Use of M integral for rubbery material problems containing multiple defects

An energy parameter based on the concept of the M integral is proposed for describing the fracture behavior of a two-dimensional multidefect rubbery mechanical system under the action of large deformation. To this end, we first define a problem-invariant parameter M_c by suitably choosing a closed contour and taking the integration with respect to the geometric center of all the enclosed defects. Attention is then 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. Also, the integration appears to be path independent so that the complicated singular stress field in the near-tip areas need not be involved in the calculation. Based on the above characteristics, it is suggested that M_c may be possibly used as a fracture parameter for describing the degradation of material and/or structural integrity caused by irreversible evolution of defects in rubbery media.