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S.E. Aleksandrov, "Qualitative Properties of Plasticity Equations for Porous Media in Plane Deformation," Mech. Solids. 45 (5), 689-700 (2010)
Year 2010 Volume 45 Number 5 Pages 689-700
DOI 10.3103/S0025654410050043
Title Qualitative Properties of Plasticity Equations for Porous Media in Plane Deformation
Author(s) S.E. Aleksandrov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str.1, Moscow, 119526 Russia, sergei_alexandrov@yahoo.com)
Abstract The instantaneous stress-strain state of a porous rigid-plastic material obeying the cylindrical yield condition and the associated flow rule is considered in the case of plane deformation. It is shown that the type of the system of equations depends on the stress state. In the hyperbolic case, the equations of characteristics and relations along them are derived. An exact solution to the model boundary-value problem with the maximum friction law taken into account is obtained. An asymptotic analysis near the maximum friction surface is performed.
Keywords porous material, rigid-plastic body, maximum friction law, qualitative analysis
References
1.  B. A. Druyanov, Applied Plasticity Theory for Porous Bodies (Mashinostroenie, Moscow, 1989) [in Russian].
2.  F. He, Q. Han, and M. J. Jackson, "Nanoparticulate Reinforced Metal Matrix Nanocomposites - a Review," Int. J. Nanoparticles 1 (4), 301-309 (2009).
3.  I. Sridhar and N. A. Fleck, "The Multiaxial Yield Behavior of an Aluminium Alloy Foam," J. Mater. Sci. 40 (15), 4005-4008 (2005).
4.  B. A. Druyanov and A. R. Pirumov, "Studying the Process of Extrusion of a Porous Material," Vestn. Mashinostr. 60 (9), 61-62 (1980).
5.  Yu. G. Oresov, L. I. Zhivov, V. A. Pavlov, and V. I. Makagon, "Technological Regimes of Hot Extrusion of Powdered Titanium," in Theory and Practice of Powder Compaction (Naukova Dumka, Kiev, 1975), pp. 146-150 [in Russian].
6.  A. G. Zalazinskii and A. P. Polyakov, "Model of a Plastically Compressible Material and Its Application to the Analysis of the Compaction of a Porous Body," Zh. Prikl. Mekh. Tekhn. Fiz. 43 (3), 140-151 (2002) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 43 (3), 457-466 (2002)].
7.  A. G. Zalazinskii, A. A. Polyakov, and A. P. Polyakov, "On Plastic Compression of a Porous Body," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 123-134 (2003) [Mech. Solids (Engl. Transl.) 38 (1), 101-110 (2003)].
8.  S. E. Aleksandrov, A. R. Pirumov, and O. V. Chesnikova, "Plastic Flow of Porous Materials in Friction Contact Area," Poroshk. Metallurg., No. 9-10, 13-20 (2008) [Powder Metall. Met. Ceram. (Engl. Transl.) 1 (9-10), 512-517 (2008)].
9.  S. E. Aleksandrov, A. R. Pirumov, and O. V. Chesnikova, "Compression of a Plastic Porous Material between Rotating Plates," Zh. Prikl. Mekh. Tekhn. Fiz. 50 (4), 128-135 (2009) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 50 (4), 651-657 (2009)].
10.  S. Aleksandrov and O. Richmond, "Singular Plastic Flow Fields near Surfaces of Maximum Friction Stress," Int. J. Non-Linear Mech. 36 (1), 1-11 (2001).
11.  S. P. Moylan, S. Kompella, S. Chandrasekar, and T. N. Farris, "A New Approach for Studying Mechanical Properties of Thin Surface Layers Affected by Manufacturing Processes," Trans. ASME J. Manuf. Sci. Engng 125, 320-315 (2003).
12.  T. A. Trunina and E. A. Kokovikhin, "Formation of Finely Dispersed Structure in Steel Surface Layers under Combined Processing with Hydropressing," Probl. Mashinostr. Nadezhn. Mashin, No. 2, 71-74 (2008).
13.  S. E. Aleksandrov, D. E. Grabko, and O. A. Shikimaka, "To the Determination of Intensive Strain Layer Thickness near the Friction Surface in Metal Forming Processes," Probl. Mashinostr. Nadezhn. Mashin, No. 3, 72-78 (2009).
14.  S. E. Aleksandrov and E. A. Lyamina, "Nonlocal Fracture Criterion near Surface Friction and Its Application to Analysis of Drawing and Extrusion," Probl. Mashinostr. Nadezhn. Mashin, No. 3, 62-68 (2007).
15.  R. E. Dutton, R. L. Goetz, S. Shamasundar, and S. L. Semiatin, "The Ring Test for P/M Materials," Trans. ASME J. Manuf. Sci. Engng 120 (4), 764-769 (1998).
16.  A. J. M. Spencer, "A Theory of the Kinetics of Ideal Soils under Plane Strain Conditions," J. Mech. Phys. Solids 12, 337-351 (1964).
17.  S. E. Aleksandrov and E. A. Lyamina, "Singular Solutions for Plane Plastic Flow of Pressure-Dependent Materials," Dokl. Ross. Akad. Nauk 383 (4), 492-495 (2002) [Dokl. Phys. (Engl. Transl.) 47 (4), 308-311 (2002)].
18.  R. J. Green, "A Plasticity Theory for Porous Solids," Int. J. Mech. Sci. 14, 215-224 (1972).
19.  A. V. Anokhina, V. A. Goloveshkin, A. R. Pirumov, and A. V. Ponomarev, "Axisymmetric Deformation of Plastically Compressible Media with an Immobile Boundary," Vestn. Mashinostr., No. 10, 17-22 (2006) [Russ. Engng Res. (Engl. Transl.) 26 (10), 12-17 (2006)].
20.  S. E. Aleksandrov and D. Harris, "Comparison of Solution Behavior for Three Models of Pressure-Dependent Plasticity: a Simple Analytical Example," Int. J. Mech. Sci. 48 (7), 750-762 (2006).
21.  S. E. Aleksandrov and G. Mishuris, "Qualitative Behavior of Viscoplastic Solutions in the Vicinity of Maximum-Friction Surfaces," J. Engng Math. 65 (2), 143-156 (2009).
Received 12 January 2010
Link to Fulltext http://www.springerlink.com/content/bk73n38339763l27/
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