Issue 29

M.L. De Bellis et alii, Frattura ed Integrità Strutturale, 29 (2014) 37-48; DOI: 10.3221/IGF-ESIS.29.05 37 Focussed on: Computational Mechanics and Mechanics of Materials in Italy A micromechanical approach for the micropolar modeling of heterogeneous periodic media M.L. De Bellis, D. Addessi Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma “Sapienza”, Via Eudossiana, 18, 00184 Roma, Italy marialaura.debellis@uniroma1.it , daniela.addessi@uniroma1.it A BSTRACT . Computational homogenization is adopted to assess the homogenized two-dimensional response of periodic composite materials where the typical microstructural dimension is not negligible with respect to the structural sizes. A micropolar homogenization is, therefore, considered coupling a Cosserat medium at the macro-level with a Cauchy medium at the micro-level, where a repetitive Unit Cell (UC) is selected. A third order polynomial map is used to apply deformation modes on the repetitive UC consistent with the macro-level strain components. Hence, the perturbation displacement field arising in the heterogeneous medium is characterized. Thus, a newly defined micromechanical approach, based on the decomposition of the perturbation fields in terms of functions which depend on the macroscopic strain components, is adopted. Then, to estimate the effective micropolar constitutive response, the well known identification procedure based on the Hill-Mandel macro-homogeneity condition is exploited. Numerical examples for a specific composite with cubic symmetry are shown. The influence of the selection of the UC is analyzed and some critical issues are outlined. K EYWORDS . Composites; Homogenization; Micropolar Continua; Periodicity. I NTRODUCTION he use of composite materials in various fields of engineering, both for standard and innovative applications, has been widely researched. A thorough understanding of the mechanical behavior of existing materials is a fundamental step towards the design of new composites, characterized by increasingly high performances. Various approaches, marked out by different formulations and modeling the materials at different scales, have been proposed to deal with the constitutive response of composite materials. This study focuses on homogenization techniques, a very effective tool to obtain accurate results with low computational efforts. The actual heterogeneous medium is analyzed at two different scales: the macro-scale, where an equivalent homogenized medium is considered, characterized by overall effective mechanical properties, and the micro-scale, where detailed information about the texture, geometry and constitutive laws of the constituents are available. Different continuum models can be adopted, at the two levels. The classical Cauchy continuum provides an appropriate description of the actual heterogeneous response in the case of small microscopic length compared to the macro-scale structural length [1, 2, 3, 4]. On the contrary, when strong strain and stress gradients at the macro-level occur, or when the microscopic length of the constituents is comparable to the wavelength of variation of the strain and stress mean fields at the macro-level, some intrinsic limits emerge. This is due to the fact that the Cauchy theory does not account for length T