Abstract
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.
Highlights
The use of composite materials in various fields of engineering, both for standard and innovative applications, has been widely researched
While the elastic Cauchy coefficients are irrespective of the Unit Cell (UC) selected, this does not occur for the bending and skew-symmetric shear Cosserat coefficients, at least with regard to computational homogenization
The perturbation fields in the presence of higher order polynomial boundary conditions is analyzed adopting three different procedures, which lead to different results
Summary
The use of composite materials in various fields of engineering, both for standard and innovative applications, has been widely researched. Among various generalized continua (second-gradient, couple stress, micropolar or multifield), a micropolar Cosserat continuum at the macro-level and a Cauchy continuum at the micro-level are used here to study the homogenized response of periodic composite materials. Higher order constitutive components are identified, when a homogeneous elastic material at the micro-level is considered Despite the drawbacks, this technique has been widely used, at least when asymptotic techniques [14] cannot be applied, as in the case of coupling micropolar and classical continua. While the elastic Cauchy coefficients are irrespective of the UC selected, this does not occur for the bending and skew-symmetric shear Cosserat coefficients, at least with regard to computational homogenization This fact is confirmed by the results obtained from the structural applications. Two numerical tests are presented to highlight the main aspects of the presented micropolar computational homogenization technique and to emphasize the differences obtained using the three procedures to describe the perturbation fields
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