Anti-plane shear Lamb's problem treated by gradient elasticity with surface energy

Georgiadis, HG; Vardoulakis, I

dc.contributor.author	Georgiadis, HG	en
dc.contributor.author	Vardoulakis, I	en
dc.date.accessioned	2014-03-01T01:13:35Z
dc.date.available	2014-03-01T01:13:35Z
dc.date.issued	1998	en
dc.identifier.issn	0165-2125	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12584
dc.subject	Boundary Condition	en
dc.subject	Boundary Integral Equation Method	en
dc.subject	Classical Solution	en
dc.subject	Contact Problem	en
dc.subject	Helmholtz Equation	en
dc.subject	Linear Elasticity	en
dc.subject	Surface Energy	en
dc.subject	Higher Order	en
dc.subject	Strain Energy Density	en
dc.subject.classification	Acoustics	en
dc.subject.classification	Mechanics	en
dc.subject.classification	Physics, Multidisciplinary	en
dc.subject.other	CRACK	en
dc.subject.other	TIP	en
dc.title	Anti-plane shear Lamb's problem treated by gradient elasticity with surface energy	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0165-2125(98)00015-8	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0165-2125(98)00015-8	en
heal.language	English	en
heal.publicationDate	1998	en
heal.abstract	The consideration of higher-order gradient effects in a classical elastodynamic problem is explored in this paper. The problem is the anti-plane shear analogue of the well-known Lamb's problem. It involves the time-harmonic loading of a half-space by a single concentrated anti-plane shear line force applied on the half-space surface. The classical solution of this problem based on standard linear elasticity was first given by J.D. Achenbach and predicts a logarithmically unbounded displacement at the point of application of the load. The latter formulation involves a Helmholtz equation for the out-of-plane displacement subjected to a traction boundary condition. Here, the generalized continuum theory of gradient elasticity with surface energy leads to a fourth-order PDE under traction and double-traction boundary conditions. This theory assumes a form of the strain-energy density containing, in addition to the standard linear-elasticity terms, strain-gradient and surface-energy terms. The present solution: in some contrast with the classical one, predicts bounded displacements everywhere. This may have important implications for more general contact problems and the Boundary-Integral-Equation Method. (C) 1998 Elsevier Science B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Wave Motion	en
dc.identifier.doi	10.1016/S0165-2125(98)00015-8	en
dc.identifier.isi	ISI:000076295800004	en
dc.identifier.volume	28	en
dc.identifier.issue	4	en
dc.identifier.spage	353	en
dc.identifier.epage	366	en