Departmental Papers (MEAM)

Document Type

Journal Article

Date of this Version

9-18-2008

Comments

Suggested Citation:
F. Willot, Y. Pellegrini, M.I. Idiart and P.P. Castañeda. (2008). "Effective-medium theory for infinite-contrast two-dimensionally periodic linear composites with strongly anisotropic matrix behavior: Dilute limit and crossover behavior." Physical Review B. 78, 104111.

© 2008 The American Physical Society
http://dx.doi.org/10.1103/PhysRevB.78.10411

Abstract

The overall behavior of a two-dimensional lattice of voids embedded in an anisotropic elastic matrix is investigated in the limit of vanishing porosity f. An effective-medium model (of the Clausius-Mossoti 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 crossover 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(f1/2), is related to strain localization and to change in character—from elliptic to hyperbolic—of the governing equations.

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Date Posted: 13 January 2011

This document has been peer reviewed.