NUMERICAL SIMULATION OF CRACK GROWTH USING EXTENDED FINITE ELEMENT METHOD

Abstract

The X-FEM attempts to improve computational challenges associated with mesh generation by not requiring
the finite element mesh to conform to cracks, and in addition, provides using higher-order elements or special finite
elements without significant changes in the formulation. The essence of the X -FEM lies in subdividing the model problem
into two distinct parts: mesh generation for the geometric domain (cracks not included), and enriching the finite element
approximation by additional functions that model the flaw(s) and other geometric entities. In the X-FEM there is no need
for the remeshing, because the mesh is not changed as the crack growths and is completely independent of the location
and geometry of the crack. The discontinuities across the crack are modeled by enrichment functions. In this
presentation, the numerical simulation of 2D LEFM accomplished using the Extended Finite Element Method [XFEM] is
discussed. XFEM has been recently accepted as a powerful tool for the numerical simulation of crack modelling in
Fracture Mechanics. According to this approach a discontinuous function and the asymptotic crack -tip displacement
functions are added to the conventional finite element formulation. These additional functions, commonly known as the
enrichment functions are derived from the theoretical background of the problem. XFEM is used i n the implementation
of 2D static and crack propagation problems with plane stress condition. Various methods of XFEM are compared with
each other and are found in good agreement with that of the benchmark solutions. Also problems on the plate with
inclined edge cracks under tensile loading are investigated.