From unit inclusion cell to large Representative Volume Element: Comparison of effective elastic properties

The concept of equivalent morphology has received much consideration in recent decades. The importance of this concept is reflected in the fact that an inclusion of any morphology can be replaced by a circular one in simulation. If this concept is confirmed, it will facilitate the modeling and simulation of complex configuration microstructures. To decide on this concept, an in–depth study is carried out in this work, trying to answer it in a clear and definitive way by trying to identify all the possible situations. For this the two types of composites, namely, periodic interpreted by an elementary cell and random interpreted by a Representative Volume Element (RVE) with 200 inclusions are considered. To be sure that the isotropy is provided by the RVE of the periodic microstructure, two types of elementary cells were treated: one circular and the other square. In order to cover all possible situations, the inclusion of the elementary cell is considered with several situations, centered position with different orientations at constant and random steps, random position with orientation at constant steps and random position and orientation at random steps. For each situation, the effective property is determined by the average of 20 cases are processed for elementary cells, while for the large RVE, the properties are obtained by a unit realization. To take into account the effect of contrast, two situations are considered, namely, rigid inclusion case and rigid matrix case. Several results are obtained and given in the conclusion. •The effect of inclusion shape on the effective linear elastic properties is investigated by considering periodic and random microstructures.•For the periodic unit–cell microstructures, the obtained effective properties, of an ellipsoidal inclusion, computed by the average of uniform orientation distributions, or random ones, never converge towards the effective property of a circular inclusion.•The effective properties computed on a unit cell do not give the same results as the large RVE with random position and random orientation in any case.