Abstract
In the framework of extended irreversible thermodynamics, the Chen-Yeh theoretical “mixture” model treats magnetorheological (MR) fluids by evolutionary constitutive equations that, in the pre-yield region, manifest the co-presence of elastic, viscoelastic and viscoplastic behaviors. However, such model is characterized by high computational complexity; so, it is hoped to find possible qualitative correspondences between the evolutionary equations of this theoretical model and the evolutionary equations of experimental ones. Therefore, in this paper, we present an innovative sequential algorithm to achieve the qualitative correspondence between the Chen-Yeh model with the Susan-Resiga experimental one that, here, under the same operating conditions and in the framework of generalized standard materials (in shear thinning flow), has been proved to be characterized by acceptable computational complexity compatible with the most important industrial applications.
Supported by the Italian National Group of Mathematical Physics (GNFM-INdAM) and the University of Messina through FFO 2019.
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Notes
- 1.
Industrially, thepre-yieldregion, for an MR fluid, is very important because it represents a sort of upper limit of theme chanical resistance of the MR fluid above which it loses its rheological characteristics to assume the properties of an ordinary fluid.
- 2.
Artificial state to separate plastic and elastic deformations.
- 3.
\(\mathbf {u}^{SP}+\mathbf {u}^{SE}=\mathbf {u}^S\), \(\xi ^S+\mathbf {u}^{SP}=X^S\) and \(\xi ^S+\mathbf {u}^S=x\).
- 4.
\(_{,i}\equiv \frac{\partial }{\partial x_i}\) stands for the partial derivatives by coordinates.
- 5.
\(W_1(\dot{\gamma })\) and \(W_2(\dot{\gamma })\) must be continuous together their first derivative to ensure smooth transitions between the two different behaviors.
- 6.
\(\dot{(\cdot )}=\frac{d}{dt}(\cdot )\), so that the time variable appeared.
- 7.
This hypothesis is plausible since in the usual rheometers it is the operating condition more frequent.
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Versaci, M., Palumbo, A. (2022). An Algorithmic Proposal for the Qualitative Comparison Between the Chen-Yeh EIT Mixture Model and the Susan-Resiga GSMs Experimental Model for MR Fluids. In: Camacho, D., Rosaci, D., Sarné, G.M.L., Versaci, M. (eds) Intelligent Distributed Computing XIV. IDC 2021. Studies in Computational Intelligence, vol 1026. Springer, Cham. https://doi.org/10.1007/978-3-030-96627-0_28
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DOI: https://doi.org/10.1007/978-3-030-96627-0_28
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