Vol. 7, No. 8-9, 2012

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
Displacement field in an elastic solid with mode-III crack and first-order surface effects

Tamran H. Lengyel and Peter Schiavone

Vol. 7 (2012), No. 8-9, 783–794
Abstract
[an error occurred while processing this directive]

We analyze a nonstandard boundary-value problem for Laplace’s equation characterizing the displacement field arising from the antiplane deformations of an infinite elastic solid containing a sharp finite crack when first-order surface effects are included on the crack faces. The surface effects are incorporated using the continuum-based surface/interface model of Gurtin and Murdoch. We establish a uniqueness result for the displacement field and use complex variable methods to reduce the problem to a series of integral equations which are solved numerically using an efficient, stable, yet convenient finite element discretization method. Our results demonstrate the effect of the surface on the displacement field and its implications for the corresponding stress distributions in the vicinity of the crack.

Keywords
displacement field, mode-III crack, antiplane deformations, surface elasticity, integral equations
Milestones
Received: 17 May 2012
Revised: 30 July 2012
Accepted: 2 August 2012
Published: 23 January 2013
Authors
Tamran H. Lengyel
Department of Mechanical Engineering
University of Alberta
4-9 Mechanical Engineering Building
Edmonton, AB  T6G 2G8
Canada
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
4-9 Mechanical Engineering Building
Edmonton, AB  T6G 2G8
Canada
http://www.mece.ualberta.ca/~schiavone/schiavon.htm