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.

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)

References in corpus (4)

• Anisotropy in granular media: classical elasticity and directed force chain network
• Localization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: exact solutions and dilute expansions
• The square-lattice F model revisited: a loop-cluster update scaling study
• Random manifolds in non-linear resistor networks: Applications to varistors and superconductors

Cited by in corpus (5)

• Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields
• Infinite-contrast periodic composites with strongly nonlinear behavior: Effective-medium theory versus full-field simulations
• Microstructural enrichment functions based on stochastic Wang tilings
• On the gradient of the Green tensor in two-dimensional elastodynamic problems, and related integrals: Distributional approach and regularization, with application to nonuniformly moving sources
• The Off-Shell Electromagnetic T-matrix: momentum-dependent scattering from spherical inclusions with both dielectric and magnetic contrast