Issue 29

M.L. De Bellis et alii, Frattura ed Integrità Strutturale, 29 (2014) 37-48; DOI: 10.3221/IGF-ESIS.29.05 47 a. The micromechanical models show locally variable trends, which, however, fluctuate around the same mean values. It emerges that, while the Cauchy model captures only a constant value of the mean rotation along the strip, the micropolar homogenized model provides a very good evaluation of the considered field with both UC1 and UC2. a) b) Figure 4 : a) Strip1 arrangement; b) Strip2 arrangement. a) b) Figure 5 : a) Horizontal displacement versus vertical abscissa; b) Rotation versus vertical abscissa. C ONCLUSIONS he micropolar computational homogenization are considered. The perturbation fields in the presence of higher order polynomial boundary conditions is analyzed adopting three different procedures, which lead to different results. The first method is based on the imposition of periodic boundary conditions, classically adopted in the standard first order homogenization, also in the presence of higher order terms of the polynomial map and provides qualitatively incorrect results. The second procedure (3 Step Homogenization) adopted, although the most complex, produces the best results. Finally, the methodology characterizing the perturbation fields on the basis of the direct observation of the large heterogeneous medium behavior gives results slightly differing from the 3 Step Homogenization, but is much simpler. Thus, this appears as the best compromise between accuracy and efficiency in correctly reproducing the actual trends of perturbation fields, when a single UC is analyzed. Moreover, the identification of the homogenized linear elastic constitutive parameters adopting the classical Hill-Mandel procedure is addressed. Considering different UCs, referred to the same composite material, it emerged that the constitutive response of the homogenized medium depends on the choice of the cell, adopting all the three procedures exploited for reproducing the perturbation fields. Indeed, while the elastic Cauchy coefficients are irrespective of the UC selected, for the bending and skew-symmetric shear micropolar coefficients this does not occur, at least not in the framework of computational homogenization. T