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The hemispherical
nanopit at the plane boundary of an elastic half-space
subjected to statically equivalent shear tractions
Changwen Mi, Zhongwei Sun and Demitris Kouris |
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Vol. 11 (2016), No. 5, 595–614
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Abstract |
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The elastic deformation of a semi-infinite substrate containing a nanosized hemispherical pit on its plane boundary crucially relies on the mechanical response of the pit surface. In this paper, we develop a micromechanical model that couples Gurtin and Murdoch’s model of surface mechanics with the classical theory of elasticity, and we explicitly evaluate the stress concentration, displacement and stress distribution resulting from a family of statically equivalent shear tractions applied on the pit surface. We found that two intrinsic dimensionless parameters, both constructed from the characteristic length and material properties, govern the highly localized elastic field. Both the magnitude and sign of these parameters are of great importance. Negative values tend to increase stress concentrations, whereas positive ones have the opposite effect. We further highlight the consequences of our analysis by comparing a number of shear tractions that correspond to the same torque. The comparison provides the means of evaluating the degree of difference in elastic fields in the immediate vicinity of statically equivalent force distributions. |
Keywords
surface mechanics, nanopit, half-space, torsional loading,
stress concentration
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Milestones
Received: 31 March 2016
Revised: 12 August 2016
Accepted: 13 August 2016
Published: 25 September 2016
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Authors |
| Changwen Mi | |
| Jiangsu Key Laboratory of
Engineering Mechanics School of Civil Engineering Southeast University 2 Sipailou Street Nanjing, 210096 China |
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| Zhongwei Sun | |
| Jiangsu Key Laboratory of
Engineering Mechanics School of Civil Engineering Southeast University 2 Sipailou Street Nanjing, 210096 China |
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| Demitris Kouris | |
| Office of the Provost South Dakota School of Mines & Technology 501 East St. Joseph Street Rapid City, SD 57701 United States |
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