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

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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 http://hdl.handle.net/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.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

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