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Energy changes in elastic plates due to holes and cracks; pp. 26–33

Full article in PDF format | doi: 10.3176/proc.2008.1.03

Reinhold Kienzler

The formation of cavities in stressed elastic plates causes changes in their energy. In particular, the change in energy due to the presence of a crack has been extensively studied over the past decades. The paper adds some comments on the old Griffith controversy and calculates then energy changes due to circular and elliptical flaws and, as a limiting case, due to a crack.

  1. Lowenstam, H. A. and Weiner, S. On Biomineralization. Oxford University Press, Oxford, 1989.

  2. Kienzler, R., Fischer, F. D. and Fratzl, P. On energy changes due to the formation of a circular hole in an elastic sheet. Arch. Appl. Mech., 2006, 75, 681–697.

  3. Inglis, C. E. Stresses in a plate due to the presence of cracks and sharp corners. Proc. Trans. Naval Architects, 1913, 55, 219–241.

  4. Griffith, A. A. The phenomena of rupture and flows in solids. Phil. Trans. Roy. Soc. London, 1920, A221, 163–198.

  5. Griffith, A. A. The theory of rupture. In Proceedings of the First International Congress of Applied Mechanics, Delft (Biezeno, C. B. and Burges, J. M., eds). 1924, 55–63.

  6. Rossmanith, H. P. (ed.). Fracture Research in Retrospect. Balkema, Rotterdam, 1997.

  7. Cotterell, B. A. A. Griffith and the foundations of fracture mechanics. In Fracture Research in Retrospect (Rossmanith, H. P., ed.). Balkema, Rotterdam, 1977, 105–122.

  8. Sih, G. C. and Liebowitz, H. On the Griffith energy criteria for brittle fracture. Int. J. Solids Struct., 1967, 3, 1–22.

  9. Fung, Y. C. Foundation of Solid Mechanics. Prentice-Hall, Englewood Cliffs, 1965.

10. Spencer, A. J. M. On the energy of a Griffith crack. Int. J. Engng. Sci., 1965, 3, 441–449.

11. Barber, J. R. Elasticity, 2nd ed. Kluwer, Dordrecht, 2002.

12. Eshelby, J. D. The force on an elastic singularity. Phil. Trans. Roy. Soc. London, 1951, A244, 87–112.

13. Eshelby, J. D. The elastic energy-momentum tensor. J. Elast.,1975, 5, 321–335.

14. Bilby, B. A. and Eshelby, J. D. Dislocations and the theory of fracture. In Fracture, an Advanced Treatise (Liebowitz, H., ed.). Academic Press, New York, 1968, Vol. 1, 99–182.

15. Sneddon, I. N. The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc. Roy. Soc. London, 1946, A187, 229–260.

16. Günther, W. Über einige Randintegrale der Elastomechanik. Abh. Braunschw. Wiss. Ges., 1962, 14, 53–72.

17. Budianski, B. and Rice, J. R. Conservation laws and energy release rates. ASME J. Appl. Mech., 1973, 40, 201–203.

18. Freund, L. B. Energy flux into the tip of an extending crack in an elastic solid. J. Elast., 1972, 2, 341–349.

19. Pöschl, T. Über eine partikuläre Lösung des biharmonischen Problems für den Außenraum der Ellipse. Math. Z., 1921, 11, 89–96.

20. Muskhelishvili, N. I. Some Basic Problems of Mathematical Elasticity. Noordhoff, Leyden, 1953.

21. Timoshenko, S. P. and Goodier, J. N. Theory of Elasticity, 3rd ed. McGraw Hill, New York, 1970.

22. Hahn, H. G. Elastizitätstheorie. Teubner, Stuttgart, 1985.

23. Gradshteyn, T. S. and Ryzhik, I. M. Table of Integrals, Series and Products. Academic Press, London, 1980.
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