Effective-medium theory for infinite-contrast two-dimensionally periodic linear composites with strongly anisotropic matrix behavior: dilute limit and crossover behavior

F. WILLOT; Y. P. PELLEGRINI; M. I. IDIART; P. PONTE CASTAÑEDA

PHYSICAL REVIEW B

The American Physical Society

Año: 2008 vol. 78 p. 1041111 - 10411117

1098-0121

The overall behavior of a 2D lattice of voids embedded in ananisotropic matrix is investigated in the limit of vanishingporosity $f$. An effective-medium model (of the Hashin-Shtrikmantype) which accounts for elastic interactions between neighboringvoids, is compared to Fast Fourier Transform numerical solutionsand, in the limits of infinite anisotropy, to exact results. Across-over between regular and singular dilute regimes is found,driven by a characteristic length which depends on $f$ and on theanisotropy strength. The singular regime, where the leading dilutecorrection to the elastic moduli is an $O(f^{1/2})$, is related tostrain localization and to change in character --- from elliptic to hyperbolic --- ofthe governing equations.