Dilatational disk and finite cylindrical inclusion in elastic nanowire

For the first time, strict analytical solutions for the elastic fields and the strain energies of an infinitely thin dilatational disk (DD) and a dilatational cylindrical inclusion (CyI) of finite length coaxially embedded in an infinite elastically isotropic cylinder with free surface are given and analyzed in detail. The solutions are represented in an integral form that is suitable for further analytical use and numerical study. The screening effect of the cylinder free surface on the elastic fields and the strain energies of the DD and the CyI is discussed. It is shown that this effect is significant for both the axial displacement and stress fields when the DD and CyI radii are comparable with the cylinder radius, however it is rather weak for the DD strain energy (the energy release does not exceed ∼10%). In contrast, for the CyI strain energy, the screening effect can be very strong. It is also shown that the hydrostatic stress is inhomogeneous and exists not only inside the CyI, as is the case with this stress for inclusions in an infinite medium, but also outside it. This stress is concentrated on the free surface at the points that are closest to the CyI boundary. Inside the CyI, the hydrostatic stress is much higher in magnitude than outside it.