Evaluation of M-integral for anisotropic elastic media with multiple defects

Through suitable selection of integration contours, M-integral is extended to the study of multi-defected fracture behavior in 2-D anisotropic elastic solids. In tact, by taking the integration with respect to the center of each defect, a problem-invariant parameter M_c is defined. Special attention is thus addressed to discussion of the physical meaning of M_c, which is shown to be related to the surface energy corresponding to formation of the defects. Based on this characteristic, it is suggested that M_c be possibly used as a fracture parameter for description of the degradation of material and/or structural integrity caused by irreversible evolution of defects in the medium. In addition, a generalized domain integral method is developed for evaluation of the M_c-integral with finite element method. The proposed numerical procedure appears to be domain-independent so that no near-tip singular behavior is involved in the calculations.