Elastic field of cylindrical inclusion

The elastic field of a cylindrical inclusion with plane or antiplane transformation strain is found under assumptions of linear isotropic homogeneous theory of elasticity. Different integral expressions are obtained from expressions known for the three-dimensional case and interpreted in terms of the theory of dislocations. The surface integrals correspond to a volume distribution of infinitesimal dislocation dipoles inside the inclusion, the line integrals to a surface distribution of dislocations in the boundary between the inclusion and matrix. The case of a shear transformation in a rectangular region is discussed in more detail in connection with twinning.