  An explicit solution, considering the interface bending resistance as
described by the Steigmann-Ogden interface model, is derived for the problem of
a spherical nano-inhomogeneity (nanoscale void/inclusion) embedded in an
infinite linear-elastic matrix under a general uniform far-field-stress
(including tensile and shear stresses). The Papkovich-Neuber (P-N) general
solutions, which are expressed in terms of spherical harmonics, are used to
derive the analytical solution. A superposition technique is used to overcome
the mathematical complexity brought on by the assumed interfacial residual
stress in the Steigmann-Ogden interface model. Numerical examples show that the
stress field, considering the interface bending resistance as with the
Steigmann-Ogden interface model, differs significantly from that considering
only the interface stretching resistance as with the Gurtin-Murdoch interface
model. In addition to the size-dependency, another interesting phenomenon is
observed: some stress components are invariant to interface bending stiffness
parameters along a certain circle in the inclusion/matrix. Moreover, a
characteristic line for the interface bending stiffness parameters is
presented, near which the stress concentration becomes quite severe. Finally,
the derived analytical solution with the Steigmann-Ogden interface model is
provided in the supplemental MATLAB code, which can be easily executed, and
used as a benchmark for semi-analytical solutions and numerical solutions in
future studies.
