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
备注：
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)
发表信息：
Physical Review B 78, 104111 (2008) [slightly different from arXiv version]
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.
Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading direction, which induces localized (singular) field configurations. The effective elastic moduli are computed as functions of the porosity in each case. Their dilute expansions feature half-integer powers of the porosity, which can be correlated to the localized field patterns. Statistical characterizations of the fields, such as their first moments and the…
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