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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.
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https://hal-cea.archives-ouvertes.fr/cea-00413019
Contributor : Yves-Patrick Pellegrini <>
Submitted on : Thursday, September 3, 2009 - 2:11:57 AM
Last modification on : Thursday, September 24, 2020 - 4:00:21 PM

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François Willot, Yves-Patrick Pellegrini, Martin I. Idiart, Pedro Ponte Castañeda. Effective-medium theory for infinite-contrast, 2D-periodic, linear composites with strongly anisotropic matrix behavior: dilute limit and cross-over behavior. Physical Review B: Condensed Matter and Materials Physics, American Physical Society, 2008, 78, pp.104111. ⟨10.1103/PhysRevB.78.104111⟩. ⟨cea-00413019⟩

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