Effect of aggregation phase on the elastic properties of a heterogeneous material
Résumé
In this study, the technique of homogenization and morphological analysis is used in order to quantify the relationship between two morphologies of voided material: two types of structures are considered. Each one is characterized by a scale which was observed. Structure 1 is an elastic matrix containing a random distribution of spherical inclusions corresponds to a smallest scale (microscopic scale). Structure 2 is a composite material consisting of spherical inclusions distributed randomly in an elastic matrix corresponds to a largest scale (mesoscopic scale). A well-known mathematical morphology technique is used in this investigation. The parameters of mathematical morphology, such as covariance, are determined and presented the relationship between the parameters of the two structures. All the obtained results suggest us to define a new concept called "the equivalent morphology". This concept is to replace the first composite containing inclusions with radius R1 by other fictif material containing inclusions with radius R2 that was expressed as a function of the parameters derived from the analysis of the initial morphology. These two composites 1 and its equivalent morphology 2 give the same effective elastic properties, but not necessarily with the same size of the deterministic representative volume element, DREV.
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