An elastic medium with sources of external and internal stresses

In this chapter, some results of the elasticity theory that are frequently used in the mechanics of heterogeneous materials are presented. Two types of sources of stress fields in a homogeneous media are considered: body forces as sources of external stress, and dislocation moments as the sources of internal stress. Integral representations of elastic fields arising from stress sources distributed in 3D-regions, on surfaces, and on lines are given and discussed. Discontinuities of the elastic fields on the borders of the regions containing the stress sources are indicated. Multipole expansions are used for presentation of the elastic fields far from the stress sources.