Caustics and quasiconformality. A new method for the evaluation of stress singularities

  • P. S. Theocaris
  • G. N. Makrakis
Original Papers
Received:

Abstract

The relation between the optical mapping of caustics and the function-theoretic concept of quasiconformality is investigated. Utilizing this relation, an experimental technique for the evaluation of the order of singularity for singular elastic fields was developed. In particular, the mapping of an infinitesimal circle onto an infinitesimal ellipse by means of the (pseudo)caustics, provides the unique possibility of directly evaluating the stress singularity by experimental means.

Keywords

Experimental Technique Mathematical Method Stress Singularity Optical Mapping Elastic Field 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. L. Williams,Stress singularities resulting from various boundary conditions in angular corners in extension, J. Appl. Mech.19, 562 (1952).Google Scholar
  2. [2]
    A. I. Kalandiia,Remarks on the singularity of elastic solutions near corners, J. Math. Mech.33, 132 (1969).Google Scholar
  3. [3]
    D. B. Bogy,Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading, J. Appl. Mech.35, 460 (1968).Google Scholar
  4. [4]
    J. Dundurs,Discussion of the: Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading, by D. B. Bogy, J. Appl. Mech.36, 650 (1969).Google Scholar
  5. [5]
    J. R. Rice and G. C. Sih,Plane problems of cracks in dissimilar media, J. Appl. Mech.32, 418 (1965).Google Scholar
  6. [6]
    V. L. Hein and F. Erdogan,Stress singularities in a two-material wedge, Int. J. Fract. Mech.7, 317 (1971).Google Scholar
  7. [7]
    A. H. England,On stress singularities in linear elasticity, Int. J. Engng. Sci.9, 571 (1971).Google Scholar
  8. [8]
    P. S. Theocaris,The order of singularity at a multiwedge corner of a composite plate, Int. J. Engng. Sci.12, 107 (1975).Google Scholar
  9. [9]
    J. R. Benthem,State of stress at the vertex of a quarter-infinite crack in a half-space, Int. J. Solids Structures13, 479 (1977).Google Scholar
  10. [10]
    R. J. Nuismer and G. P. Sendeckyj,On the changing order of singularity at crack tip, J. Appl. Mech.44, 427 (1977).Google Scholar
  11. [11]
    G. P. Sendeckyj,Debonding of rigid curvilinear inclusions in longitudinal shear deformation, Engng. Fract. Mech.6, 33 (1974).Google Scholar
  12. [12]
    P. S. Theocaris and G. N. Makrakis,The kinked crack solved by Mellin transform, J. Elasticity16, 393 (1986).Google Scholar
  13. [13]
    J. Hutchinson,Singular behaviour at the end of a tensile crack in a hardening material, J. Mech. Phys. Solids16, 13 (1968).Google Scholar
  14. [14]
    P. S. Theocaris,Experimental evaluation of stress concentration and intensity factors, inMechanics of fracture (ed. G. C. Sih), vol.7, Martinus Nijhoff Publishers 1981.Google Scholar
  15. [15]
    P. S. Theocaris,Local yielding around crack-tip in plexiglass, J. Appl. Mech.37, 409 (1970).Google Scholar
  16. [16]
    P. S. Theocaris and C. Razem,Deformed boundaries determined by the method of caustics, J. Strain Analysis12, 223 (1977).Google Scholar
  17. [17]
    Yung-Chen Lu,Singularity theory and an introduction to catastrophe theory, Springer-Verlag, Berlin 1976.Google Scholar
  18. [18]
    R. Courant and D. Hilbert,Methods of mathematical physics, vol. II (Chapt. IV, p. 374), Interscience Publishers, New York 1962.Google Scholar
  19. [19]
    L. Bers,Theory of pseudo-analytic functions, Lecture notes, Inst. Math. Mech., New York University 1953.Google Scholar
  20. [20]
    L. Bers,On a theorem of Mori and the definition of quasiconformality, Trans. Amer. Math. Soc.84, 78 (1956).Google Scholar
  21. [21]
    L. Ahlfors,On quasiconformal mappings, J. Analyses Math.4, 1 (1954).Google Scholar
  22. [22]
    M. A. Lavrent'ev,Variational methods for boundary value problems for systems of elliptic equations (transl. from Russian by J. Radok), D. Noordhoff Ltd., Groningen, The Netherlands 1963.Google Scholar
  23. [23]
    N. I. Muskhelishvili,Some basic problems of the mathematical theory of elasticity, Noordhoff Int. Publishing, Leyden 1975.Google Scholar
  24. [24]
    P. S. Theocaris,Blunting phenomena in cracked ductile plates under mixed mode conditions, Engng. Fract. Mech.31, 255 (1988).Google Scholar

Copyright information

© Birkhäuser Verlag 1989

Authors and Affiliations

  • P. S. Theocaris
    • 1
  • G. N. Makrakis
    • 1
  1. 1.Department of Engng. SciencesAthens National Technical UniversityAthensGreece

Personalised recommendations