscoelastic, shear-thinning glass-forming fluids shows a rich set of phenomena that are not easy to capture in simple constitutive models. To learn about the material, several rhelogical protocols aimed at measuring the transient stress/strain evolution are commonly used: startup flow, flow cessation, and large-amplitude oscillatory shear (LAOS) are among them. Microscopic theory on the basis of the integration throuh transients framework combined with mode-coupling theory (ITT-MCT) pioneered by Fuchs and Cates suggests non-trivial integral equations capturing the flow history of the material. Since these are difficult to solve and also difficult to generalize, simplified models on the basis of the Maxwell model and fluidity models have been developed. Here we investigate these nonlinear generalized Maxwell-type models for the transient stress- and strain-evolution in a glass-forming material under various driving protocols. We developed numerical methods to solve these models, that are (as ITT-MCT) typically formulated as strain-controlled models, also under stress-controlled conditions. We apply our methods to various non-stationary situations including creep tests, LAOS, and recovery rheology as suggested by Kamani and Rogers recently.