The problem of sharp notch in couple-stress elasticity

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:48

Article

Gourgiotis, P. A.¹  Georgiadis, H. G.¹ 

[1] Natl Tech Univ Athens, Mech Div, GR-15773 Zografos, Greece

关键词: Sharp notch;    Cracks;    Granular media;    Microstructure;    Micro-mechanics;    Couple-stress elasticity;    Asymptotic analysis;    Boundary layer;   

DOI  :  10.1016/j.ijsolstr.2011.05.010

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Ltd. All rights reserved.

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