The problem of sharp notch in couple-stress elasticity

Gourgiotis, PA; Georgiadis, HG

dc.contributor.author	Gourgiotis, PA	en
dc.contributor.author	Georgiadis, HG	en
dc.date.accessioned	2014-03-01T01:37:27Z
dc.date.available	2014-03-01T01:37:27Z
dc.date.issued	2011	en
dc.identifier.issn	0020-7683	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21503
dc.subject	Asymptotic analysis	en
dc.subject	Boundary layer	en
dc.subject	Couple-stress elasticity	en
dc.subject	Cracks	en
dc.subject	Granular media	en
dc.subject	Micro-mechanics	en
dc.subject	Microstructure	en
dc.subject	Sharp notch	en
dc.subject.classification	Mechanics	en
dc.subject.other	Additional boundary condition	en
dc.subject.other	Anti-symmetric	en
dc.subject.other	Asymptotic field	en
dc.subject.other	Asymptotic technique	en
dc.subject.other	Couple-stress elasticity	en
dc.subject.other	Eigenvalue problem	en
dc.subject.other	Granular media	en
dc.subject.other	Half-space	en
dc.subject.other	Higher-order systems	en
dc.subject.other	Microstructural properties	en
dc.subject.other	Notch problems	en
dc.subject.other	Plane strain condition	en
dc.subject.other	Polar coordinate systems	en
dc.subject.other	Remote regions	en
dc.subject.other	Sharp notch	en
dc.subject.other	Standard theories	en
dc.subject.other	Asymptotic analysis	en
dc.subject.other	Boundary layers	en
dc.subject.other	Cracks	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Standards	en
dc.subject.other	Elasticity	en
dc.title	The problem of sharp notch in couple-stress elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijsolstr.2011.05.010	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijsolstr.2011.05.010	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	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.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Solids and Structures	en
dc.identifier.doi	10.1016/j.ijsolstr.2011.05.010	en
dc.identifier.isi	ISI:000293431600003	en
dc.identifier.volume	48	en
dc.identifier.issue	19	en
dc.identifier.spage	2630	en
dc.identifier.epage	2641	en