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IssuesArchive of Issues2001-5pp.47-55

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A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov, "On one case of plane flow of Bingham media," Mech. Solids. 36 (5), 47-55 (2001)
Year 2001 Volume 36 Number 5 Pages 47-55
Title On one case of plane flow of Bingham media
Author(s) A. V. Gnoevoi (Moscow)
D. M. Klimov (Moscow)
V. M. Chesnokov (Moscow)
Abstract Statements of some problems for Bingham flows with a rigid core are shown to contradict the physical meaning of these problems. For a plane problem of Bingham flow in a channel with deformable walls, under the assumption that there exists a quasi-rigid core, it is shown that the boundary conditions on the interface between the shear and rigid regions are violated. A thin layer approximation is considered for the solution of the problem of plane flow of a Bingham medium between two smooth deformable surfaces. The solution of the problem is obtained under the assumption that there are three regions in the flow: two regions of shear flow adjacent to the deformable surfaces and the third region of plastic flow between these two. The general solution obtained allows us to construct, as a special case, the solution for the plastic flow and the solution of the Prandtl problem for a plastic layer compressed by two rigid parallel plates. The results are compared with those obtained by other authors.
References
1.  A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov, On the Theory of Bingham Flows [in Russian], Preprint No. 626, In-t Problem Mekhaniki RAN, Moscow, 1998.
2.  M. Reiner, Deformation, Strain and Flow. An Elementary Introduction to Rheology [Russian translation], Gostekhizdat, Moscow, 1963.
3.  G. Henky, "On slow stationary flows in plastic bodies with applications to rolling, forging and drawing," in Yu. N. Rabotnov (Editor), Theory of Plasticity [Russian translation], pp. 136-156, Izd-vo Inostr. Lit-ry, 1948.
4.  M. P. Volarovich and A. M. Gutkin, "Viscoplastic flow between two plane parallel walls or in the annular space between two coaxial tubes," Zh. Tekhn. Fiziki, Vol. 16, No. 3, pp. 321-328, 1946.
5.  V. P. Myasnikov, "Flow of a viscoplastic medium with complex shear," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, No. 5, pp. 76-87, 1961.
6.  P. M. Ogibalov and A. Kh. Mirzadzhanzade, Nonstationary Motion of Viscoplastic Media [in Russian], Izd-vo MGU, Moscow, 1977.
7.  V. P. Myasnikov, "On the compression of a viscoplastic layer by rigid plates," Izv. AN SSSR. Mekh. i Mashinostr., No. 4, pp. 92-96, 1963.
8.  G. G. Lipscomb and M. M. Denn, "Flow of Bingham fluids in complex geometries," Non-Newt. Fluid. Mech., Vol. 14, No. 4, pp. 337-346, 1984.
9.  L. M. Kachanov, Principles of the Theory of Plasticity [in Russian], Nauka, Moscow, 1969.
10.  A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov, A Study of Viscoplastic Flows in Channels and Cavities with Variable Shape of Their Walls [in Russian], Poligrafservis, Moscow, 1995.
11.  B. Saint-Venant, "On the derivation of equations of interior motions arising in solid plastic bodies beyond the limits of elasticity," in Yu. N. Rabotnov (Editor), Theory of Plasticity, Izd-vo Inostr. Lit-ry, Moscow, 1948.
12.  M. D. Van Dyke, Perturbation Methods in Fluid Mechanics [Russian translation], Mir, Moscow, 1967.
13.  N. N. Malinin, Applied Theory of Plasticity and Creep [in Russian], Mashinostroenie, Moscow, 1975.
Received 18 September 2000
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