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This paper extends the L -integral concept (Knowles and Stermberg in Arch. Rat. Mech. Anal. 44: 187–211, 1972; Budiansky and Rice in J. Appl. Mech. 40:201–203, 1973; Herrmann and Herrmann in J. Appl. Mech. 48:525–530, 1981) to study the degradation of a brittle elastic plan caused by irreversible evolution: the coalescence between two neighborly located holes under tensile loading. Attention is focused on the change in the L -integral before, during, and after coalescence of the two holes. Using finite element analyses, the influences of different orientations of the two holes, different coalescence path curves connecting the rims of the two holes, and different crack length from one hole’s rim to another hole’s rim on the L -integral are studied in detail. It is found that variable tendencies of the L -integral before, during, and after coalescence of the different orientations of the two holes show quite different features. Unlike those for the single defect, the L -integral for the two holes before coalescence could be either positive or negative representing energy release or energy absorbing induced from the two holes’ rotation, respectively, whereas such feature disappears after coalescence of the two holes occurs and a single complicated defect forms. It is concluded that the L -integral does play an important role in description of the damage extent and damage evolution. Thus, besides the M -integral (Chen in Int. J. Solids. Struct. 38:3193–3212, 2001; Chen in Int. J. Solids. Struct. 38:3213–3233, 2001; Chang and Chien in Int. J. Fract. 114:267–289, 2002; Chang and Peng in ASCE J. Eng. Mech. 130:589–598, 2004; Hu and Chen in Acta Mech. 204:109–121, 2009; Hu and Chen in ASME J. Appl. Mech. 76, 061017-1-12, 2009), the L -integral as another outside variable feature should also be adopted in the description of damage evolution in brittle materials. Finally, two elliptic holes of the same shape and orientation, two elliptic holes of the same shape and different orientation, two elliptic holes of different shapes and the same orientation, and the most general two elliptic holes of different shapes and orientations are calculated and discussed.
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