Experimental Mechanics

, Volume 36, Issue 2, pp 99–112 | Cite as

Determination of elastic-plastic stresses and strains from measured surface strain data

  • M. A. Sutton
  • X. Deng
  • J. Liu
  • L. Yang


A rigorous approach founded in the fundamental principles of plasticity is used to develop an accurate numerical algorithm for the determination of stresses and elastic and plastic strains from total strain data measured on a structure surface. The approach used to develop the algorithm and its relationship to both the flow theory of plasticity and recent advances in tangent stiffness-based numerical solution procedures for elastic-plastic boundary value problems are presented. Verification of the method for plane stress problems is demonstrated. A discussion of how the method can be used with measured surface displacement data is proved.

Key words

elastic-plastic strain separation experimental strain data reduction stress field estimation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kobayashi, A. S., ed., Handbook on Experimental Stress Analysis, SEM Publisher (1993).Google Scholar
  2. 2.
    Mendelson, A., Plasticity: Theory and Application, Krieger Publishing (1983).Google Scholar
  3. 3.
    Owen, D.R.J. andHinton, E., Finite Element in Plasticity: Theory and Practice, Pineridge Press, Swansea, England (1980).Google Scholar
  4. 4.
    Wilkins, M. L., “Calculation of Elastic-Plastic Flow,”Methods of Computational Physics, vol. 3, eds. B. Alder, S. Fernback andM. Roternerg, Academic Press, New York (1964).Google Scholar
  5. 5.
    Krieg, R. D. and Key, S. W., “Implementation of a Time-Independent Plasticity Theory into Structural Computer Programs,” ASME AMD 20: Constitutive Equations in Viscoelasticity, eds. J. A. Stricklin and K. J. Saczalski, ASME, 125–137 (1976).Google Scholar
  6. 6.
    Hughes, T.J.R. andShakib, F., “Pseudo-Corner Theory: A Simple Enhancement of J 2 Flow Theory for Applications Involving Non-proportional Loading,”Eng. Comput.,3,116–120 (1986).Google Scholar
  7. 7.
    Rice, J. R. andTracy, D. M., “Computational Fracture Mechanics,”Numerical and Computer Methods in Structural Mechanics, eds. S. J. Fenves, N. Perrone, A. Robinson andW. C. Schnobrich, Academic Press, New York (1973).Google Scholar
  8. 8.
    Tracy, D. M., “Finite Element Solutions for Crack-Tip Behavior in Small-Scale Yielding,”J. Eng. Mat. and Technol.,98 (2),146–151 (1976).Google Scholar
  9. 9.
    Krieg, R. D. andKrieg, D. B., “Accuracies of Numerical Solution Methods for the Elastic-Perfectly Plastic Model,”J. Pressure Vessel Technol.,99 (4),510–515 (1977).Google Scholar
  10. 10.
    Schreyer, H. L., Kulak, R. F. andKramer, J. M., “Accurate Numerical Solutions for Elastic-Plastic Models,”J. Pressure Vessel Technol.,101,226–234 (1979).Google Scholar
  11. 11.
    Deng, X., “Dynamic Crack Propagation in Elastic-Plastic Solids,”Ph.D. dissertation, California Institute of Technology, Pasadena (1990).Google Scholar
  12. 12.
    Marcal, P. V., “A Stiffness Method for Elastic-Plastic Problems,”Int. J. Mech. Sci.,7,220–238 (1965).Google Scholar
  13. 13.
    Marcal, P. V. andKing, I. P., “Elastic-Plastic Analysis of Two-Dimensional Stress Systems by the Finite Element Method,”Int. J. Mech. Sci.,9,143–155 (1967).CrossRefGoogle Scholar
