Numerical Computation of the Overall Moduli of Two Dimensional Infinite Media with Cracks
The overall elastic moduli of a solid are changed when the solid is damaged by cracks. For a finite solid, the size influence has been investigated and it has been found that for a given crack density, increasing crack size reduce the overall moduli . For an infinite solid, it is obviously impossible to make the computation with all cracks. Classical methods suggest computing the overall moduli with the solution of the crack opening displacement of one single crack. The interaction between cracks is neglected or taken into account approximately. In this paper, the overall moduli of two dimensional infinite solids with cracks are computed numerically. From numerical simulations, it has been found that the interaction between cracks can be neglected if the distance between them is three times larger than the crack size. So one can compute the opening displacement on one crack with the presence of cracks nearby and use the crack opening displacement to compute the overall moduli. The numerical values are smaller than those of the method of diluted distribution but greater than those of the differential scheme and the self consistent method. They are also slight greater than the numerical results of bounded cracked solids. For small values of crack density however, the numerical results of both infinite solids and bounded solids are close to the estimation of the differential scheme.
M.H Aliabadi, S. Abela, S. Baragetti, M. Guagliano and Han-Seung Lee
H.P. Yin "Numerical Computation of the Overall Moduli of Two Dimensional Infinite Media with Cracks", Key Engineering Materials, Vols. 417-418, pp. 241-244, 2010