THE NUMERICAL-CALCULATION OF 2-DIMENSIONAL EFFECTIVE MODULI FOR MICROCRACKED SOLIDS

There exist several micromechanics models for the determination of the effective moduli of microcracked solids, and crack density is the onl y parameter in these models that characterizes the effect of microcrac king. A numerical hybrid BEM method, in conjunction with a unit cell m odel, is proposed in the present paper to evaluate these micromechanic s models. A unit cell, which can be considered as a representative blo ck in the solid, contains randomly distributed microcracks. The unit c ell is then assumed to be periodic in the solid so as to account For i nteractions between cracks inside and outside the cell. There are stoc hastic variations of the estimated moduli for different microcrack dis tributions. Two groups of microcracks with the same crack density, one with a low number of large cracks and the other with a large number o f small cracks, show the same range of stochastic variations and the s ame mean of effective moduli for random distributions of microcracks. The effective moduli based on this numerical method for randomly distr ibuted cracks and parallel cracks are compared with those from various micromechanics models. While the differential method provides the clo sest estimation to the mean of the numerical results at low crack dens ity, the generalized self-consistent method is much more accurate at r elatively high crack density.