Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity

Grentzelou, CG; Georgiadis, HG

dc.contributor.author	Grentzelou, CG	en
dc.contributor.author	Georgiadis, HG	en
dc.date.accessioned	2014-03-01T01:23:18Z
dc.date.available	2014-03-01T01:23:18Z
dc.date.issued	2005	en
dc.identifier.issn	0020-7683	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16888
dc.subject	Couple-stress elasticity	en
dc.subject	Crack problems	en
dc.subject	Dipolar stresses	en
dc.subject	Generalized continuum theories	en
dc.subject	Gradient elasticity	en
dc.subject	Microstructure	en
dc.subject	Uniqueness	en
dc.subject.classification	Mechanics	en
dc.subject.other	Anisotropy	en
dc.subject.other	Elasticity	en
dc.subject.other	Mathematical models	en
dc.subject.other	Microstructure	en
dc.subject.other	Problem solving	en
dc.subject.other	Stresses	en
dc.subject.other	Theorem proving	en
dc.subject.other	Couple stress elasticity	en
dc.subject.other	Crack problems	en
dc.subject.other	Dipolar stresses	en
dc.subject.other	Generalized continuum theories	en
dc.subject.other	Gradient elasticity	en
dc.subject.other	Uniqueness	en
dc.subject.other	Cracks	en
dc.title	Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijsolstr.2005.02.045	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijsolstr.2005.02.045	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	The present work deals with the uniqueness theorem for plane crack problems in solids characterized by dipolar gradient elasticity. The theory of gradient elasticity derives from considerations of microstructure in elastic continua [Mindlin, R.D., 1964. Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51-78] and is appropriate to model materials with periodic structure. According to this theory, the strain-energy density assumes the form of a positive-definite function of the strain (as in classical elasticity) and the second gradient of the displacement (additional term). Specific cases of the general theory employed here are the well-known theory of couple-stress elasticity and the recently popularized theory of strain-gradient elasticity. These cases are also treated in the present study. We consider an anisotropic material response of the cracked plane body, within the linear version of gradient elasticity, and conditions of plane-strain or anti-plane strain. It is emphasized that, for crack problems in general, a uniqueness theorem more extended than the standard Kirchhoff theorem is needed because of the singular behavior of the solutions at the crack tips. Such a theorem will necessarily impose certain restrictions on the behavior of the fields in the vicinity of crack tips. In standard elasticity, a theorem was indeed established by Knowles and Pucik [Knowles, J.K., Pucik, T.A., 1973. Uniqueness for plane crack problems in linear elastostatics. J. Elast. 3, 155-160], who showed that the necessary conditions for solution uniqueness are a bounded displacement field and a bounded body-force field. In our study, we show that the additional (to the two previous conditions) requirement of a bounded displacement-gradient field in the vicinity of the crack tips guarantees uniqueness within the general form of the theory of dipolar gradient elasticity. In the specific cases of couple-stress elasticity and pure strain-gradient elasticity, the additional requirement is less stringent. This only involves a bounded rotation field for the first case and a bounded strain field for the second case. (c) 2005 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.2005.02.045	en
dc.identifier.isi	ISI:000232519900005	en
dc.identifier.volume	42	en
dc.identifier.issue	24-25	en
dc.identifier.spage	6226	en
dc.identifier.epage	6244	en