Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: Ⅰ-theory

摘要

This paper is concerned with the development of an improved second-order homogenization method incorporating field fluctuations for nonlinear composite materials. The idea is to com- bine the desirable features of two different, earlier methods making use of "linear comparison composites", the properties of which are chosen optimally form suitable designed variational principles. The first method (Ponte Castaneda, J. Mech. Phys. Solide 39 (1991) 45) makes use of the "secant" moduli of the phases, evaluated at the second moments of the strain field over the phases, and delivers bounds, but these bounds are only exact to first -order in the heterogeneity contrast.