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Article Dans Une Revue International Journal for Multiscale Computational Engineering Année : 2011

## Elastic and electrical behavior of some random multiscale highly-contrasted composites

François Willot
Dominique Jeulin

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#### Résumé

The role of a non-uniform distribution of heterogeneities on the elastic as well as electrical properties of composites is studied numerically and compared with available theoretical results. Specifically, a random model made of embedded Boolean sets of spherical inclusions (see e.g. Jean et al, 2007) serves as the basis for building simple two-scales microstructures of granular''-type. Materials with infinitely-contrasted'' properties are considered, i.e. inclusions elastically behave as rigid particles or pores, or as perfectly-insulating or highly-conducting heterogeneities. The inclusion spatial dispersion is controlled by the ratio between the two characteristic lengths of the microstructure. The macroscopic behavior as well as the local response of composites are computed using full-field computations, carried out with the "Fast Fourier Transform" method (Moulinec and Suquet, 1994). The entire range of inclusion concentration, and dispersion ratios up to the separation of length scales are investigated. As expected, the non-uniform dispersion of inhomogeneities in multi-scale microstructures leads to increased reinforcing or softening effects compared to the corresponding one-scale model (Willot and Jeulin, 2009); these effects are however still significantly far apart from Hashin-Shtrikman bounds. Similar conclusions are drawn regarding the electrical conductivity.

### Dates et versions

hal-00553376 , version 1 (07-01-2011)

### Identifiants

• HAL Id : hal-00553376 , version 1
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### Citer

François Willot, Dominique Jeulin. Elastic and electrical behavior of some random multiscale highly-contrasted composites. International Journal for Multiscale Computational Engineering, 2011, 9 (3), pp.305-326. ⟨10.1615/IntJMultCompEng.v9.i3.40⟩. ⟨hal-00553376⟩

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