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陈宜亨

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M-integral analysis for two-dimensional solids with strongly interacting microcracks. Part Ⅰ: in an infinite brittle solid

陈宜亨Yi-Heng Chen*

Y.-H. Chen International Journal of Solids and Structures 38 (2001) 3193-3212,-0001,():

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摘要/描述

This paper addresses and alternative description for brittle solids with strongly interacting microcracks. The basic idea starts from the M-integral analysis customatil used in single crack problems. As an initial attempt, the discussion is limited to the infinite two-dimensional cases and the microcracks are assumed to be stationary. It is proved from the global-local contributed from the two components of the Jk vector (Knowles and Sternberg, 1972, Budiansky and Rice, 1973) and the coordinates of each microcrack center. The later is concerned not only with the crack tip SIFs, but also with the contribution arising from the traction-free surfaces of each crak (Herrmann and Herrmann, 1981). A detailed proof for the vanishing nature of the Jk vector along a closed contour surrounding all the microcracks is presented, from which the confsion about the dependence of the M integral on the origin selection of global coor-dinates is clarified. Two numerical examples are shown in tables and figures tocomfirm the dervied conclusions. It is shown that the M integralis equivalent to the decrease of the total potential energy of the microcracking soilds although the strongly interacting situations are taken into account. Therefore, a simple relation between the M integral and the L integral is established under the assumption mentioned above. It is concluded that the M-integral analysis, from the physical point of view, does play important role and provide an effective measure in evaluatin the damage level of brittle solids with strongly interacting and randomly distributed microcracks. Although only the stationary microcracks are considered in the present investigation, the derived conclusions could actually be extended to treat much more useful problems, in which the multi-cracks may become critical and may grow during loading histories.

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