Misfit stress and energy in composite nanowire with polygonal core

Abstract

In this article we present for the first time an analytical solution to the boundary-value problem in the classical theory of elasticity for a core-shell cylinder with an eccentric prismatic core having a trapezoidal cross section and subjected to uniform dilatation eigenstrain. In doing so, we represent the trapezoidal prism as a superposition of long straight dilatational lines located along the cylinder axis. The complex potential approach has been employed to satisfy the boundary conditions on the cylinder free surface. Found in a concise and transparent closed form, the elastic stresses exerted by the dilatational line and dilatational prismatic inclusion (of trapezoidal cross section) in cylindrical body are demonstrated with maps. The mean stress is employed to obtain the analytical expression of strain energy stored by the dilatational inclusion in form of regular prism symmetrically placed in cylindrical body. It is proved that the strain energy is identical to the one of cylindrical inclusion with the same cross section area.