https://hal-mines-paristech.archives-ouvertes.fr/hal-00553376Willot, FrançoisFrançoisWillotCMM - Centre de Morphologie Mathématique - MINES ParisTech - École nationale supérieure des mines de Paris - PSL - Université Paris sciences et lettresJeulin, DominiqueDominiqueJeulinCMM - Centre de Morphologie Mathématique - MINES ParisTech - École nationale supérieure des mines de Paris - PSL - Université Paris sciences et lettresElastic and electrical behavior of some random multiscale highly-contrasted compositesHAL CCSD2011HomogenizationLinear elastic mediaLinear conductorsReinforced compositesMultiscale modelsPorous mediaPercolationRVE[PHYS.MECA.MEMA] Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph][SPI.MECA.MEMA] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of materials [physics.class-ph]Willot, François2011-01-07 14:58:482021-11-17 12:27:112011-01-11 09:35:49enJournal articleshttps://hal-mines-paristech.archives-ouvertes.fr/hal-00553376/document10.1615/IntJMultCompEng.v9.i3.40application/pdf1The 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.