A variety of estimates of the effective properties of heterogeneous media utilize the solution of the boundary value problem of the relevant field for a single inclusion of one material in a matrix of another material. Such estimates include effective properties of dispersions in the dilute-concentration limit (Chapter 19), a variety of effective-medium type approximations (Chapter 18), and rigorous bounds on the effective properties (Chapter 21). In this chapter we will derive single-inclusion solutions for all four classes of problems, focusing on spherical and ellipsoidal inclusions.
KeywordsConcentration Field Trap Surface Lame Constant Ellipsoidal Inclusion Infinite Matrix
Unable to display preview. Download preview PDF.