Eshelby's inclusion

[1][2] Eshelby started with a thought experiment on the possible stress, strain, and displacement fields in a linear elastic body containing an inclusion.

In particular, he considered the situation in which the inclusion has undergone a transformation (such as twinning or localized thermal expansion) but its change in shape and size are restricted because of the surrounding material.

Also the strain states in the body and the inclusion are potentially inhomogeneous and complicated.

"[1] Eshelby's finding that the strain and stress field inside the ellipsoidal inclusion is uniform and has a closed-form solution, regardless of the material properties and initial transformation strain (also called the eigenstrain), has spawned a large amount of work in the mechanics of composites.

The results find their applications in the effective medium theory for heterogeneous elastic materials.

An inclusion in a linear elastic body. The stiffness tensor of the body is C 0 and that of the inclusion is C i . When the body and the inclusion have different elastic properties the inclusion is called an inhomogeneity . A transformation strain changes the shape and size of the inclusion.