The diffusion of a discontinuity of the shear stress at the boundary of a viscoplastic half-plane |
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| Institution: | 1. Dept. of Industrial Engg., Eindhoven Univ. of Technology, Eindhoven 5600MB, The Netherlands;2. McCombs School of Business, University of Texas, Austin, TX 78712, United States;1. Institute for Problems in Mechanics of the Russian Academy of Sciences,Vernadsky Ave 101 Bldg 1, Moscow, 119526, Russia; Bauman Moscow State Technical University, 2nd Baumanskaya Str 5/1, Moscow, 105005, Russia; National Research Nuclear University TMEPhIT, Kashirskoye shosse 31, Moscow, 115409, Russia; Moscow Technological University, Vernadsky Ave 78, Moscow, 119454, Russia;2. Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India;1. Laboratoire des Sciences de l''Ingénieur Appliquées à la Mécanique et au Génie Electrique (SIAME), Université de Pau et des Pays de l''Adour – IFR – A. Jules Ferry, 64000 Pau, France;2. Aragón Institute for Engineering Research (I3A), Thermal Engineering and Energy Systems Group, University of Zaragoza, Agustín Betancourt Building, C/María de Luna 3, 50018 Zaragoza, Spain;3. Ecole Nationale Supérieure d''Arts et Métiers, ENSAM Marjane II, BP-4024 Meknès Ismailia, Morocco;1. Zachary Departments of Civil Engineering, Texas A&M University, College Station, TX 77843, USA;2. Institute Center for Energy, Mechanical and Materials Engineering Department, Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates |
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| Abstract: | For the problem of the diffusion of a discontinuity of the shear stress at the boundary of a half-plane, which is a special case of the general problem of the diffusion of a vortex layer, the classes of media and types of assignment of boundary conditions for which self-similar solutions exist are discussed. For a viscoplastic medium in a half-plane the problem reduces to the problem in a layer of time-variable thickness, the solution of which does not possess the property of analyticity. The long-term asymptotic of this problem are investigated. In the case where, at an accessible boundary, it is possible simultaneously to measure both the shear stress and the horizontal velocity, an algorithm is proposed for finding a quantity that is difficult to measure, A namely, the thickness of the zone of viscoplastic flow. |
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