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Numerical simulation of the crack 2D by the finite element incorporated the discontinuity

This paper describes some results from the analysis of cracked plates using XFEM. Extended finite elements allow the entire crack to be represented independently of the meshing. The elements employ discontinuous functions and the facture mechanics two dimensional asymptotic crack tip displacement fields. The Fortran source code of Cast3M applies these elements to a set of examples. | Vietnam Journal of Mechanics, VAST, Vol. 30, No. 2 (2008) , pp. 80 - 88 NUMERICAL SIMULATION OF THE CRACK 2D BY THE FINITE ELEMENT INCORPORATED THE DISCONTINUITY Nguyen Truong Giang Institute of Mechanics, VAST Abstract. I)~termining stress intensity factors is important in fracture mechanics. The extended finite element method (XFEM) provides a robust and accurate to determine factors. This paper describes some results from the analysis of cracked plates using XFEM. Extended finite elements a llow the entire crack to be represented independently of the meshing. The elements employ discontinuous functions and the facture mechanics two dimensional asymptotic crack tip displacement fields. The Fortran source code of Cast3M applies these elements to a set of examples. The obtained stress and deformation fields are used to compute stress intensity factors via interaction integrals. The results are compared with these obtained from conventional FEM to demonstrate the advantages of the employing the new elements. 1. INTRODUCTION XFEM 1.1. Governing·equation Consider a domain D, bounded by f. The boundary is partitioned into three sets: f UJ ft and f c as shown in Fig. l. Displacements are prescribed on f UJ tractions are prescribed on ft and re is assumed to be the tractions free. Fig . 1. Body with an internal crack Numerical simulation of the crack 2D by the finite element incorporated th e discontinuity 81 . The equilibrium equations and boundary conditions for this problem are \! . a +b= a . n = [on 0 in rt n (1) a . n = 0 on r e u = fl on r u· The space of admissible displacement fields is defined by U = {v E V : v =fl on ru;v discontinuous on re}. The weak form of the equilibrium equations is given by l a (u) : c (v) dD = / b · vdSl + / [ · vdru E U. Jn Jn Jrt (2) Belytschko and Black, 1999 [3] show that (2) is equivalent to the strong form (1), and includes the traction-free conditions prevailing on the opposing surfaces of the crack. 1.2. The .