Nonsteady Plain-Strain Ideal Plastic Flow Considering Elastic Dead Zone

  • Wonoh Lee
  • Kwansoo Chung
  • Tae Jin Kang
  • Jae Ryoun Youn
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 114)


Ever since the ideal forming theory has been developed for process design purposes, application has been limited to sheet forming and, for bulk forming, to two-dimensional steady flow. Here, application for the nonsteady case was made under the plane-strain condition. In the ideal flow, material elements deform following the minimum plastic work path (or mostly proportional true strain path) so that the ideal plane-strain flow can be effectively described using the two-dimensional orthogonal convective coordinate system. Besides kinematics, schemes to optimize preform shapes for a prescribed final part shape and also to define the evolution of shapes and fhctionless boundary tractions were developed. For demonstration purposes, numerical calculations were made for an automotive part under forging.


Nonsteady ideal bulk forming Rigid perfect plasticity Method of characteristics Orthogonal convective coordinate system 


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  1. 1.
    Richmond, O. and Devenpeck, M.L., 1962, A die profile for maximum efficiency in strip drawing, Proc. 4th U.S. Natn. Cong. Appl. Mech., 1053–1057.Google Scholar
  2. 2.
    Hill, R., 1967, Ideal forming operations for perfectly plastic solids, J. Mech. Phys. Solids, 15, 223–227.CrossRefGoogle Scholar
  3. 3.
    Richmond, O. and Morrison, H.L., 1967, Streamlined wire drawing dies of minimum length, J. Mech. Phys. Solids, 15, 195–203.CrossRefGoogle Scholar
  4. 4.
    Chung, K. and Richmond, O., 1993, A deformation theory of plasticity based on minimum work paths, Int. J. Plasticity, 9, 907–920.CrossRefGoogle Scholar
  5. 5.
    Chung, K. and Richmond, O., 1994, The mechanics of ideal forming, J. Appl. Mech., 61, 176–181.CrossRefGoogle Scholar
  6. 6.
    Chung, K., Yoon, J.W. and Richmond, O., 2000, Ideal sheet forming with frictional constraints, Int. J. Plasticity, 16, 595–610.CrossRefGoogle Scholar
  7. 7.
    Richmond O. and Chung, K., 2000, Ideal stretch forming processes for minimum weight axisymmetric shell structures, Int. J. Mech. Sci., 42, 2455–2468.CrossRefGoogle Scholar
  8. 8.
    Richmond, O. and Alexandrov, S., 2000, Nonsteady planar ideal plastic flow: general and special analytic solution, J. Mech. Phys. Solids, 48, 1735–1759CrossRefGoogle Scholar
  9. 9.
    Richmond O. and Alexandrov, S., 2002, The theory of general and ideal plastic deformation of Tresca solids, Acta Mechanica XXX, 1–10.Google Scholar
  10. 10.
    Alexandrov S., 2001, Private communication.Google Scholar
  11. 11.
    Chung, K., Lee, W. and Richmond, O., 2002, Nonsteady plane-strain ideal plastic flow, Int. J. Plasticity (submitted)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Wonoh Lee
    • 1
  • Kwansoo Chung
    • 1
  • Tae Jin Kang
    • 1
  • Jae Ryoun Youn
    • 1
  1. 1.School of Materials Science and EngineeringSeoul National UniversitySeoulKorea

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