Field Fluctuations and Macroscopic Properties of Two-Phase Composite Materials

M. I. IDIART; P. PONTE CASTAÑEDA

Washington D.C.

Congreso; 2003 ASME International Mechanical Engineering Congress; 2003

American Society of Mechanical Engineers

A homogenization method for nonlinear heterogeneous media was introduced recently by Ponte Casta~neda ({em Ponte Casta~neda, P., 2002, J. Mech. Phys. Solids} {f 50}, 737--757). This novel method incorporates information about the phase averages and fluctuations of the stress and strain fields in a suitably chosen linear comparison composite, and can therefore be used to obtain estimates not only for the effective behavior but also for the corresponding field averages and fluctuations in each phase of the nonlinear composite. Such information about the fields can be useful in understanding phenomena such as percolation, damage, and fatigue.The method makes use of a linear thermoelastic comparison composite that has the same microstructure as the nonlinear composite. The homogenization is then carried out for a linear material using any of the methods available for linear heterogeneous media (such as Hashin-Shtrikman and self-consistent). The properties of the linear comparison composite are obtained using a variational procedure in such a way that the estimates are optimal within some simplifying assumptions. Previous methods based on the idea of a linear comparison composite use the secant modulus evaluated at the second moments or the tangent modulus evaluated at the phase average of the fields. This method uses a ``generalized secant modulus´´ which is somewhat intermediate between the two. The method delivers estimates that are exact to second order in the heterogeneity contrast and that do not violate any rigorous bounds.