## Contributions

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Author index ►Martin Boisly, Markus Kästner, Jörg Brummund, Volker Ulbricht

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Large amplitude oscillatory shear of the Prandtl element analysed by Fourier Transform Rheology

Appl. Rheol.24:3 (2014) 35478 (11 pages) ►

This work contributes to the theory of strain controlled large amplitude oscillatory shear (LAOS) as well as modelling the key properties of type III behavior of Hyun, the decreasing storage modulus and a loss modulus with considerable maximum. The latter two can be modelled with the help of the Prandtl element. Since it is a yield stress fluid, the use of LAOS is necessary to calculate the storage and loss modulus. Furthermore, a condition is presented which has to be met in order to avoid even harmonics. The storage and loss modulus as well as the higher harmonics of the Prandtl element are determined analytically in this work. They are given as mathematical functions which can be discussed conveniently. This allows the identification of characteristic points which are related to material parameters of the Prandtl element and enable a physically motivated material parameter identification. Beside this, it is observed that the yield strain do not coincide with the crossover G'(γ) = G''(γ) but with the increasing of the loss modulus and the decreasing of the storage modulus. Thanks to the analytical calculations, it is also obvious that the stress response of yield stress fluids does not necessarily include even harmonics. In this work the steady state stress response of the Prandtl element is also presented as Lissajous plots and Pipkin diagrams to visualise the rheological fingerprint.► Cite this publication as follows:

Boisly M, Kastner M, Brummund J, Ulbricht V: Large amplitude oscillatory shear of the Prandtl element analysed by Fourier Transform Rheology, Appl. Rheol. 24 (2014) 35478.

This work contributes to general theoretical aspects of yield stress fluids with significance for practical phenomenological material modeling. It introduces a terminology so that the material class .yield stress fluid. is defined and can be distinguished from the terms .solid. and .liquid.. This new material classification is based on two criteria, the equilibrium relation and the flow function. In line with this terminology, an experimental procedure for classifying the material behavior is presented. The second key aspect of this paper is a discussion on the proper definition of the term .viscosity.. The benefit of the differential viscosity over the dynamic viscosity in case of non-Newtonian fluids in general is worked out. This is shown by the most elementary yield stress fluid, the friction element, because it is the basis of the yield stress concept. Its constitutive equations are given for positive as well as negative strain rates and are also able to represent the preyield behavior. The theory presented in this article is also applied to the Maxwell, Kelvin-Voigt, and Bingham element to demonstrate the working principle.

Supplementary Informationis contained as an attachment to the reprint-pdf.

► Cite this publication as follows:

Boisly M, Kastner M, Brummund J, Ulbricht V: General aspects of yield stress fluids - Terminology and definition of viscosity, Appl. Rheol. 24 (2014) 14578.

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