Modal Stress Intensity Factor Using Extended Finite Element Method


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The aim of this paper is the determination of the evolution of the modal stress intensity factor (MSIF) for a non-propagating crack subjected to dynamic loading using the extended finite element method (X-FEM). The main advantage of this method coupled with the modal analysis is its capability in modeling cracks independently of the mesh and in a reduced computational time compared to the finite element method coupled with dynamic iterative method. The proposed procedure is applied to a reference problem (cracked plate). The MSIFs obtained agree well with those found by indirect boundary element (IBEM), weight function and Newmark’s explicit methods.



Edited by:

Amanda Wu




B. Abdelkader et al., "Modal Stress Intensity Factor Using Extended Finite Element Method", Applied Mechanics and Materials, Vol. 232, pp. 686-690, 2012

Online since:

November 2012




[1] T. Belytschko and T. Black: Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, Vol. 45, pp.601-620, (1999).


[2] Y. Abdelaziz, A. Nabbou and A. Hamouine : A state-of-the-art review of the X-FEM for computational fracture mechanics. Applied Mathematical Modelling, Vol. 33, pp.4269-4282, (2009).


[3] N. Moës, J. Dolbow and T. Belytschko: A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, Vol. 46 (1999), pp.133-150.


[4] H. D. Bui, H. Maigre and D. Rittel: A new approach to the experimental determination of the dynamic stress intensity factor. Int. J. Solids Structures, Vol. 29, pp.2881-2895, (1992).


[5] J. F Doyle, S.A. Rizzi: Frequency domain stress intensity calibration of damped cracked panels. International Journal of Fracture, Vol. 61, pp.123-130, (1993).


[6] E. Galenne, S. Andrieux and L. Ratier: A modal approach to linear fracture mechanics for dynamic loading at low frequency. Journal of Sound and Vibration, Vol. 299, pp.283-297, (2007).


[7] A. Zamani, R. Gracie and M.R. Eslami: Higher order tip enrichment of eXtended Finite Element Methodin thermoelasticity. ComputMech, Vol. 46 (2010), p.851–866.


[8] A. K. Chopra, in: Dynamics of structures theory and Applications to Earthquake Engineering, Third Edition, edited by Pearson Prentice Hall, (2007).

[9] S. Mohammadi, in: Extended Finite Element Method for Fracture Analysis of Structures, edited by Blackwell Publishing Ltd Singapore, (2008).

[10] P. H. Wen: Dynamic fracture mechanics: Displacement discontinuity method, edited by computation mechanics publications Southampton UK and Boston USA, Vol 29, (1996).