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arXiv · 0804.2817

Effective-medium theory for infinite-contrast, 2D-periodic, linear composites with strongly anisotropic matrix behavior: dilute limit and cross-over behavior

Francois Willot·Yves-Patrick Pellegrini·Martin I. Idiart·Pedro Ponte Castaneda
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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.

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Francois Willot, Yves-Patrick Pellegrini, Martin I. Idiart, Pedro Ponte Castaneda. 2008-04-17. Effective-medium theory for infinite-contrast, 2D-periodic, linear composites with strongly anisotropic matrix behavior: dilute limit and cross-over behavior. https://doi.org/10.1103/physrevb.78.104111

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