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Interaction and Multiscale Mechanics
  Volume 4, Number 2, June 2011, pages 123-137
DOI: http://dx.doi.org/10.12989/imm.2011.4.2.123
 
open access

An analysis of an elastic solid incorporating a crack under the influences of surface effects in plane & anti-plane deformations
Chun Il Kim

 
Abstract
    We review a series of crack problems arising in the general deformations of a linearly elastic solid (Mode-I, Mode-II and Mode-III crack) and, perhaps more significantly, when the contribution of surface effects are taken into account. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. We show that the deformations of an elastic solid containing a single crack can be decoupled into in-plane (Mode-I and Mode-II crack) and anti-plane (Mode-III crack) parts, even when the surface mechanics is introduced. In particular, it is shown that, in contrast to classical fracture mechanics (where surface effects are neglected), the incorporation of surface elasticity leads to the more accurate description of a finite stress at the crack tip. In addition, the corresponding stress fields exhibit strong dependency on the size of crack.
 
Key Words
    surface elasticity; mode-I, II, III; plane deformations; anti-plane deformations; crack tip analysis; complete exact solution; Cauchy singular integro-differential equations.
 
Address
Chun Il Kim: Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada
 

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