Fields In Terms Of Functions Research Articles

A micromechanical approach for the Cosserat modeling of composites

The present paper deals with the homogenization problem of periodic composite materials, considering a Cosserat continuum at the macro-level and a Cauchy continuum at the micro-level. Consistently with the strain-driven approach, the two levels are linked by a kinematic map based on a third order polynomial expansion. Because of the assumed regular texture of the composite material, a Unit Cell (UC) is selected; then, the problem of determining the displacement perturbation fields, arising when second or third order polynomial boundary conditions are imposed on the UC, is investigated. A new micromechanical approach, based on the decomposition of the perturbation fields in terms of functions which depend on the macroscopic strain components, is proposed. The identification of the linear elastic 2D Cosserat constitutive parameters is performed, by using the Hill–Mandel technique, based on the macrohomogeneity condition. The influence of the selection of the UC is analyzed and some critical issues are outlined. Numerical examples for a specific composite with cubic symmetry are shown.

Micromechanical approach for the micropolar modeling of heterogeneous periodic media

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.