The numerical calculation of two-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 only parameter in these models that characterizes the effect of microcracking. A numerical hybrid BEM method, in conjunction with a unit cell model, is proposed in the present paper to evaluate these micromechanics models. A unit cell, which can be considered as a representative block in the solid, contains randomly distributed microcracks. The unit cell is then assumed to be periodic in the solid so as to account for interactions between cracks inside and outside the cell. There are stochastic variations of the estimated moduli for different microcrack distributions. Two groups of microcracks with the same crack density, one with a low number of large cracks and the other with a large number of small cracks, show the same range of stochastic variations and the same mean of effective moduli for random distributions of microcracks. The effective moduli based on this numerical method for randomly distributed cracks and parallel cracks are compared with those from various micromechanics models. While the differential method provides the closest estimation to the mean of the numerical results at low crack density, the generalized self-consistent method is much more accurate at relatively high crack density.