Size dependence of stress field around a prolate spheroidal nanosized cavity in an elastic cylindrical medium under remote torsion

When the size of materials and structures shrinks to nanometer, the influence of surface energy on their stress field becomes more important in nanoscale due to their relatively high surface-to-volume ratios compared to that of a macro-scale domain. Based on Gurtin-Murdoch surface elasticity theory, displacement potentials are used to solve the three dimensional boundary-value problems involving non-classical boundary conditions represented by the generalized Young-Laplace equations. The stress field around a nanoscale prolate spheroidal cavity in an isotropic homogeneous and infinite elastic cylindrical medium under remote torsion is obtained. Compared to classical results, the present formulations render the significant effect of the surface energy on the stress field when the size of cavity is reduced to nanometer. Numerical results show that the intensity of the influence depends on not only the size and the shape of the cavity but also the proximity of the cavity to the edge and the surface energy effect.