Closed-form solution for a circular nano-inhomogeneity with interface effects in an elastic plane under uniform remote heat flux

Abstract

We study the uncoupled steady-state thermo-elastic problem of a circular nano-inhomogeneity embedded in an elastic plane subjected to a uniform remote heat flux. Nanoscale influences are included in the continuum-based model of deformation by incorporating interface effects arising from both heat conduction and elasticity (in the absence of surface tension) on the material interface. Complex variable methods are used to derive closed-form solutions for the corresponding temperature and thermal stress fields. Numerical examples are presented to examine how each of the heat or elastic interface effects influence the thermal stress field. In fact, we show that the contribution of heat related interface effects to the thermal stress field decays in both the matrix and the inhomogeneity as the heat conductivity of the inhomogeneity increases. On the other hand, the contribution of elastic interface effects to the thermal stress field decays in the matrix but increases for the inhomogeneity as the inhomogeneity becomes harder.