This paper determines the elastic fields in a positive half-space embedded with a spherical inhomogeneity under the context of Steigmann–Ogden surface/interface mechanical model. The half-space is loaded by an equal-biaxial far-field tension applied at infinity. While bulk domains are treated as linearly isotropic elastic solids, both the half-space plane boundary and the matrix/inhomogeneity interface are modeled by the Steigmann–Ogden theory. The well-developed method of Boussinesq displacement potentials is used to solve the elastostatic Navier’s equations of equilibrium. In view of the geometry and loading configurations, four sets of cylindrical and spherical harmonic potentials are carefully proposed to solve the problem. Implementation of the nonclassical Steigmann–Ogden boundary conditions at both the half-space free surface and the spherical interface results in a semianalytical solution in the form of infinite Legendre series. Extensive parametric studies are performed with respect to the surface and interface Steigmann–Ogden material parameters, shear moduli ratio between the spherical inhomogeneity and its surrounding matrix, and the inhomogeneity radius-to-depth ratio. Comparison and contrast with the well known Gurtin–Murdoch model reveals the significance of surface flexural rigidities at both boundaries of the considered mechanical model. When compared with the effects of matrix/inhomogeneity interface, the surface tension, Lamé constants and flexural rigidities at the half-space plane boundary are of secondary importance. This work is able to shed some lights on the modeling of self-organized adatoms and islands that is essential in the semiconductor industry.

本文在Steigmann–Ogden表面/界面力学模型的背景下，确定了嵌入球形不均匀性的正半空间中的弹性场。半空间由无限远处施加的等双轴远场张力加载。虽然将体畴视为线性各向同性的弹性固体，但半空间平面边界和基质/非均匀性界面均由Steigmann-Ogden理论建模。发达的Boussinesq位移势方法用于求解弹力平衡Navier方程。考虑到几何形状和载荷配置，精心提出了四组圆柱和球形谐波电势来解决该问题。在半空间自由表面和球面界面上都实现了非经典的Steigmann–Ogden边界条件，从而得到了无限勒让德级数形式的半解析解。针对表面和界面Steigmann–Ogden材料参数，球形不均匀性及其周围基体之间的剪切模量比以及不均匀性半径与深度之比，进行了广泛的参数研究。与著名的Gurtin-Murdoch模型的比较和对比表明，在所考虑的力学模型的两个边界上，表面抗弯刚度的重要性。与基体/不均匀界面的影响相比，在半空间平面边界处的表面张力，拉梅常数和抗弯刚度次要。