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Energies of circular inclusions: sliding versus bonded interfaces

The elastic strain energies of circular inclusions with sliding and bonded interfaces are compared. It is shown that the energy in the inclusion with a sliding interface due to uniform eigenstrain is greater than the energy in the inclusion with a bonded interface if the Poisson ratio of the material is less than 1/6, and smaller if it is greater than 1/6. The total energy in the inclusion and the matrix due to uniform eigenstrain is always smaller in the case of a sliding inclusion. The opposite is true for the inclusion under remote uniform loading at infinity. The relationships between the energies of sliding and bonded inhomogeneities are also derived.