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A simple approach for calculation of anisotropic effective elastic properties of
cracked materials is presented. Square computational domain containing randomly distributed
cracks under plane strain conditions is considered. Effective elastic properties are expressed in
terms of average displacement discontinuities on cracks in three test problems: uniaxial loading
in two orthogonal directions and pure shear. These problems are solved using the displacement
discontinuity method. Resulting effective compliances are averaged over realizations with
different crack distributions. This approach is employed for calculation of effective elastic
properties for two particular crack configurations: (i) one family of parallel cracks and (ii) two
families of parallel cracks inclined at angle 30°.
Crack densities up to 0.8 are considered. It is
shown that for both configurations the effective elastic properties are orthotropic even at large
crack densities. Dependencies of Young's moduli on crack density are obtained. At crack
densities up to 0.1, the effective properties can be estimated analytically using the noninteraction
approximation (NIA). At higher crack densities, the NIA strongly overestimates
effective stiffnesses. Quantitative agreement with results obtained in the literature using more
sophisticated methods is demonstrated.
Keywords: effective elastic properties; cracked materials; crack interactions; orthotropy; noninteraction approximation; boundary element method; displacement discontinuity method. |
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