Abstract :
This paper presents a fast and accurate solution for crack interaction problems in
infinite- and half- plane solids. The newsolution is based on themethod of complex potentials
developed by Muskhelishvili for the analysis of plane linear elasticity, and it is formulated
through three steps. First, the problem is decomposed into a set of basic problems, and for each
sub-problem, there is only one crack in the solid. Next, after a crack-dependent conformal
mapping, the modified complex potentials associated with the sub-problems are expanded
into Laurent’s series with unknown coefficients, which in turn provides a mechanism to
exactly implement in the form of Fourier series the boundary condition in each sub-problem.
Finally, taking into account the crack interaction via a perturbation approach, an iterative
algorithm based on fast Fourier transforms (FFT) is developed to solve the unknown Fourier
coefficients, and the solution of the whole problem is readily obtained with the superposition
of the complex potentials in each sub-problem. The performance of the proposed method is
fully investigated by comparing with benchmark results in the literatures, and superb accuracy
and efficiency is observed in all situations including patterns where cracks are closely spaced.
Also, the new method is able to cope with interactions among a large number of cracks, and
this capability is demonstrated by a calculation of effective moduli of an elastic solid with
thousands of randomly-spaced cracks.
