The problem of sharp notch in couple-stress elasticity

✍ Scribed by P.A. Gourgiotis; H.G. Georgiadis

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 585 KB
• Volume: 48
• Category: Article
• ISSN: 0020-7683
• DOI: 10.1016/j.ijsolstr.2011.05.010

✦ Synopsis

The problem of sharp notch in couple-stress elasticity is considered in this paper. The problem involves a sharp notch in a body of infinite extent. The body has microstructural properties, which are assumed to be characterized by couple-stress effects. Both symmetric and anti-symmetric loadings at remote regions are considered under plane-strain conditions. The faces of the notch are considered traction free. To determine the field around the tip of the notch, a boundary-layer approach is followed by considering an expansion of the displacements in a form of separated variables in a polar coordinate system. Our analysis is in the spirit of the Knein-Williams and Karp-Karal asymptotic techniques but it is much more involved than its corresponding analysis of standard elasticity due to the complicated boundary value problem (higher-order system of governing PDEs and additional boundary conditions as compared to the standard theory). Eventually, an eigenvalue problem is formulated and this, along with the restriction of a bounded potential energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed as limit cases of the general notch problem. Certain deviations from the standard classical elasticity results are noted.