研究期間：10108~10207;In this proposed research, a problem-invariant Mc-integral is proposed as an energy parameter for characterizing the fracture behavior of 3-D multi-cracked elastic solids. Based on the concept of the M-integral, Mc is defined by suitably choosing a closed surface and taking the integration with respect to the geometric center of all the enclosed cracks. Note that the physical meaning for 3-D Mc, which is to be related to the surface energy corresponding to creation of the cracks, does not hold in a manner as that for 2-D Mc and needs to be properly reformulated. Also, it is to be shown that the 3-D integration is surface-independent in a modified sense. With this property, a closed surface remote from the crack fronts can be chosen so that the 3-D Mc can be accurately evaluated with finite element solutions even when the near-front areas are not simulated with very fine grids.