On the stress analysis around a nanoinhomogeneity emb e dde d in a half-space with the account of Steigmann-Ogden interface effects

This paper examines the interface elasticity between an elastic half-space and a spherical nanoinhomogeneity subjected to a unidirectional far-field tension that is parallel to the half-space plane boundary. The spherical interface is modeled by the full version of Steigmann-Ogden interface theory. Due to their marginal significance, the effects of half space plane boundary are neglected. The problem is solved by decomposing the unidirectional load into an all-around and an equal-but-opposite traction field. Benefitting from the property of axial symmetry, the former subproblem is solved by the sole use of Boussinesq displacement potentials. The latter condition is addressed by six harmonic functions extracting from Boussinesq, Papkovich-Neuber and Dougall displacement potentials. The relations between cylindrical and spherical harmonic functions are employed to clear the tractions along the half-space plane boundary and to satisfy the nonclassical traction equilibrium conditions across the matrix/nanoinhomogeneity interface. Truncating the resultant infinite series and equating the coefficients preceding Legendre polynomials, associated Legendre functions as well as their derivatives lead to a system of algebraic equations with respect to the dimensionless unknown parameters in displacement potentials. Extensive parametric studies are further performed in order to analyze the importance of interface tension, interface Lame constants, interface flexural rigidities, shear moduli ratio and nanoinhomogeneity radius-to-depth ratio on stress distributions and stress concentrations. Comparisons against both the classical and the Gurtin-Murdoch solutions help to clarify the separate effects of individual interface material properties. Stresses inside a soft nanoinhomogeneity is most affected by the additional incorporation of interface flexural rigidities. In addition, the deviatoric component of the interface curvature change tensor is found to be more important than the mean part for the proposed nanoinhomogeneity problem. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study examines the interface elasticity between an elastic half-space and a spherical nanoinhomogeneity. By decomposing the load and using different displacement potentials, the problem is successfully solved. Parametric studies reveal the important influences of interface tension, interface Lame constants, and other factors on stress distributions and stress concentrations.