Configurational Mechanics Applied to Strength — of — Materials

  • R. Kienzler
  • G. Herrmann
Part of the International Centre for Mechanical Sciences book series (CISM, volume 427)


Defects, especially cracks, are treated on the basis of engineering-type theories of bars, beams, shafts, discs, plates and shells. The present contribution is concerned with conservation and balance laws in one- and two-dimensional theories of Strength — of — Materials and provides a method to calculate stress-intensity factors for structural members with cracks.


Cylindrical Shell Strain Energy Density Plate Theory Shell Theory Middle Surface 
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  1. Bazant, Z.P. (1990). Justification and improvement of Kienzler and Herrmann’s estimate of stress intensity factors of cracked beam. Engineering Fracture Mechanics 36: 523–525.CrossRefGoogle Scholar
  2. Benthem, J.P., and Koiter, W. T. (1973). Asymptotc approximations to crack problems. In: Sih, G.C. (ed.), Mechanics of Fracture I. Noordhoff: Leyden. 131–178.Google Scholar
  3. Eschenauer, H.,Olhoff, N., and Schnell, W. (1997). Applied Structural Mechanics. Springer: Berlin.CrossRefGoogle Scholar
  4. Eshelby, J.D. (1975). The calculus of energy release rates. In: Sih, G.C., van Elst, H. C., and Broek, D. (eds.), Prospects of Fracture Mechanics. Noordhoff: Leyden. 69–84.Google Scholar
  5. Flügge, W. (1972). Tensor Analysis and Continuum Mechanics. Springer: Berlin.CrossRefMATHGoogle Scholar
  6. Flügge, W. (1973). Stresses in Shells. Springer: New York.CrossRefMATHGoogle Scholar
  7. Fung, Y.C. (1965). Foundations of solid mechanics. Prentice-Hall: Englewood Cliffs, N.J.Google Scholar
  8. Gao, H., and Herrmann G. (1992). On estimates of stress intensity factors for cracked beams and pipes. Engineering Fracture Mechanics 41: 695–706.CrossRefGoogle Scholar
  9. Günther, W. (1962). Über einige Randintegrale der Elastomechanik. Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft 14: 53–72.MATHGoogle Scholar
  10. Herrmann, G., and Sosa H. (1986). On bars with cracks. Engineering Fracture Mechanics 24: 889–894.CrossRefGoogle Scholar
  11. Irwin, G.R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate. Journal of Applied Mechanics 24: 361–364.Google Scholar
  12. Kienzler, R. (1982). Eine Erweiterung der klassischen Schalentheorie; der Einfluß von Dickenverzerrungen und Querschnittsverwölbungen. Ingenieur Archiv 52: 311–322.CrossRefMATHGoogle Scholar
  13. Kienzler, R. (1986). On existence and completeness of conservation laws associated with elementary beam theory. International Journal of Solids and Structures 22: 789–796.MathSciNetCrossRefMATHGoogle Scholar
  14. Kienzler, R. (1993). Konzepte der Bruchmechanik. Braunschweig: Vieweg.Google Scholar
  15. Kienzler, R., and Golebiewska-Herrmann, A. (1985). Material conservation laws in higher-order shell theories. International Journal of Solids and Structures 21: 1035–1045.CrossRefMATHGoogle Scholar
  16. Kienzler, R., and Herrmann, G. (1986 a). On material forces in elementary beam theory. Journal of Applied Mechanics 53: 561–564.Google Scholar
  17. Kienzler, R., and Herrmann, G. (1986 b). An elementary theory of defective beams. Acta Mechanica 62: 37–46.Google Scholar
  18. Kienzler, R., and Herrmann, G. (2000). Mechanics in Material Space. Berlin: Springer.CrossRefMATHGoogle Scholar
  19. Kirchhoff, G.R. (1850). Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Crelles Journal für die reine und angewandte Mathematik. 40: 51–88.CrossRefMATHGoogle Scholar
  20. Knott, J. F. (1973). Fundamentals of Fracture Mechanics. London: Butterworths.Google Scholar
