An Eshelby inclusion of parabolic shape in an anisotropic elastic plane

An analytical solution is derived to the Eshelby's problem of a parabolic inclusion undergoing uniform in-plane and anti-plane eigenstrains in an anisotropic elastic plane. The stresses, total strains and rigid-body rotation are found to be uniform inside the parabolic inclusion. In addition, we obtain real-form expressions of these internal uniform physical quantities in terms of the reduced elastic compliances and the imposed eigenstrains. The constant Eshelby's tensor inside the parabolic inclusion can be completely determined by the reduced elastic compliances.

Automated summary

An analytical solution for the Eshelby's problem of a parabolic inclusion with uniform in-plane and anti-plane eigenstrains in an anisotropic elastic plane is derived. It is found that the stresses, total strains, and rigid-body rotation inside the parabolic inclusion are uniform. Real-form expressions of these internal uniform physical quantities in terms of the reduced elastic compliances and imposed eigenstrains are obtained. The constant Eshelby's tensor inside the parabolic inclusion can be completely determined by the reduced elastic compliances.