Displacement Extrapolation Method : An alternative to J-integral for stress intensity factors computation using X-FEM

Stress intensity factors (SIFs) computation techniques based on J-integral methods [1] are widely used in finite element codes. However, the Displacement Extrapolation Method (DEM) [2] is an alternative way to compute them. The idea is to process an extrapolation based on the relative displacement of the crack face nodes. This method is generally less accurate than integral methods, but it requires much less computational resources. The method is well documented and is implemented in some finite element software. The X-FEM introduced in [3] is suited for crack problems. However, the literature on DEM in the X-FEM case seems to be non-existent in the present time. This paper tries to fill this lack in the literature by describing a new method using X-FEM. The approach followed here is only developed for Linear Elastic Fracture Mechanics. Note that the finite element software Code_Aster [4] already computes SIFs with DEM in X-FEM, but in a slightly different way.