A modified Kachanov method for analysis of solids with multiple cracks

Kachanov proposed an approximate method for the analysis of multiple cracks by assuming that traction in each crack can be represented as a sum of a uniform component and a non-uniform component, and the interaction among the cracks are only due to the uniform components. These assumptions simplify considerably the mathematics and allow ‘closed-form’ solutions to be obtained for some cases. However, it is noted that the assumptions may not be valid when the cracks are very close. Therefore, an improved method of elastic solids with closely spaced multiple cracks is proposed. Unlike the Kachanov method, traction in a crack is decomposed into a linearly varying component and a non-uniform component so that the sum of the two components to be equal to the traction along the crack length. It is further assumed that the interaction effect due to the non-uniform component can be neglected, and therefore, only the effect of the linearly varying component has to be considered. The accuracy of the present method is validated by comparing the results of two and three collinear open cracks obtained by the present method with those of the exact solutions and the original Kachanov method. Applications of the approach in solving non-collinear parallel crack and friction crack problems are also presented to demonstrate the versatility and accuracy of the method.