Effects of Parallel Crack Distributions on Effective Elastic Properties - a Numerical Study

This paper is concerned with numerical studies of effective elastic properties of cracked solids. We concentrate on two dimensional media containing different patterns of parallel crack distributions. We use the Rotated Staggered Grid (RSG) which allows one to simulate elastic wave propagation very accurately in fractured media. Our aim is to compare the predictions given by several effective medium theories to the effective properties we derive from our numerical experiments. Namely, these are the ``Non-interaction approximation (NIA)'', the ``Differential scheme (DS)'' and an extension of the DS (EDS). According to our results, the DS theory and its extension perform well. Simulations of media containing very few cracks prove that for our setup the effective properties stabilize at low numbers of cracks. Finally, we studied parallel cracks clustered in stacked columns. We found that, as expected, the shielding effects dominate in such patterns.