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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2012, Volume 53, Issue 3, Pages 150–157
(Mi pmtf1373)
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This article is cited in 3 scientific papers (total in 3 papers)
Quasi-static compression and spreading of an asymptotically thin nonlinear viscoplastic layer
D. V. Georgievskii, V. S. Yushutin Lomonosov Moscow State University, Moscow, 119991, Russia
Abstract:
The problem of quasi-static compression and spreading (squeezing) of a thin viscoplastic layer between approaching absolutely rigid
parallel-arranged plates is solved using asymptotic integration methods rapidly developed in recent years in the mechanics of deformable thin bodies. A solution symmetric about the coordinate axes is sought in the same region of the layer as in the classical Prandtl problem. The layer material is characterized by a yield point and a hardening function relating the intensities of the stress and strain rate tensors. The conditions of no-flow and reaching certain values by tangential stresses are imposed on the plate surfaces. The coefficients at the terms of the asymptotic expansions corresponding to the minus first and zero powers of the small geometrical parameter are obtained. An approximate analytical solution in the case of power hardening and large Saint-Venant numbers is given. The physical meaning of the roughness coefficient characterizing the cohesion between the plates and viscoplastic material is discussed.
Keywords:
viscoplastic flow, Bingham material, Prandtl problem, asymptotic expansion, compression, spreading, squeezing.
Received: 25.04.2011
Citation:
D. V. Georgievskii, V. S. Yushutin, “Quasi-static compression and spreading of an asymptotically thin nonlinear viscoplastic layer”, Prikl. Mekh. Tekh. Fiz., 53:3 (2012), 150–157; J. Appl. Mech. Tech. Phys., 53:3 (2012), 437–443
Linking options:
https://www.mathnet.ru/eng/pmtf1373 https://www.mathnet.ru/eng/pmtf/v53/i3/p150
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