The sliding inclusion under shear

The elastic fields due to a spheroidal inclusion, which undergoes constant shear eigenstrains and a spheroidal inhomogeneity under uniform shear stress applied at infinity are investigated. The interface between the material and the spheroid allows free sliding (cannot sustain shear tractions). The Papkovich-Neuber displacement potentials in the form of infinite series are used in the analysis. The dependence of stresses and displacements on the shear moduli ratio, Poisson's ratio and the shape of the subdomain is analyzed. It is discovered that stresses in the sliding spheroidal subdomain are not uniform, unlike the perfectly bonded inclusion solution where Eshelby's result holds. The applications to the evaluation of average elastic properties of the composites with sliding interfaces are also investigated and it is observed that sliding causes relaxation of the elastic moduli.