Energy theorems and the J-integral in dipolar gradient elasticity

Georgiadis, HG; Grentzelou, CG

dc.contributor.author	Georgiadis, HG	en
dc.contributor.author	Grentzelou, CG	en
dc.date.accessioned	2014-03-01T01:24:18Z
dc.date.available	2014-03-01T01:24:18Z
dc.date.issued	2006	en
dc.identifier.issn	0020-7683	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17208
dc.subject	Crack problems	en
dc.subject	Dipolar stresses	en
dc.subject	Energy release rate	en
dc.subject	Energy theorems	en
dc.subject	Generalized continuum theories	en
dc.subject	Gradient elasticity	en
dc.subject	J-integral	en
dc.subject	Microstructure	en
dc.subject	Uniqueness	en
dc.subject	Variational principles	en
dc.subject.classification	Mechanics	en
dc.subject.other	Computational methods	en
dc.subject.other	Cracks	en
dc.subject.other	Microstructure	en
dc.subject.other	Potential energy	en
dc.subject.other	Stresses	en
dc.subject.other	Theorem proving	en
dc.subject.other	Crack problems	en
dc.subject.other	Dipolar stresses	en
dc.subject.other	Energy release rate	en
dc.subject.other	Energy theorems	en
dc.subject.other	Generalized continuum theories	en
dc.subject.other	Gradient elasticity	en
dc.subject.other	J-integral	en
dc.subject.other	Uniqueness	en
dc.subject.other	Variational principles	en
dc.subject.other	Elasticity	en
dc.title	Energy theorems and the J-integral in dipolar gradient elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijsolstr.2005.08.009	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijsolstr.2005.08.009	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	Within the framework of Mindlin's dipolar gradient elasticity, general energy theorems are proved in this work. These are the theorem of minimum potential energy, the theorem of minimum complementary potential energy, a variational principle analogous to that of the Hellinger-Reissner principle in classical theory, two theorems analogous to those of Castigliano and Engesser in classical theory, a uniqueness theorem of the Kirchhoff-Neumann type, and a reciprocal theorem. These results can be of importance to computational methods for analyzing practical problems. In addition, the J-integral of fracture mechanics is derived within the same framework. The new form of the J-integral is identified with the energy release rate at the tip of a growing crack and its path-independence is proved. The theory of dipolar gradient 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 second gradient of the displacement (additional term). Specific cases of the general theory considered here are the well-known theory of couple-stress elasticity and the recently popularized theory of strain-gradient elasticity. The latter case is also treated in the present study. (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.2005.08.009	en
dc.identifier.isi	ISI:000239711000017	en
dc.identifier.volume	43	en
dc.identifier.issue	18-19	en
dc.identifier.spage	5690	en
dc.identifier.epage	5712	en