Journal of Materials Science

, Volume 41, Issue 20, pp 6510–6519 | Cite as

A model for predicting the evolution of multiple cracks on multiple length scales in viscoelastic composites

  • D. H. Allen
  • C. R. Searcy


A model is presented herein for predicting the evolution of numerous cracks on multiple length scales, the objective of such a model being to develop the capability to predict failure of structural components to perform their intended tasks. Such a capability would then be useful as a predictive tool for designing structural components so as not to fail, but rather to succeed in performing their intended tasks. The model developed herein is somewhat involved, being based in continuum mechanics and thermodynamics, but is nevertheless expected to be cost effective (wherever sufficient accuracy permits) when compared to more costly experimental means of determining component life. An essential ingredient within the context of the model is that cracks must develop on widely differing length scales. Where this is observed to occur in nature, which is surprisingly often, there are potential simplifications over more generally described but practically untenable approaches, that can lead to (at least partly) computational multiscale algorithms capable of assimilating failure due to multiple cracking with a high degree of accuracy. The model presented herein will be briefly described within a mathematical framework, and an example problem will be presented that is representative of certain currently relevant technologies.


Local Scale Crack Opening Displacement Cohesive Zone Damage Parameter Cohesive Zone Model 
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.



The authors are grateful for funding received for this research from the US Army Research Laboratory under contract no. W911NF-04-2-0011.


  1. 1.
    Da Vinci L (1970) In: Richter JP (ed) The notebooks of Leonardo Da VinciGoogle Scholar
  2. 2.
    Galileo G (1636) Dialogues concerning two new sciences, Promethus BooksGoogle Scholar
  3. 3.
    Griffith AA (1920) Philos Trans R Soc Lond A221:163Google Scholar
  4. 4.
    Eshelby JD (1957) Proc R Soc A421:376Google Scholar
  5. 5.
    Hashin Z (1964) Appl Mech Rev 17:1Google Scholar
  6. 6.
    Hill R (1965) J Mech Phys Solids 12:213CrossRefGoogle Scholar
  7. 7.
    Allen DH (2002) Composites Sci Technol 61:2223CrossRefGoogle Scholar
  8. 8.
    Day WA (1972) The thermodynamics of simple materials with fading memory, Springer Tracts in Natural Philosophy. Springer-Verlag, New YorkGoogle Scholar
  9. 9.
    Timoshenko SP (1972) History of strength of materials. McGraw HillGoogle Scholar
  10. 10.
    Allen DH (1994) In: Talreja R (ed) Damage mechanics of composite materials. Elsevier, pp 79–114Google Scholar
  11. 11.
    Boyd JG, Costanzo F, Allen DH (1993) Int J Damage Mech 2:209Google Scholar
  12. 12.
    Costanzo F, Boyd JG, Allen DH (1996) J Mech Phys Solids 44(3):333CrossRefGoogle Scholar
  13. 13.
    Allen DH, Yoon C (1998) Int J Solids Struct 35:4035CrossRefGoogle Scholar
  14. 14.
    Vakulenko AA, Kachanov ML (1971) Mekh Tver Tela 4:159Google Scholar
  15. 15.
    Searcy CR (2004) A multiscale model for predicting damage evolution in heterogeneous media. Ph.D. Thesis. Texas A&M UniversityGoogle Scholar
  16. 16.
    Dugdale DS (1960) J Mech Phys Solids 8:100CrossRefGoogle Scholar
  17. 17.
    Barenblatt GI (1962) Adv Appl Mech 7:55CrossRefGoogle Scholar
  18. 18.
    Allen DH, Searcy CR (2001a) Int J Fract 107:159CrossRefGoogle Scholar
  19. 19.
    Allen DH, Searcy CR (2001b) Mech Mater 33:177CrossRefGoogle Scholar
  20. 20.
    Costanzo F, Allen DH (1993) Int J Fract 63(1):27CrossRefGoogle Scholar
  21. 21.
    Costanzo F, Allen DH (1996) Int J Eng Sci 33(15):2197CrossRefGoogle Scholar
  22. 22.
    Yoon C, Allen DH (1999) Int J Fract 96:56CrossRefGoogle Scholar
  23. 23.
    Zocher MA, Allen DH, Groves SE (1997) Int J Numer Methods Eng 40:2267CrossRefGoogle Scholar
  24. 24.
    Foulk JW, Allen DH, Helms KLE (2000) Comput Methods Appl Mech Eng 183:51CrossRefGoogle Scholar
  25. 25.
    Phillips ML, Yoon C, Allen DH (1999) J Eng Mater Technol 21:436Google Scholar
  26. 26.
    Cauchy A (1823) Bulletin de la Société Philomatique 9Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.College of EngineeringUniversity of Nebraska-LincolnLincolnUSA
  2. 2.Stress EngineeringHoustonUSA

Personalised recommendations