Effective-medium theory for infinite-contrast, 2D-periodic, linear composites with strongly anisotropic matrix behavior: dilute limit and cross-over behavior
Abstract
The overall behavior of a 2D lattice of voids embedded in an anisotropic matrix is investigated in the limit of vanishing porosity f. An effective-medium model (of the Hashin-Shtrikman type) which accounts for elastic interactions between neighboring voids, is compared to Fast Fourier Transform numerical solutions and, in the limits of infinite anisotropy, to exact results. A cross-over between regular and singular dilute regimes is found, driven by a characteristic length which depends on f and on the anisotropy strength. The singular regime, where the leading dilute correction to the elastic moduli is an O(f^{1/2}), is related to strain localization and to change in character - from elliptic to hyperbolic - of the governing equations.
Keywords
Cite
@article{arxiv.0804.2817,
title = {Effective-medium theory for infinite-contrast, 2D-periodic, linear composites with strongly anisotropic matrix behavior: dilute limit and cross-over behavior},
author = {Francois Willot and Yves-Patrick Pellegrini and Martin I. Idiart and Pedro Ponte Castaneda},
journal= {arXiv preprint arXiv:0804.2817},
year = {2008}
}
Comments
17 pages, 7 low-res figures, 4 low-res tables of figures. Table II in BW to minimize submission size (color version from YPP on request)