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A novel procedure is proposed for evaluation of stress intensity factors of planar Mode III shear cracks perpendicular to a nearby interface between two isotropic elastic solids. Shear cracks traversing a flat layer bonded to two different elastic solids are also analyzed. The method is based on superposition of singular near tip stress and displacement fields generated by both the main crack and certain image cracks. Both the main and the image cracks are loaded by self-equilibrating shear tractions of different magnitude, such that matching parts of the said fields are made to satisfy traction and displacement continuity conditions at the interface. Selected comparisons with results obtained by different methods show good agreement. Applications of the method to other crack problems are discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]