) /2)sin( /2),cos( ), cos( /2)sin( /2), sin( sin( ( ) r F x . -For void nodes, we add the following enrichment [9]: 0 (x) < 0 (inside of the void) ( ) 1 ( ) 0 (outside of the void) if V x if x . (3) Where is the level set function of voids The approximate displacement fields are as follows: H Br i I i I k i k k i i i i i u x V x N x u N x H x a N x F x b 4 1 , ( ) ( ) ( ) ( ) ( ) ( ) ( ) (4) In addition to traditional unknown ui, we consider the unknowns ai and bk corresponding to the enrichment functions H et Fk, respectively. Split node Tip node Simple node void node Void Crack tip Crack Domain Fig. 1 Types of XFEM enrichments of the meshed domain. 3. Interaction integral method for SIF computation There are several methods to evaluate the SIF. In this work we use the J integral method by using the interaction integral (Fig.2). Because its global character, this method is the most stable technique. Fig.2 Method of SIF computing: interaction integral technique. This method introduced by Sih et al [8], combines with the actual field an auxiliary field satisfying the boundary conditions of the problem. In this case, The J integral is given as follows:
RkJQdWJsaXNoZXIy MjM0NDE=