Inclusions, Inhomogeneities and Cavities

Overall mechanical properties and local strain and stress field averages, caused in individual phases of heterogeneous solids by remotely applied uniform strain or stress, are often derived from estimates of local fields in ellipsoidal homogeneous inclusions and inhomogeneities, bonded to a large volume of a surrounding matrix or ‘comparison medium’. The attraction of this approach lies in the relative simplicity of evaluation of the local fields, and in the adaptability of ellipsoidal shapes, such as prolate or oblate ellipsoids, spheroids, cylinders, spheres, penny-shaped discs or slits, to represent either short or long fibers, particles, voids and cracks of different shapes. Transition from local fields in a single inhomogeneity to those in interacting inhomogeneities comprising composite aggregates and polycrystals is accomplished, in part, by assigning certain properties to the comparison medium, as shown in Chaps. 6 and 7.