Analytical expression for the distribution of elastic strain created by a polyhedral inclusion with arbitrary eigenstrain

Analytical expressions for the displacement vector, stain tensor, and Eshelby tensor have been obtained in the case where an inclusion in an elastically isotropic infinite medium has a polyhedral shape. The eigenstrain (e.g., the lattice mismatch) is assumed to be constant inside the inclusion but not obligatorily hydrostatic. The obtained expressions describe the strain both inside the inclusion and in its environment. It has been shown that a complex three-dimensional configuration of the elastic strain field (as well as of the displacement vector field) is reduced to a combination of simple functions having an illustrative physical and geometrical interpretation.