Abstract
Assuming a rigid viscoplastic material model, it is shown thatthe velocity fields adjacent to surfaces of maximum friction mustsatisfy sticking conditions. This means that the stress boundarycondition, the maximum friction law, may be replaced by the velocityboundary condition. Axisymmetric flows without rotation and planar flowsare considered. Applications of the upper bound theorem are discussed.
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Adams, M.J., Briscoe, B.J., Corfield, G.M., Lawrence, C.J. and Papathanasiou, T.D., 'An analysis of the plane-strain compression of viscoplastic materials', ASME J. Appl.Mech. 64, 1997, 420-424.
Alexandrov, S.E., 'Velocity field near its discontinuity in an arbitrary flow of an ideal rigid-plastic material', Izv. RAN MTT (Mechanics of Solids) 30(5), 1995, 111-117 [translated from Russian].
Alexandrov, S.E. and Druyanov, B.A., 'Friction conditions for plastic bodies', Izv. RAN MTT (Mechanics of Solids) 27(4), 1992, 110-115 [translated from Russian].
Alexandrov, S.E. and Richmond, O., 'Asymptotic behavior of velocity field near surfaces with maximum friction for axisymmetric plastic flow of Tresca material', Soviet Phys. Dokl. 360(4), 1998, 480-482 [in Russian].
Alexandrov, S. and Richmond, O., 'Singular plastic flow fields near surfaces of maximum friction stress', Internat. J. Non-Linear Mech., 1999, accepted for publication.
Alexandrov, S.E., Danilov, V.L. and Chikanova, N.N., 'On the modeling of sticking zones in axisymmetric metal forming operations, using a creep constitutive equation', Izv. RAN MTT (Mechanics of Solids) 35(1), 2000, 149-151 [in Russian].
Azarkhin, A. and Richmond, O., 'Limits to adhesive friction', in Numerical Methods in Industrial Forming Processes, J.-L. Chenot, R.D. Wood and O.C. Zienkiewicz (eds.), Balkema, Rotterdam, 1992, 143-148.
Balaji, P.A., Sundararajan, T. and Lal, G.K., 'Viscoplastic deformation analysis and extrusion die design by FEM', ASME J. Appl. Mech. 58, 1991, 644-650.
Cristescu, N., 'Plastic flow through conical converging dies, using a viscoplastic constitutive equation', Internat. J. Mech. Sci. 17, 1975, 425-433.
Hammad, K.J. and Vradis, G.C., 'Creeping flow of a Bingham plastic through axisymmetric sudden contractions with viscous dissipation', Internat. J. Heat Mass Transfer 39, 1996, 1555-1567.
Hill, R., 'A general method of analyses for metal-working processes', J. Mech. Phys. Solids 11, 1963, 305-326.
Kobayashi, S., Oh, S.-I. and Altan, T., Metal Forming and the Finite-Element Method, Oxford University Press, New York, 1989, 32.
Lubliner, J., Plasticity Theory, MacMillan, New York, 1990, 105.
Malinin, N.N., Creep in Metal Forming, Mashinostroenie, Moscow, 1986, 91 [in Russian].
Rebelo, N. and Kobayashi, S., 'A coupled analysis of viscoplastic deformation and heat transfer-II', Internat. J. Mech. Sci. 22, 1980, 707-718.
Sokolovskii, V.V., 'Equations of plastic flow in surface layer', Prikl. Mat. Mech. (PMM) 20, 1956, 328-334 [in Russian].
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Alexandrov, S., Alexandrova, N. On the Maximum Friction Law in Viscoplasticity. Mechanics of Time-Dependent Materials 4, 99–104 (2000). https://doi.org/10.1023/A:1009851621518
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DOI: https://doi.org/10.1023/A:1009851621518