11.02.2013 Views

Computational Methods for Debonding in Composites

Computational Methods for Debonding in Composites

Computational Methods for Debonding in Composites

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

7 Interaction Between Intraply and Interply Failure <strong>in</strong> Lam<strong>in</strong>ates 159<br />

Both the delam<strong>in</strong>ation model and the soften<strong>in</strong>g plasticity model, put a serious<br />

restriction on the maximum element size <strong>in</strong> the regions where failure occurs. The<br />

cohesive zone <strong>in</strong> delam<strong>in</strong>ation and the localization band <strong>in</strong> <strong>in</strong>traply failure have to be<br />

spanned by more than one element. In the already relatively costly three dimensional<br />

framework, which is necessary to cover all possible failure events, this means that<br />

there is a limit to the size of the structure that can be analyzed without excessive<br />

growth of computation time.<br />

Acknowledgements This research is supported by the Technology Foundation STW (under grant<br />

DCB.6623) and the M<strong>in</strong>istry of Public Works and Water Management, The Netherlands.<br />

References<br />

1. Bazant ZP, Pijaudier-Cabot G (1989) J Eng Mech 115:755–767<br />

2. Bazant ZP, Oh B (1983) Crack band theory <strong>for</strong> fracture of concrete. Mater Struct 16:155–177<br />

3. Bićanić N, Pearce CJ, Owen DRJ (1994) Failure predictions of concrete like materials us<strong>in</strong>g<br />

soften<strong>in</strong>g Hoffman plasticity model. In: Mang H, Bićanić N, de Borst R (eds) Proceed<strong>in</strong>gs of<br />

EURO-C 1994. P<strong>in</strong>eridge Press, Swansea<br />

4. Camanho PP, Dávila CG, de Moura MF (2003) Numerical simulation of mixed-mode<br />

progressive delam<strong>in</strong>ation <strong>in</strong> composite materials. J Compos Mater 37:1415–1438<br />

5. Camanho PP, Dávila CG, P<strong>in</strong>ho ST et al. (2006) Prediction of <strong>in</strong> situ strengths and matrix<br />

crack<strong>in</strong>g <strong>in</strong> composites under transverse tension and <strong>in</strong>-plane shear. Compos Part A 37:165–<br />

176<br />

6. Daniel IM, Ishai O (2006) Eng<strong>in</strong>eer<strong>in</strong>g Mechanics of Composite Materials. Ox<strong>for</strong>d university<br />

press, New York<br />

7. Dávila CG, Camanho PP, Rose CA (2005) Failure criteria <strong>for</strong> FRP lam<strong>in</strong>ates. J Compos Mater<br />

39:323–345<br />

8. Hager WW (1988) Applied Numerical L<strong>in</strong>ear Algebra. Prentice–Hall, Englewood Cliffs, NJ<br />

9. Hash<strong>in</strong> Z (1980) Failure Criteria <strong>for</strong> Unidirectional Fiber <strong>Composites</strong>. J Appl Mech 47:<br />

329–334<br />

10. H<strong>in</strong>ton MJ, Soden PD (1998) Predict<strong>in</strong>g failure <strong>in</strong> composite lam<strong>in</strong>ates: the background to the<br />

exercise. Compos Sci Tech 58:1001–1010<br />

11. Hoffman O (1967) The Brittle Strength of orthotropic materials. J Compos Mater 1:200–206<br />

12. Jiang WG, Hallett SR, Green BG, Wisnom MR (2007) A concise <strong>in</strong>terface constitutive law<br />

<strong>for</strong> analysis of delam<strong>in</strong>ation and splitt<strong>in</strong>g <strong>in</strong> composite materials and its application to scaled<br />

notched tensile specimens. Int J Numer <strong>Methods</strong> Eng 69:1982–1995<br />

13. Li X, Duxbury PG, Lyons P (1994) Considerations <strong>for</strong> the application and numerical implementation<br />

of stra<strong>in</strong> harden<strong>in</strong>g with the Hoffman yield criterion. Comput Struct 52:633–644<br />

14. Mi Y, Crisfield A, Hellweg HB, Davies GAO (1998) Progressive delam<strong>in</strong>ation us<strong>in</strong>g <strong>in</strong>terface<br />

elements. J Compos Mater 32:1246–1272<br />

15. Muhlhaus HB, Aifantis EC (1991) A variational pr<strong>in</strong>ciple <strong>for</strong> gradient plasticity. Int J Solids<br />

Struct 28:845–858<br />

16. Nairn JA, Hu S (1994) Matrix microcrack<strong>in</strong>g. In: Talreja R (ed) Damage Mechanics of<br />

Composite Materials. Elsevier science, Amsterdam<br />

17. Puck A, Schürmann H (1998) Failure analysis of FRP lam<strong>in</strong>ates by means of physically based<br />

phenomenological models. Compos Sci Technol 58:1045–1067<br />

18. Remmers JJC, Wells GN, de Borst R (2003) A solid-like shell element allow<strong>in</strong>g <strong>for</strong> arbitrary<br />

delam<strong>in</strong>ations. Int J Numer Method Eng 58:2013–2040<br />

19. Schellekens JCJ, de Borst R (1990) The use of the Hoffman yield criterion <strong>in</strong> f<strong>in</strong>ite element<br />

analysis of anisotropic composites. Comput Struct 37:1087–1096

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!