Abstract
The goal of this article is to provide some essential results for the solution of a regularized viscoplastic frictional flow model adapted from the extensive mathematical analysis of the Bingham model. The Bingham model is a standard for the description of viscoplastic flows and it is widely used in many application areas. However, wet granular viscoplastic flows necessitate the introduction of additional non-linearities and coupling between velocity and stress fields. This article proposes a step toward a frictional coupling, characterized by a dependence of the yield stress to the pressure field. A regularized version of this viscoplastic frictional model is analysed in the framework of stationary flows. Existence, uniqueness and regularity are investigated, as well as finite-dimensional and algorithmic approximations. It is shown that the model can be solved and approximated as far as a frictional parameter is small enough. Getting similar results for the non-regularized model remains an issue. Numerical investigations are postponed to further works.
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El Khouja, N., Roquet, N. & Cazacliu, B. Analysis of a Regularized Bingham Model with Pressure-Dependent Yield Stress. J. Math. Fluid Mech. 17, 723–739 (2015). https://doi.org/10.1007/s00021-015-0230-9
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DOI: https://doi.org/10.1007/s00021-015-0230-9