Abstract
A systematic method is presented for estimating the overall properties of solids with periodically distributed cracks. In view of the periodicity, the displacement, strain and stress fields of the cracked solid can be expressed in Fourier series. Elastic solids with periodically distributed flat voids are considered first. The results for cracks are then obtained by letting the thickness aspect ratio of the void approach zero. This limiting process is performed with care. The only approximation involved is the distribution of the homogenization eigenstrains, which is assumed to be piecewise constant. The estimate of overall elastic moduli, crack opening displacements and stress intensity factors eventually reduces to the calculation of several infinite series. The formulation is valid for elliptic as well as two-dimensional line (slit-like) cracks and cracks with arbitrary shapes. It fully includes the interaction effects.
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