Spherical nano-inhomogeneity with the Steigmann-Ogden interface model under general uniform far-?eld stress loading

摘要

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 in?nite linear-elastic matrix under a general uniform far-?eld-stress (including ten-sile 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 ?eld, considering the inter-face bending resistance as with the Steigmann-Ogden interface model, differs signi?cantly from that con-sidering 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 in-variant 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.