The Overall Elastic Response of Composite Materials

Abstract

If a composite is modeled as a randomly inhomogeneous medium, an “overall modulus operator” relates the ensemble average of the stress to that of the strain. This paper reviews methods for estimating the overall modulus operator when only a limited amount of statistical information on the composite is available. The most securely based estimates come from bounds on the energy. Such bounds induce bounds on the components of the overall modulus operator and have a precise status, independent of the pointwise quality of the approximating fields from which they are derived. Other approximations are also outlined, however; these include perturbation series, estimates obtained from making ad hoc closure assumptions, and self-consistent estimates. The paper concludes with a discussion of possible future developments.