Dynamic modeling by XFEM of cracked 2D structures containing inclusion
Résumé
The present work deals with the dynamic modeling of 2D cracked structures containing inclusions using the extended finite element method (XFEM) [1], designed as an appropriate technique to treat this type of material discontinuity problems [2]. For this purpose, a computer code was developed in this study to evaluate the mixed mode dynamic stress intensity factor (DSIF) via the interaction integral method [3] based on the J integral. The computer code is validated by comparing the obtained results with those of Phan et al [4] using the Symmetric Galerkin Boundary Element Method (SGBEM) for a reference example. It concerns a cracked plate containing an inclusion of various positions under the action of dynamic Heaviside loading. The correlation between results is remarkable thus proving the efficiency of this approach. Then the influence of some parameters such as geometry, mass, stiffness of the inclusion and the material damping on the FICD value is discussed. Note that, at this stage, the study is limited to the case of stationary cracks (no dynamic crack propagation). References [1] Belytschko T, Black T. ;Elastic crack growth in finite elements with minimal remishing. (1999), Int J numer Meth Engng, pp. 601-620. [2] Sukumar N, Möes N, Moran B, Belytschko T; Extended finite element method for three-dimensional crack modelling. 1549–70, s.l. : Int J Numer Meth Eng, 2000, Vol. 48. [3] Soheil Mohammadi ; Extended Finite Element Method for Fracture Analysis of Structures, edité par Blackwell Publishing Ltd Singapore, (2008). [4] A.-V. Phan , L.J. Gray , A. Salvadori ; Transient analysis of the dynamic stress intensity factors using SGBEM for frequency-domain elastodynamics , Comput. Methods Appl. Mech. Engrg. 199 (2010) 3039–3050
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