Balance laws and energy release rates for cracks in dipolar gradient elasticity

Grentzelou, CG; Georgiadis, HG

dc.contributor.author	Grentzelou, CG	en
dc.contributor.author	Georgiadis, HG	en
dc.date.accessioned	2014-03-01T01:28:00Z
dc.date.available	2014-03-01T01:28:00Z
dc.date.issued	2008	en
dc.identifier.issn	0020-7683	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18659
dc.subject	Balance laws	en
dc.subject	Conservation laws	en
dc.subject	Dipolar stresses	en
dc.subject	Energy release rates	en
dc.subject	Generalized continuum theories	en
dc.subject	Gradient elasticity	en
dc.subject	Microstructure	en
dc.subject	Path-independent integrals	en
dc.subject.classification	Mechanics	en
dc.subject.other	Crack propagation	en
dc.subject.other	Elasticity	en
dc.subject.other	Gradient methods	en
dc.subject.other	Microstructure	en
dc.subject.other	Strain energy	en
dc.subject.other	Stresses	en
dc.subject.other	Balance laws	en
dc.subject.other	Conservation laws	en
dc.subject.other	Dipolar stresses	en
dc.subject.other	Generalized continuum theories	en
dc.subject.other	Gradient elasticity	en
dc.subject.other	Path-independent integrals	en
dc.subject.other	Energy release rate	en
dc.title	Balance laws and energy release rates for cracks in dipolar gradient elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijsolstr.2007.08.007	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijsolstr.2007.08.007	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	It is the purpose of this work to derive the balance laws (in the Gunther-Knowles-Sternberg sense) pertaining to dipolar gradient elasticity. The theory of dipolar gradient (or grade 2) elasticity derives from considerations of microstructure in elastic continua [Mindlin, R.D., 1964. Microstructure in linear elasticity. Arch. Rational 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 gradient of both strain and rotation (additional terms). The balance laws are derived here through a more straightforward procedure than the one usually employed in classical elasticity (i.e. Noether's theorem). Indeed, the pertinent balance laws are obtained through the action of the standard operators of vector calculus (grad, curl and div) on appropriate forms of the Hamiltonian of the system under consideration. These laws are directly related to the energy release rates in the processes of crack translation, rotation and self-similar expansion. Under certain conditions, they are identified with conservation laws and path-independent integrals are obtained. (c) 2007 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.2007.08.007	en
dc.identifier.isi	ISI:000251775000013	en
dc.identifier.volume	45	en
dc.identifier.issue	2	en
dc.identifier.spage	551	en
dc.identifier.epage	567	en