Vol. 12, No. 3, 2017

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ISSN: 1559-3959
Stress concentration around a nanovoid eccentrically embedded in an elastic lamina subjected to far-field loading

Changwen Mi

Vol. 12 (2017), No. 3, 329–351

Stress concentration is one of the major challenges threatening the health and integrity of engineering structures. This paper analyzes the stress distributions around a spherical nanovoid near two parallel free surfaces. The loading is all-around uniform tension at infinity, perpendicular to the axis of symmetry of the infinite strip. Both plane surfaces of the strip assume traction free boundary conditions whereas the spherical void surface is modeled as a mathematical thin-film of Gurtin and Murdoch type. The method of Boussinesq’s displacement functions is used in the analysis and the solutions are expressed semianalytically in terms of infinite series of Legendre functions and improper integrals involving Bessel functions. Numerical calculations are performed to illustrate the dependence of elastic fields on surface material properties, model size, void radius, and eccentricity. The results suggest the likelihood of optimizing stress concentrations in metallic materials and structures by the proper design of surface material properties, particularly of the residual surface stress.

stress concentration, surface mechanics, elastic lamina, size dependence, displacement function method
Received: 13 September 2016
Revised: 22 December 2016
Accepted: 17 January 2017
Published: 9 February 2017
Changwen Mi
Jiangsu Key Laboratory of Engineering Mechanics, School of Civil Engineering
Southeast University
2 Sipailou Street
Nanjing, 210096