Field fluctuations and macroscopic properties for nonlinear composites

M. I. IDIART; P. PONTE CASTAÑEDA

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

Elsevier

Año: 2003 vol. 40 p. 7015 - 7033

0020-7683

A recently introduced nonlinear homogenization method ({\em Ponte Casta\~neda, P., 2002, J. Mech. Phys. Solids} {\bf 50}, 737--757) is used to estimate the effective behavior and the associated strain and stress fluctuations in a fibrous composite with power-law phases subjected to anti-plane strain or in-plane strainloading. Using the Hashin-Shtrikman estimates for the relevant ``linear comparison composite,'' results are generated for two-phase systems, including fiber-reinforced and fiber-weakened composites. These results, which are known to be exact to second-order in the heterogeneity contrast, are found to satisfy all known bounds. Explicit analytical expressions are obtained for the special case of rigid-ideally plastic composites, including results for arbitrary contrast and fiber concentration. The effective properties, as well as the phase averages and fluctuations predicted for these strongly nonlinear composites appear to be consistent with deformation mechanisms involving shear bands. More specifically, in the case where the fibers are stronger than the matrix, the bands tend to avoid the fibers, and in the opposite case they become attracted to the fibers.