Archive of Applied Mechanics

, Volume 81, Issue 12, pp 1935–1952 | Cite as

A general analytic solution for plane strain bending under tension for strain-hardening material at large strains

  • Sergei AlexandrovEmail author
  • Ken-ichi Manabe
  • Tsuyoshi Furushima


A new analytic solution for plane strain bending under tension of a sheet is proposed for elastic-plastic, isotropic, incompressible, strain-hardening material at large strains. Numerical treatment is only necessary to calculate ordinary integrals and solve transcendental equations. No restriction is imposed on the hardening law. All governing equations and boundary conditions are exactly satisfied. The only exception is that the actual stress distribution over the ends of the sheet is replaced with a concentrated force and a concentrated bending moment. The through-thickness distribution of residual stresses and a measure of springback are also found. The range of validity of the solution is determined. An illustrative example is provided for Swift’s hardening law.


Bending under tension Strain hardening Large strains Residual stresses Analytic solution 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Sergei Alexandrov
    • 1
    Email author
  • Ken-ichi Manabe
    • 2
  • Tsuyoshi Furushima
    • 2
  1. 1.A.Yu. Ishlinsky Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia
  2. 2.Department of Mechanical EngineeringTokyo Metropolitan UniversityTokyoJapan

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