Self-Consistent Techniques for Heterogeneous Media

The basis for the estimates is given in the form of an auxiliary solution characterizing the behavior of a single embedded site. Both classical self-consistent methodologies (SCM) and rationalized differential formulations (DCM) are developed, with emphasis on physical realism, applications to polycrystalline and various composite materials (including porous media and plate bending) are compared favorably with many experimental results. Recent attempts to generate effective plasticity/creep models plus estimates of thermal/electrical/pore-fluid transmissivity, are examined critically. A general conclusion is that DCM provides remarkably accurate descriptions but that even more detailed characterization of microstructure methodologies is essential for extreme circumstances, such as discrete site interaction or dominance of nicrogeometric connectivity. Fully numerical simulation may be avoided by specializations of exact integral equations: among these, only the self-consistent approximation and a few isolated second-order estimates have been explored.