抄録
The partial differential equation is derived for the macroscopic total strain of the material containing many randomly oriented slit-like cracks with respect to the crack density of the crack by introducing a infinitesimally small amount of the crack into the matrix of the material according to the procedure of the differential scheme. By solving this differential equation, the macroscopic total strain, the average interaction stress and hence the macroscopic elastic moduli are formulated as a function of the crack density of the crack. On the contrary to the results obtained by the ordinary Mori-Tanaka thorem, the resulting macroscopic elastic modulus asymptotically tends to zero as the crack density of the crack increases. The present result is in good agreement with the numerical results given by Huang et al. especially at relatively low crack density.
