Stress fields and Eshelby forces on half-plane inhomogeneities with eigenstrains and strip inclusions meeting a free surface

The stress field due to a half-plane inhomogeneity with plane eigenstrain is obtained by a limiting procedure from the one of a circular Eshelby inhomogeneity/inclusion. This field, which requires tractions to be applied at infinity to be sustained, has minimum strain energy versus any other superposed homogeneous one, and is the Eshelby solution inside plus the Hill jump conditions. By superposition, the stresses due to an infinite strip (Eshelby property domain) inhomogeneity with eigenstrain are obtained, and, by superposition periodic strips or laminates can be obtained. By cancelling the stresses on a free-surface, strips of inclusions meeting a free surface are solved. They exhibit tensile stresses under the free surface, and logarithmic singularities in the tensile stress at the vertex, which may initiate cracking. The Eshelby self-forces on the boundary of circular and half-plane inhomogeneities are computed.