  14. 14.
    Marques, J.M.M.C., “Stress Computation in Elastoplasticity,”Eng. Comput.,1,42–51 (1984).Google Scholar
  15. 15.
    Deng, X., “Negative Plastic Flow and Its Prevention in Elasto-Plastic Finite Element Computation,”Finite Elements in Analysis and Design,7,181–191 (1990).CrossRefGoogle Scholar
  16. 16.
    Keil, S. andBenning, O., “On the Evaluation of Elasto-Plastic Strains Measured with Strain Gages,”Exp. Mech.,19 (8),265–270 (1979).CrossRefGoogle Scholar
  17. 17.
    Kang, B.S.J. andKobayashi, A. S., “J-Resistance Curves in Aluminum SEN Specimens Using Moiré Interferometry,”Exp. Mech. 28 (2),159–169 (1988).Google Scholar
  18. 18.
    Cardenas-Garcia, J. F., Read, D. T. andMoulder, J. C., “Experimental Study of Path Independence of the J-Integral in an Aluminum Tensile Panel,”Exp. Mech.,27 (3),328–332 (1987).Google Scholar
  19. 19.
    Guery, M. andFrancois, D., “Analyse experimentale des champs de contraintes planes elasto-plastiques par la methode du moire,”Journal de Mecanique theorique et appliquee,4 (1),139–155 (1985).Google Scholar
  20. 20.
    Sharpe, W. N., “On the Measurement of Elastoplastic Stresses,”Exp. Mech.,32 (1),62–67 (1992).Google Scholar
  21. 21.
    ABAQUS, Finite Element Program Version 4.9, Hibbett, Karlsson and Sorenson, Providence, RI (1992).Google Scholar
  22. 22.
    Deng, X., PSOLID: A Finile Element Program for Elastic-Plastic Solids, California Institute of Technology, Pasadena (1988).Google Scholar
  23. 23.
    Sutton, M. A., Turner, J. L., Bruck, H. A. andChae, T. L., “Full-Field Representation of the Discretely Sampled Surface Deformations for Displacement and Strain Analysis,”Exp. Mech.,31 (2),168–177 (1991).Google Scholar
  24. 24.
    Post, D., Han, B. T. andIfju, P., High Sensitivity Moiré, Springer-Verlag, New York (1994).Google Scholar
  25. 25.
    Han, G., Sutton, M. A. andChao, Y. J., “A Study of Stationary Crack-Tip Deformation Fields in Thin Sheets by Computer Vision,”Exp. Mech.,34 (2),125–140 (1994).CrossRefGoogle Scholar
  26. 26.
    Han, G., Sutton, M. A., Chao, Y. J. andLyons, J. S., “A Study of Stable Crack Growth in Thin SEC Specimens of 304 Stainless Steel by Computer Vision,”Eng. Fract. Mech.,52, (3),525–555 (1995).Google Scholar
  27. 27.
    Dawicke, D. S. andSutton, M. A., “CTOA and Crack-Tunneling Measurements in Thin Sheet 2024-T3 Aluminum Alloy,”Exp. Mech.,34 (4),357–369 (1994).CrossRefGoogle Scholar
  28. 28.
    Sutton, M. A., Bruck, H. A. andMcNeill, S. R., “Determination of Deformations Using Digital Correlation with the Newton-Raphson Method for Partial Differential Corrections,”Exp. Mech.,29 (3),261–267 (1989).Google Scholar
  29. 29.
    Sutton, M. A. andMcNeill, S. R., “The Effects of Subpixel Image Restoration on Digital Correlation Error Estimates,”Opt. Eng.,27 (3),163–175 (1988).Google Scholar
  30. 30.
    Dohrmann, C. R. and Busby, H. R., “Spline Function Smoothing and Differentiation of Noisy Data on a Rectangular Grid,” Proc. 6th Int. Conf. on Exp. Mech., 843–849 (1988).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1996

Authors and Affiliations

  • M. A. Sutton
    • 1
  • X. Deng
    • 1
  • J. Liu
    • 1
  • L. Yang
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of South CarolinaColumbia

Personalised recommendations