A UNIFIED MODEL FOR THE PROPERTIES OF COMPOSITE MATERIALS

摘要

A model is described for calculating the properties of a specific kind of composite material consisting of an elastic substrate with embedded inclusions. The model requires that four scatter cross-sections be calculated from the scatter properties of the individual inclusions constituting the ensemble population. The composite properties then follow simply from these scatter cross-sections. Central to the model is the concept of multiple scattering for which there is a large body of literature of which three references, namely Foldy , Sabina and Willis and Kim et al [3], are relevant to the work here. The present author however believes that unresolved issues remain and attempts to address them here. The basis of the analysis here is that, with inclusions randomly scattered throughout the substrate material, the problem may be considered a stochastic one where fields within the substrate are considered only through their averaged properties. Then two approaches are considered. In the first, inclusions are distributed uniformly in a substrate occupying all space. Then a solution is sought where incident and scattered fields are the same and therefore form a single self-consistent field. The analysis then proceeds by' replacing the summations of scattered fields from distinct inclusions by integrals in an averaging process. The resulting homogenous spatial integral equations then reduce to wavenumber eigenvalue equations in phase space.