Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity

Gourgiotis, PA; Georgiadis, HG

dc.contributor.author	Gourgiotis, PA	en
dc.contributor.author	Georgiadis, HG	en
dc.date.accessioned	2014-03-01T01:31:40Z
dc.date.available	2014-03-01T01:31:40Z
dc.date.issued	2009	en
dc.identifier.issn	0022-5096	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19873
dc.subject	Asymptotics	en
dc.subject	Cracks	en
dc.subject	Dipolar gradient elasticity	en
dc.subject	Hypersingular integral equations	en
dc.subject	Microstructure	en
dc.subject.classification	Materials Science, Multidisciplinary	en
dc.subject.classification	Mechanics	en
dc.subject.classification	Physics, Condensed Matter	en
dc.subject.other	Asymptotic solutions	en
dc.subject.other	Asymptotics	en
dc.subject.other	Classical theory	en
dc.subject.other	Crack driving force	en
dc.subject.other	Crack problems	en
dc.subject.other	Critical stress	en
dc.subject.other	Dipolar gradient elasticity	en
dc.subject.other	Elastic strain	en
dc.subject.other	Elastic stress	en
dc.subject.other	Finite part integrals	en
dc.subject.other	Full-field	en
dc.subject.other	Generalized continuum theories	en
dc.subject.other	Gradient elasticity	en
dc.subject.other	Gradient theory	en
dc.subject.other	Hadamard	en
dc.subject.other	Hypersingular integral equation	en
dc.subject.other	Hypersingular integral equations	en
dc.subject.other	J integral	en
dc.subject.other	Linear expression	en
dc.subject.other	Local maximum	en
dc.subject.other	Material constant	en
dc.subject.other	Material microstructures	en
dc.subject.other	Maximum values	en
dc.subject.other	Microstructured materials	en
dc.subject.other	Microstructured solids	en
dc.subject.other	Mindlin	en
dc.subject.other	Numerical treatments	en
dc.subject.other	Plane-strain	en
dc.subject.other	Strain energy density	en
dc.subject.other	Strain fields	en
dc.subject.other	Strain tensor	en
dc.subject.other	Strengthening effect	en
dc.subject.other	Stress distribution	en
dc.subject.other	Williams	en
dc.subject.other	Asymptotic analysis	en
dc.subject.other	Boundary element method	en
dc.subject.other	Continuum mechanics	en
dc.subject.other	Differential equations	en
dc.subject.other	Elasticity	en
dc.subject.other	Elastohydrodynamics	en
dc.subject.other	Fracture mechanics	en
dc.subject.other	Functions	en
dc.subject.other	Integral equations	en
dc.subject.other	Microstructure	en
dc.subject.other	Strain energy	en
dc.subject.other	Stress analysis	en
dc.subject.other	Stress concentration	en
dc.subject.other	Tensors	en
dc.subject.other	Crack tips	en
dc.title	Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jmps.2009.07.005	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jmps.2009.07.005	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	The present study aims at determining the elastic stress and displacement fields around the tips of a finite-length crack in a microstructured solid under remotely applied plane-strain loading (mode I and II cases). The material microstructure is modeled through the Toupin-Mindlin generalized continuum theory of dipolar gradient elasticity. According to this theory, the strain-energy density assumes the form of a positive-definite function of the strain tensor (as in classical elasticity) and the gradient of the strain tensor (additional term). A simple but yet rigorous version of the theory is employed here by considering an isotropic linear expression of the elastic strain-energy density that involves only three material constants (the two Lame constants and the so-called gradient coefficient). First, a near-tip asymptotic solution is obtained by the Knein-Williams technique. Then, we attack the complete boundary value problem in an effort to obtain a full-field solution. Hypersingular integral equations with a cubic singularity are formulated with the aid of the Fourier transform. These equations are solved by analytical considerations on Hadamard finite-part integrals and a numerical treatment. The results show significant departure from the predictions of standard fracture mechanics. In view of these results, it seems that the classical theory of elasticity is inadequate to analyze crack problems in microstructured materials. Indeed, the present results indicate that the stress distribution ahead of the crack tip exhibits a local maximum that is bounded. Therefore, this maximum value may serve as a measure of the critical stress level at which further advancement of the crack may occur. Also, in the vicinity of the crack tip, the crack-face displacement closes more smoothly as compared to the standard result and the strain field is bounded. Finally, the J-integral (energy release rate) in gradient elasticity was evaluated. A decrease of its value is noticed in comparison with the classical theory. This shows that the gradient theory predicts a strengthening effect since a reduction of crack driving force takes place as the material microstructure becomes more pronounced. (C) 2009 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Journal of the Mechanics and Physics of Solids	en
dc.identifier.doi	10.1016/j.jmps.2009.07.005	en
dc.identifier.isi	ISI:000271337400008	en
dc.identifier.volume	57	en
dc.identifier.issue	11	en
dc.identifier.spage	1898	en
dc.identifier.epage	1920	en