Multi-step dilatational inclusion in an elastically isotropic cylinder

We consider an elastic inclusion in a cylinder with isotropic materials properties. The inclusion possesses a multi-step dependence of the dilatational eigenstrain along the cylinder axis. Basing on the solution for the trace of the stress tensor of the dilatational inclusion with sharp boundaries (single-step inclusion) the stored elastic energy of the multi-step inclusion is determined and analyzed. Then, the found analytical solution for the inclusion energy is used to investigate the energy properties of the transition region between the cylinder domains with a constant level of dilatational eigenstrain. The application of the obtained results to the relevant physical problems of mechanical behavior of hybrid nanodisk/nanowire (ND/NW) semiconductor heterostructures is discussed.