Numerical Simulation of Crack Propagation

  • Meinhard KunaEmail author
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 201)


Prediction of the crack propagation process is of great importance for many fracture mechanical issues.


Crack Front Cohesive Zone Model Cohesive Element Void Volume Fraction Cohesive Stress 
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.


Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


  1. 1.
    Dhondt G (1998) Cutting of a 3-D finite element mesh for automatic mode I crack propagation calculations. Int J Numer Meth Eng 42:749–772zbMATHCrossRefGoogle Scholar
  2. 2.
    Mishnaevsky L, Weber U, Schmauder S (2004) Numerical analysis of the effect of microstructures of particle-reinforced metallic materials on the crack growth and fracture resistance. Int J Fract 125:33–50zbMATHCrossRefGoogle Scholar
  3. 3.
    Bazant ZP, Oh BH (1983) Crack band theory for fracture and concrete. Mater Struct 16:155–177Google Scholar
  4. 4.
    deBorst R (2002) Fracture in quasi-brittle materials: a review of continuum damage-based approaches. Eng Fract Mech 69:95–112Google Scholar
  5. 5.
    Hillerborg A, Rots JG (1989) Crack concepts and numerical modelling. In: Elfgren L (ed) Fracture mechanics of concrete structures. Chapman & Hall, London, New York, pp 128–146Google Scholar
  6. 6.
    Nishioka T, Atluri SN (1980) Numerical modeling of dynamic crack propagation in finite bodies by moving singular elements. J Appl Mech 47:570–582MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Murthy KSRK, Mukhopadhyay M (2000) Adaptive finite element analysis of mixed-mode crack problems with automatic mesh generator. Int J Numer Meth Eng 49:1087–1100zbMATHCrossRefGoogle Scholar
  8. 8.
    Nishioka T, Furutsuka J, Tchouikov S, Fujimoto T (2002) Generation-phase simulation of dynamic crack bifurcation phenomenon using moving finite element method based on Delaunay automatic triangulation. Comput Model Eng Simul 3:129–145Google Scholar
  9. 9.
    Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite element method: its basis and fundamentals, vol 1. Elsevier, AmsterdamzbMATHGoogle Scholar
  10. 10.
    Schöllmann M, Fulland M, Richard HA (2003) Development of a new software for adaptive crack growth simulations in 3D structures. Eng Fract Mech 70:249–268Google Scholar
  11. 11.
    Wriggers P (2001) Nichtlineare Finite-Elemente-Methoden. Springer, BerlinCrossRefGoogle Scholar
  12. 12.
    Meyer A, Rabold F, Scherzer M (2006) Efficient finite element simulation of crack propagation using adaptive iterative solvers. Commun Numer Methods Eng 22:93–108MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7:55–129MathSciNetCrossRefGoogle Scholar
  14. 14.
    Dugdale D (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–104CrossRefGoogle Scholar
  15. 15.
    Needleman A (1987) A continuum model for void nucleation by inclusion debonding. J Appl Mech 54:525–531zbMATHCrossRefGoogle Scholar
  16. 16.
    Brocks W, Cornec A (2003) Cohesive models—special issue. Eng Fract Mech 70(14):1741–1986CrossRefGoogle Scholar
  17. 17.
    Brocks W, Cornec A, Scheider I (2003) Computational aspects of nonlinear fracture mechanics. In: Milne I, Ritchie RO, Karihaloo B (eds) Comprehensive structural integrity—numerical and computational methods, vol 3. Elsevier, Oxford, pp 127–209CrossRefGoogle Scholar
  18. 18.
    Rose JH, Ferrante J, Smith JR (1981) Universal binding energy curves for metals and bimetallic interfaces. Phys Rev Lett 47:675–678CrossRefGoogle Scholar
  19. 19.
    Needleman A (1990) An analysis of tensile decohesion along an imperfect interface. Int J Fract 42:21–40CrossRefGoogle Scholar
  20. 20.
    Tvergaard V, Hutchinson JW (1992) The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. J Mech Phys Solids 40:1377–1397zbMATHCrossRefGoogle Scholar
  21. 21.
    Scheider, I (2001) Bruchmechanische Bewertung von Laserschweißverbindungen durch numerische Rissfortschrittsimulation mit dem Kohäsivzonenmodell. Ph.D. thesis, Technische Universität HamburgGoogle Scholar
  22. 22.
    Hillerborg A, Modeer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 6:773–782CrossRefGoogle Scholar
  23. 23.
    Bazant ZP (1993) Current status and advances in the theory of creep and interaction with fracture. In: Bazant ZP, Ignacio CC (eds) Proceedings of the 5th international RILEM symposium on creep and shrinkage of concrete, Chapman & Hall, Barcelona, pp 291–307Google Scholar
  24. 24.
    Xu X, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42:1397–1434zbMATHCrossRefGoogle Scholar
  25. 25.
    Ortis M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44:1267–1282CrossRefGoogle Scholar
  26. 26.
    Schwalbe KH, Scheider I, Cornec A (2013) Guidelines for applying cohesive models to the damage behaviour of engineering materials. Springer, HeidelbergGoogle Scholar
  27. 27.
    Rousselier G (1987) Ductile fracture models and their potential in local approach of fracture. Nucl Eng Des 105:97–111CrossRefGoogle Scholar
  28. 28.
    Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile materials. J Eng Mater Technol 99:2–15CrossRefGoogle Scholar
  29. 29.
    Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 32(1):157–169CrossRefGoogle Scholar
  30. 30.
    Richard HA, Sander M, Kullmer G, Fulland M (2004) Finite-Elemente-Simulation im Vergleich zur Realität—Spannungsanalytische und bruchmechanische Untersuchungen zum ICE-Radreifenbruch. Materialprüfung 46:441–448Google Scholar
  31. 31.
    ESIS P2 (1992) Procedure for determining the fracture behaviour of materials. Technical report, European Structural Integrity SocietyGoogle Scholar
  32. 32.
    Abendroth M (2005) Identifikation elastoplastischer und schädigungsmechanischer Materialparameter aus dem Small Punch Test. Ph.D. thesis, TU Bergakademie FreibergGoogle Scholar
  33. 33.
    Abendroth M, Kuna M (2006) Identification of ductile damage and fracture parameters from the small punch test using neural networks. Eng Fract Mech 73:710–725CrossRefGoogle Scholar
  34. 34.
    Klingbeil D, Brocks W, Fricke S, Arndt S, Reusch F, Kiyak Y (1998) Verifikation von Schädigungsmodellen zur Vorhersage von Rißwiderstandskurven für verschiedene Probengeometrien und Materialien im Rißinitiierungsbereich und bei großem Rißwachstum. Technical report, BAM-V.31 98/2, Bundesanstalt für Materialforschung und -prüfungGoogle Scholar
  35. 35.
    ASTM-E 1820 (2007) Standard test method for measurement of fracture toughness. Technical report, American Society for Testing and Materials, West ConshohockenGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute für Mechanik und FluiddynamikTU Bergakademie FreibergFreibergGermany

Personalised recommendations