Aßmus (Eds.), Advanced Methods of Mechanics for Materials and Structures, pp. Ivanova, E., Vilchevskaya, E., Müller, W.H., 2016, Time derivatives in material and spatial description – What are the differences and why do they concern us?, in K. Müller, W.H., Vilchevskaya, E.N., Weiss, W., 2017, A meso-mechanics approach to micropolar theory: A farewell to material description, Physical Mesomechanics, 20(3), pp. Glane, S., Rickert, W., Müller, W.H., Vilchevskaya, E., 2017, Micropolar media with structural transformations: Numerical treatment of a particle crusher, Proceedings of XLV International Summer School - Conference APM 2017, pp. 49-70.įomicheva, M., Vilchevskaya, E.N., Müller, W., Bessonov, N., 2019, Milling matter in a crusher: Modeling based on extended micropolar theory, Continuum Mechanics and Thermodynamics (in print). 1759-1780.īain, O., Billingham, J., Houston, P., Lowndes, I., 2015, Flows of granular material in two-dimensional channels, Journal of Engineering Mathematics, 98(1), pp. Ivanova, E.A., Vilchevskaya, E.N., 2016, Micropolar continuum in spatial description, Continuum Mechanics and Thermodynamics, 28(6), pp. The correctness of the algorithm is checked by specializing to the case of a flow through a tunnel of constant cross-section under the influence of gravity, for which an analytical solution is available.Įremeyev, V.A., Lebedev, L.P., Altenbach, H., 2012, Foundations of micropolar mechanics, Springer Science & Business Media, Heidelberg, New York, Dordrecht, London.Įringen, A.C., Kafadar, C.B., 1976, Polar field theories, In: Continuum physics IV, Academic Press, London. Numerical results for velocities, stresses, and for the pressure dependence of the funnel flow are presented. As a prerequisite for the study of the fully coupled initial boundary value 2D-flow problem of a micropolar fluid the funnel flow of a Navier-Stokes fluid is investigated based on an implicit finite difference scheme using the Thomas algorithm. The need for using numerical methods of fluid mechanics is emphasized. Then a review of the current state-of-the-art is presented and a necessary extension of the problem is motivated.

Initially the fundamental equations of micropolar media are revisited and the problem of structural changes of micropolar media moving in a crusher is explained. In this paper foundations are laid for a future solution of a fully coupled flow problem for the micropolar medium undergoing structural change in a funnel-shaped crusher.

Nicolay bessonov