On micromechanical modeling of orthotropic solids with parallel cracks

Abstract

A detailed comparison of the accuracy of several popular micromechanical schemes utilized for prediction of the effective elastic properties of materials with parallel cracks is presented. In particular, the non-interaction, Mori–Tanaka, differential and self-consistent schemes are compared against the direct finite element simulations. The latter are performed on the periodic representative volume elements containing 30 strongly oblate spheroids representing the penny-shaped cracks. This work extends the existent results to a more general class of matrix materials – orthotropic materials, which requires the ability to calculate the Eshelby tensor for an ellipsoid in non-isotropic matrix. In addition to the implementation of the integration procedure used for the Eshelby tensor calculation, this work also presents a variation of the Random Sequential Adsorption algorithm modified for periodic structures.Analysis of the results indicates that in the case of parallel nearly flat cracks (strongly oblate spheroids) the overall out-of-plane moduli are best predicted by the differential scheme. On the other hand, Mori–Tanaka scheme should be used for estimation of the in-plane moduli. It also appears that as the cracks are inflated from strongly oblate spheroids to slightly deformed spheres, the best choice of the micromechanical scheme for the out-of-plane properties gradually shifts towards Mori–Tanaka.