On two micromechanics theories for determining micro-macro relations in heterogeneous solids

The average-held theory and the homogenization theory are briefly reviewed and compared. These theories are often used to determine the effective moduli of heterogeneous materials from their microscopic structure in such a manner that boundary-value problems for the macroscopic response can be formulated. While these two theories are based on different modeling concepts, it is shown that they can yield essentially the same effective moduli and boundary-value problems. A. hybrid micromechanics theory is proposed in view of this correspondence. This theory leads to a more accurate computation of the effective moduli, and applies to a broader class of microstructural models. Hence, the resulting macroscopic boundary-value problem gives better estimates of the macroscopic response of the material. In particular, the hybrid theory can account for the effects of the macrostrain gradient on the macrostress in a natural manner. (C) 1999 Elsevier Science Ltd. All rights reserved.