Vol. 11, No. 5, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 3, 249–351
Issue 2, 147–247
Issue 1, 1–146

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
Cover
Editorial Board
Research Statement
Scientific Advantage
Submission Guidelines
Submission Form
Subscriptions
Author Index
To Appear
 
ISSN: 1559-3959
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

Vol. 11 (2016), No. 5, 595–614
Abstract

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
Milestones
Received: 31 March 2016
Revised: 12 August 2016
Accepted: 13 August 2016
Published: 25 September 2016
Authors
Changwen Mi
Jiangsu Key Laboratory of Engineering Mechanics
School of Civil Engineering
Southeast University
2 Sipailou Street
Nanjing, 210096
China
Zhongwei Sun
Jiangsu Key Laboratory of Engineering Mechanics
School of Civil Engineering
Southeast University
2 Sipailou Street
Nanjing, 210096
China
Demitris Kouris
Office of the Provost
South Dakota School of Mines & Technology
501 East St. Joseph Street
Rapid City, SD 57701
United States