Physics – Condensed Matter – Materials Science
Scientific paper
2008-04-17
Physical Review B 78, 104111 (2008) [slightly different from arXiv version]
Physics
Condensed Matter
Materials Science
17 pages, 7 low-res figures, 4 low-res tables of figures. Table II in BW to minimize submission size (color version from YPP o
Scientific paper
10.1103/PhysRevB.78.104111
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.
Castaneda Pedro Ponte
Idiart Martin I.
Pellegrini Yves-Patrick
Willot Francois
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