Effective-medium theory for infinite-contrast, 2D-periodic, linear composites with strongly anisotropic matrix behavior: dilute limit and cross-over behavior - Archive ouverte HAL Access content directly
Journal Articles Physical Review B: Condensed Matter and Materials Physics (1998-2015) Year : 2008

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

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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.

Dates and versions

cea-00413019 , version 1 (03-09-2009)

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Cite

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 (1998-2015), 2008, 78, pp.104111. ⟨10.1103/PhysRevB.78.104111⟩. ⟨cea-00413019⟩
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