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International Journal for Multiscale Computational Engineering

Impact factor: 1.103

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v9.i3.40
pages 305-326

ELASTIC AND ELECTRICAL BEHAVIOR OF SOME RANDOMMULTISCALE HIGHLY-CONTRASTED COMPOSITES

Francois Willot
MINES-ParisTech, Centre de Morphologie Mathématique, Mathématiques et Systémes, France
Dominique Jeulin
MINES-ParisTech, Centre de Morphologie Mathématique, Mathématiques et Systémes, France

ABSTRACT

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., Proc. Eur. Conf. on Constitutive Models for Rubber, ECCMR 2007, Paris, Sept. 4-7) serves as the basis for building simple two-scale 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 transfor method (C. R. Acad. Sci. Paris II, 318: 1417-1423, 1994). The entire range of inclusion concentrations 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.