Analysing the large amplitude oscillatory shear response of a bingham-hooke model in pipkin space and by fourier Transform rheology to predict weak strain overshoots

Abstract

The work presented in this paper contributes to theory behind the modelling of strain-controlled large amplitude oscillatory shear (LAOS) with weak strain overshoot. The latter term refers to a decreasing strain amplitude dependent storage modulus and a peak in loss modulus. These physical nonlinearities are restricted in this work in order to remain within the geometrically linear theory measured for an inertial system. It is also premised that yielding causes weak strain overshoot. Yielding is modelled with the aid of the Bingham–Hooke model consisting of a Hookean spring connected in series to a Bingham model. In addition, the Bingham–Hooke model is connected in parallel to an rCross model, the LAOS response of which was investigated with the aid of FT rheology in [Boisly et al., Journal of Non-Newtonian Fluid Mechanics 225 (2015) 10–27]. The LAOS behaviour of the Bingham–Hooke model is analysed in this work using Fourier Transform (FT) rheology and Lissajous plots in Pipkin space. This approach facilitates the identification of so-called characteristic points of FT harmonics. These are distinct points – for example maximum loss modulus – easy to determine experimentally and can therefore be used for the purposes of parameter identification. Analytical methods are applied to relate material parameters to characteristic points. It is therefore possible to identify material parameters deterministically without minimising residuals with the aid of nonlinear optimisation algorithms. This insight enables the authors to analytically model nonlinear phenomena based on the characteristic points of FT harmonics. The entire set of elastic, viscous and plastic material parameters – η0, η∞, K1, G, η and yield stress τy – are identified by evaluating the characteristic points of the storage and loss modulus.