Sheet Necking—I. Validity of Plane Stress Assumptions of the Long-Wavelength Approximation

  • J. W. Hutchinson
  • K. W. Neale
  • A. Needleman


Two special solutions are used to illustrate the errors involved in the analysis of sheet necking from invoking plane stress assumptions. The first is an exact solution for the growth-rate of a small amplitude, sinusoidal thickness variation in a sheet of material characterized by \(\dot \in \) = ασ n in simple tension. The plane stress assumptions become accurate when the ratio of variation wavelength to average thickness exceeds four and otherwise lead to overestimates of the actual growth-rate. When this same ratio is approximately unity the relative size of the thickness variation decays with increasing deformation—an effect not predicted by a plane stress analysis. The second special solution is obtained using a perturbation expansion with the nonlinear long-wavelength solution (i.e., the plane stress solution) as the lowest order contribution. In this way explicit corrections to the plane stress solution are obtained. Selected comparisons with fully nonlinear finite element calculations are made.


Sheet Metal Plane Stress Form Limit Diagram Minimum Section Hydrostatic Tension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Z. Marciniak, K. Kuczyński, Int. J. Mech. Sci., 9 (1967), 609.CrossRefGoogle Scholar
  2. [2]
    J. W. Hutchinson and H. Obrecht, Fracture 1977, ICF4 (ed. D. M. R. Taplin), 1 (1977), 101.Google Scholar
  3. [3]
    J. W. Hutchinson and K. W. Neale, Acta Met., 25 (1977), 839.CrossRefGoogle Scholar
  4. [4]
    E. J. Appleby and O. Richmond, to be published.Google Scholar
  5. [5]
    P. W. Bridgman, Studies in Large Plastic Flow and Fracture, Harvard University Press (1964).Google Scholar
  6. [6]
    A. Needleman and C. F. Shih, to be published.Google Scholar

Copyright information

© Plenum Press, New York 1978

Authors and Affiliations

  • J. W. Hutchinson
    • 1
  • K. W. Neale
    • 2
  • A. Needleman
    • 3
  1. 1.Harvard UniversityCambridgeUSA
  2. 2.Université de SherbrookeSherbrookeCanada
  3. 3.Brown UniversityProvidenceUSA

Personalised recommendations