Issue 58

K. Benyahi et alii, Frattura ed Integrità Strutturale, 58 (2021) 319-343; DOI: 10.3221/IGF-ESIS.58.24

Figure 14: Homogenized mechanical characteristics for different volume fraction of cylindrical inclusions.

It is also noted that the estimations of the semi-analytical model of Mori-Tanaka [35], and the results of the periodic homogenization method developed in this study are quite close. And that for very low volume fractions (less than 15%) caused by a weak interaction between the phases. On the other hand, for volume fractions greater than 15%, the effective mechanical properties are overestimated, a deviation is observed which can be caused by a phenomenon of interaction between the inclusions. We conclude, that the periodic homogenization method (PBC) gives mechanical characteristics more rigid, than those of the semi-analytical model (Mori-Tanaka model). Introduction of damage into the problem of homogenization We implemented a Mazars damage model ([29], [30]) for spheroidal and ellipsoidal shaped inclusions, and the model of Bouafia et al. ([31], [32]) for cylindrical shaped inclusions in the Abaqus calculation code by the use of a subroutine (Umat). Calculations on a RVE containing 10 inclusions with type localization conditions (PBC), allowed us to study the

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