Accounting for spatial distribution in mean-field homogenization of particulate composites
Résumé
Several mean-fields homogenization methods are readily available to estimate the effective properties of particulate composites, which take into consideration the particles volume fraction, shapes and orientations. Some of them also account for the spatial distribution of the particles. For instance, the Ponte-Castañeda and Willis (PCW) model embeds a parametrization of the global distribution law, while the Interaction Direct Derivative (IDD) model associates a matrix cell to each inclusion, that should be representative of close interactions. In the literature, IDD is commonly reduced to the particular case of the classical Mori and Tanaka (MT) scheme or to the aforementioned PCW model, and therefore, the application of its most general form is somehow lacking. In addition, spatial distribution laws used within the PCW model, are, in many cases, specified separately from the microstructural configurations. On this basis, the present study proposes a novel approach to calibrate and exploit IDD and PCW models in 2D linear conductive composite materials, provided that a representative image of the microstructure is available. We discuss the links between the models and the range of validity of the IDD model by addressing its possible lack of symmetry. In particular, when IDD is not applicable, both an IDD-based PCW model and a two-step scheme are proposed. Finally, an image analysis method using Voronoı̈ diagrams, inspired by an original proposition by Du and Zheng (Acta Mechanica, 2002, 157, 61-80), is implemented to define the cells associated to each inclusion and supply the models. The method is validated by comparisons between the obtained IDD and PCW estimates, the MT model and benchmark full-field (FF) numerical simulations. Possible extensions to realistic elastic composites are discussed.
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