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Vector form Intrinsic Finite Element Based Approach to Simulate Crack Propagation

Published online by Cambridge University Press:  30 October 2017

Y. F. Duan ,
S. M. Wang ,
R. Z. Wang ,
C. Y. Wang  and
E. C. Ting
Y. F. Duan
Affiliation:
College of Civil Engineering and ArchitectureZhejiang UniversityHangzhou, China
S. M. Wang
Affiliation:
College of Civil Engineering and ArchitectureZhejiang UniversityHangzhou, China
R. Z. Wang*
Affiliation:
National Center for Research on Earthquake EngineeringTaipei, Taiwan
C. Y. Wang
Affiliation:
Department of Civil EngineeringNational Central UniversityTaoyuan, Taiwan
E. C. Ting
Affiliation:
School of Civil EngineeringPurdue UniversityWest Lafayette, USA
*
*Corresponding author (rzwang@ncree.narl.org.tw)
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Abstract

This paper presents a new approach to simulate the propagation of elastic and cohesive cracks under mode-I loading based on the vector form intrinsic finite element method. The proposed approach can handle crack propagation without requiring global stiffness matrices and extra weak stiffness elements. The structure is simulated by mass particles whose motions are governed by the Newton's second law. Elastic and cohesive crack propagation are simulated by proposed VFIFE-J-integral and VFIFE-FCM methods, respectively. The VFIFE-J-integral method is based on vector form intrinsic finite element (VFIFE) and J-integral methods to calculate the stress intensity factors at the crack tips, and the VFIFE-FCM method combines VFIFE and fictitious crack models (FCM). When the stress state at the crack tip meets the fracture criterion, the mass particle at the crack tip is separated into two particles. The crack then extends in the plate until the plate splits into two parts. The proposed VFIFE-J-integral method was validated by elastic crack simulation of a notched plate, and the VFIFE-FCM method by cohesive crack propagation of a three point bending beam. As assembly of the global stiffness matrix is avoided and each mass particle motion is calculated independently, the proposed method is easy and efficient. Numerical comparisons demonstrate that the present results predicted by the VFIFE method are in agreement with previous analytical, numerical and experimental works.

Keywords

Crack propagationVFIFIE-J-integral methodVFIFE-FCM methodCohesive force
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 6 , December 2017 , pp. 797 - 812
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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References

