Size-dependence stress field of an infinite matrix with a nanosized spheroidal inhomogeneity under hydrostatic loading

The effect of surface energy on the stress field of a nanosized spheroidal inhomogeneity embedded in an infinite matrix is analyzed based on the surface elasticity theory. Using the method of potential functions, we obtained the elastic field of heterogeneous material subjected to a hydrostatic loading. It is shown that when the size of the inhomogeneity reduces to nanometers, the contribution from surface energy becomes important. The results are evidently different from the classical results, and are useful to the failure analysis and prediction of the effective moduli of heterogeneous materials containing nanosized inhomogeneities.