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

作者：Alexandrov Sergei^*; Manabe Ken ichi; Furushima Tsuyoshi

来源：Archive of Applied Mechanics, 2011, 81(12): 1935-1952.

DOI：10.1007/s00419-011-0529-9

• Bending under tension
• Strain hardening
• Large strains
• Residual stresses
• Analytic solution

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.

• 出版日期2011-12