1. Griffith, A. A., “The Phenomena of Rupture and Flow in Solids,” Philosophical Transactions of the Royal Society of London, A221, pp. 163–198 (1920).Google Scholar
2. Ewalds, H. and Wanhill, R., Fracture Mechanics, Edward Arnold, New York (1989).Google Scholar
3. Irwin, G. R., “Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate,” Journal of Applied Mechanics, 24, pp. 361–364 (1957).Google Scholar
4. Bažant, Z. P. and Planas, J., Fracture and Size Effect in Concrete and Other Quasi-Brittle Materials, CRC Press, Boca Raton (1998).Google Scholar
5. Moës, N. and Belytschko, T., “Extended Finite Element Method for Cohesive Crack Growth,” Engineering Fracture Mechanics, 69, pp. 813–833 (2002).Google Scholar
6. Hillerborg, A., Modéer, M. and Petersson, P. E., “Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements,” Cement and Concrete Research, 6, pp. 773–782 (1976).CrossRefGoogle Scholar
7. Hillerborg, A., “The Theoretical Basis of a Method to Determine the Fracture Energy GF of Concrete,” Material and Structures, 18, pp. 291–296 (1985).Google Scholar
8. Xu, S. L. and Rrinhardt, H. W., “Determination of Double-K Criterion for Crack Propagation in Quasi-Brittle Fracture, Part I: Experimental Investigation of Crack Propagation,” International Journal of Fracture, 98, pp. 111–149 (1999).CrossRefGoogle Scholar
9. Karihaloo, B. L., Fracture Mechanics and Structural Concrete, Longman Scientific & Technical, New York, pp. 1–45 (1995).Google Scholar
10. Belytschko, T., Fish, J. and Engelmann, B. E., “A Finite Element with Embedded Localization Zones,” Computer Methods in Applied Mechanics and Engineering, 70, pp. 59–89 (1988).CrossRefGoogle Scholar
11. Zhuang, Z. and O'donoghue, P. E., “The Recent Development of Analysis Methodology for Rapid Crack Propagation and Arrest in Gas Pipelines,” International Journal of fracture, 101, pp. 269–290 (2000).Google Scholar
12. Miehe, C. and Gürses, E., “A Robust Algorithm for Configurational-Force-Driven Brittle Crack Propagation with R-Adaptive Mesh Alignment,” International Journal for Numerical Methods in Engineering, 72, pp. 127–155 (2007).Google Scholar
13. Blandford, G. E., Ingraffea, A. R. and Liggett, J. A., “Two-Dimensional Stress Intensity Factor Computations Using the Boundary Element Method,” International Journal for Numerical Methods in Engineering, 17, pp. 387–404 (1981).Google Scholar
14. Belytschko, T. and Tabbara, M., “Dynamic Fracture Using Element-Free Galerkin Methods,” International Journal for Numerical Methods in Engineering, 39, pp. 923–938 (1996).3.0.CO;2-W>CrossRefGoogle Scholar
15. Mellenk, J. M. and Babuška, I., “The Partition of Unity Finite Element Method: Basic Theory and Application,” Computer Methods in Applied Mechanics and Engineering, 139, pp. 289–314 (1996).Google Scholar
16. Babuška, I. and Melenk, J. M., “The Partition of Unity Method,” International Journal for Numerical Methods in Engineering, 40, pp. 727–758 (1997).Google Scholar
17. Babuška, I., Banerjee, U. and Osborn, J. E., “Generalized Finite Element Methods: Main Ideas, Results, and Perspective,” International Journal of Computational Methods, 1, pp. 67–103 (2004).Google Scholar
18. Moës, N. and Belytschko, T., “Extended Finite Element Method for Cohesive Crack Growth,” Engineering Fracture Mechanics, 69, pp. 813–833 (2002).Google Scholar
19. Song, J. H., Areias, P. M. A. and Belytschko, T., “A Method for Dynamic Crack and Shear Band Propagation with Phantom Nodes,” International Journal for Numerical Methods in Engineering, 67, pp. 868–893 (2006).CrossRefGoogle Scholar
20. Liu, W., Yang, Q. D., Mohammadizadeh, S. and Su, X. Y., “An Efficient Augmented Finite Element Method for Arbitrary Cracking and Crack Interaction in Solids,” International Journal for Numerical Methods in Engineering, 99, pp. 438–468 (2014).Google Scholar
21. Ting, E. C., Shih, C. and Wang, Y. K., “Fundamentals of a Vector Form Intrinsic Finite Element: Part I. Basic Procedure and a Plane Frame,” Journal of Mechanics, 20, pp. 113–122 (2004).Google Scholar
22. Ting, E. C., Shih, C. and Wang, Y. K., “Fundamentals of a Vector Form Intrinsic Finite Element: Part II. Plane Solid Elements,” Journal of Mechanics, 20, pp. 123–132 (2004).CrossRefGoogle Scholar
23. Shih, C., Wang, Y. K. and Ting, E. C., “Fundamentals of a Vector Form Intrinsic Finite Element: Part III. Convected Material Frame and Examples,” Journal of Mechanics, 20, pp. 133–143 (2004).Google Scholar
24. Ting, E. C., Duan, Y. F. and Wu, T. Y., Vector Mechanics of Structure, Science Press, BeiJing (2012).Google Scholar
25. Wang, C. Y., Wang, R. Z., Chuang, C. C. and Wu, T. Y., “Nonlinear Dynamic Analysis of Reticulated Space Truss Structures,” Journal of Mechanics, 22, pp. 199–212 (2006).CrossRefGoogle Scholar
26. Xu, R., Li, D. X., Jiang, J. P. and Liu, W., “Adaptive Fuzzy Vibration Control of Smart Structure with VFIFE Modeling,” Journal of Mechanics, 31, pp. 671–682 (2015).Google Scholar
27. Wu, T. Y., Wang, R. Z. and Wang, C. Y., “Large Deflection Analysis of Flexible Planar Frames,” Journal of the Chinese Institute of Engineers, 29, pp. 593–606 (2006).Google Scholar
28. Wang, R. Z., Tsai, K. C. and Lin, B. Z., “Extremely Large Displacement Dynamic Analysis of Elastic–Plastic Plane Frames,” Earthquake Engineering and Structural Dynamics, 40, pp. 1515–1533 (2011).Google Scholar
29. Wu, T. Y. and Ting, E. C., “Large Deflection Analysis of 3D Membrane Structures by a 4-Node Quadrilateral Intrinsic Element,” Thin-Walled Structures, 46, pp. 261–275 (2008).Google Scholar
30. Wu, T. Y., “Dynamic Nonlinear Analysis of Shell Structures Using a Vector Form Intrinsic Finite Element,” Engineering Structures, 56, pp. 2028–2040 (2013).CrossRefGoogle Scholar
31. Yu, Y., Paulino, G. H. and Luo, Y., “Finite Particle Method for Progressive Failure Simulation of Truss Structures,” Journal of Structural Engineering ASCE, 137, pp. 1168–1181 (2011).Google Scholar
32. Duan, Y. F. et al., “Entire-Process Simulation of Earthquake-Induced Collapse of a Mockup Cable-Stayed Bridge by Vector Form Intrinsic Finite Element (VFIFE) Method,” Advances in Structural Engineering, 17, pp. 347–360 (2014).Google Scholar
33. Duan, Y. F. et al., “Vector Form Intrinsic Finite Element Analysis for Train and Bridge Dynamic Interaction,” Journal of Bridge Engineering (In press).Google Scholar
34. Sáze, A., Gallego, R. and Domínguez, J., “Hypersingular Quarter-Point Boundary Element for Crack Problems,” International Journal for Numerical Methods in Engineering, 38, pp. 1681–1701 (1995).Google Scholar
35. Erdogan, F., “Stress Intensity Factors,” Applied Mechanics, 50 (1983).Google Scholar
36. Fan, S. C., Liu, X. and Lee, C. K., “Enriched Partition of-Unity Finite Element Method for Stress Intensity Factors at Crack Tips,” Computers and Structures, 82, pp. 445–461 (2004).Google Scholar
37. Duarte, C. A., “The Hp Clouds Method,” Ph.D Dissertation, University of Texas, Austin, Texas, U.S. (1996).Google Scholar
38. Comite Euro-International du Beton, CEB-FIP Mode Code 1990, Thomas Telford Services Ltd, Thomas Telford House, Lausanne, Switzerland (1993).Google Scholar
39. Karihaoo, B. L. and Nallathambi, P., “Notched Beam Test: Mode I Fracture Toughness,” Fracture Mechanics Test Methods for Concrete, pp. 1–86 (1991).Google Scholar