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 Mc is defined. Special attention is thus addressed to discussion of the physical meaning of Mc, which is shown to be related to the surface energy corresponding to formation of the defects. Based on this characteristic, it is suggested that Mc 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 Mc-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.