  21. Koiter, W.T. (1960). A consistent first approximation in the general theory of thin elastic shells. In: Koiter, W.T. (ed.). Proceedings of the Symposium on the Theory of Thin Elastic Shells. Amsterdam: North-Holland. 12–33.Google Scholar
  22. Krätzig, W.B. (1980). On the structure of consistent linear shell theories. In: Koiter, W.T., and Mikhailov, G.K. (eds.). Proceedings of the 3’ d IUTAM Symposium on Shell Theory. Amsterdam: North-Holland. 353–368.Google Scholar
  23. Li, S., and Shyy, W. (1997). On invariant integrals in the Marguerre–von Kârmân shallow shell. International Journal of Solids and Structures 34: 2927–2944.MathSciNetMATHGoogle Scholar
  24. Lo, K.K. (1980). Path independent integrals for cylindrical shells and shells of revolution. International Journal of Solids and Structures 16: 701–707.MathSciNetCrossRefMATHGoogle Scholar
  25. Mindlin, R.D. (1951). Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates. Journal of Applied Mechanics 73: 31–38.Google Scholar
  26. Müller, W.H., Hen-mann, G., and Gao, H. (1993 a). A note on curved cracked beams. International Journal of Solids and Structures 30: 1527–1532.Google Scholar
  27. Müller, W.H., Herrmann, G., and Gao, H. (1993 b). Elementary strength theory of cracked beams. Theoretical and Applied Fracture Mechanics 18: 163–177.Google Scholar
  28. Naghdi, P.M. (1972). The Theory of Shells and Plates. In: Truesdell, C. (ed.). Flügge’s Handbuch der Physik. Berlin: Springer. IVa/2: 425–640.Google Scholar
  29. Nicholson, J.W., and Simmonds, J.G. (1980). Sanders’ energy-release rate integral for arbitrarily loaded shallow shells and its asymptotic evaluation for circular cylinders. Journal of Applied Mechanics 47: 363–369.CrossRefMATHGoogle Scholar
  30. Niordson, F.I. (1985). Shell Theory. Amsterdam: North-Holland.MATHGoogle Scholar
  31. Reissner, E. (1944). On the theory of bending of elastic plates. Journal of Mathematics and Physics 23: 184–191.MathSciNetMATHGoogle Scholar
  32. Reissner, E. (1945). The effect of transverse shear deformation on the bending of elastic plates. Journal of Applied Mechanics 12: A69 - A77.MathSciNetMATHGoogle Scholar
  33. Reissner, E. (1947). On bending of elastic plates. Quarterly of Applied Mathematics 5: 55–68.MathSciNetMATHGoogle Scholar
  34. Rösel, R. (1986). Duality under dependency inversion and Noether theory for second-order Lagrangians. International Journal of Solids and Structures 22: 819–832.MathSciNetCrossRefMATHGoogle Scholar
  35. Sanders, J.L. (1982). Circumferential through-cracks in cylindrical shells under tension. Journal of Applied Mechanics 49: 103–107.CrossRefMATHGoogle Scholar
  36. Sanders, J.L. (1983). Circumferential through-crack in a cylindrical shell under combined bending and tension. Journal of Applied Mechanics 50: 221.CrossRefGoogle Scholar
  37. Sosa, H.A. (1986). On the analysis of bars, beams and plates with defects. Ph. D. Thesis, Stanford University.Google Scholar
  38. Sosa, H.A., and Eischen J.W. (1986). Computation of stress intensity factors for plate bending via a path-independent integral. Engineering Fracture Mechanics 25: 451–462.CrossRefGoogle Scholar
  39. Sosa, H.A., and Herrmann, G. (1989). On invariant integrals in the analysis of cracked plates. International Journal of Fracture 40: 111–126.MathSciNetCrossRefGoogle Scholar
  40. Sosa, H.A., Rafalski, P., and Herrmann, G. (1988). Conservation laws in plate theories. Ingenieur Archiv 58: 305–320.CrossRefMATHGoogle Scholar
  41. Timoshenko, S.P., and Woinowsky-Krieger, S. (1970). Theory of Plates and Shells. New York: McGraw-Hill 2nd ed.Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • R. Kienzler
    • 1
  • G. Herrmann
    • 2
  1. 1.University of BremenBremenGermany
  2. 2.Stanford UniversityStanfordUSA

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