Novel approach to FE solution of crack problems in the Laplacian-based gradient elasticity

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dc.contributor.authorSkalka, Petrcs
dc.contributor.authorNavrátil, Petrcs
dc.contributor.authorKotoul, Michalcs
dc.coverage.issue1cs
dc.coverage.volume95cs
dc.date.accessioned2021-12-09T12:55:01Z
dc.date.available2021-12-09T12:55:01Z
dc.date.issued2016-04-01cs
dc.description.abstractStress/strain concentration around a crack tip in ceramic foam-like structures, where the characteristic size of the foam cell is comparable with a typical length over which field quantities change significantly, is analysed. It is convenient to replace the foam structure by an effective continuum which retains all necessary characteristic features of the foam. To this end a homogenized cracked open cell ceramic foam is analysed using the strain/stress model based upon an implicit dependence of the non-local stress and strain on the local stress and strain in the form of an inhomogeneous Helmholtz equation which is solved together with the equilibrium equations. To preserve the advantage of the uncoupled system of equations, which means that one set of equations is solved prior the other one and that two sets of shape functions can be chosen independently, are current sequence of well posed boundary value problems is constructed which can be solved using a classical 8-nodes isoparametric element for 2D problems. The key idea behind the suggested procedure consists in replacing the scale parameter l by a parameter increment dl chosen arbitrarily small. The given small disturbance causes are distribution of the local stress/displacement field. After the new local stress/displacement field is known, another disturbance is introduced and so on. The procedure is stopped when the solution, exhibiting boundary layer behaviour, leads to the cohesive-like zone with length reaching a value uniquely related to the scale parameter l.en
dc.description.abstractV rámci této publikace je analyzována deformačně-napěťová odezva v blízkém okolí čela trhliny, která je situována uprostřed zkušebního vzorku (keramická pěna s otevřenou pórovitostí) kolmo vzhledem k jeho zatížení. K řešení byla použita teorie gradientní elasticity, která zohledňuje charakteristický rozměr dané struktury (zde Kelvinova buňka). Vzhledem k časové a hardwarové náročnosti řešení na diskrétní struktuře byla provedena homogenizace materiálových charakteristik a deformačně-napěťová odezva je řešena, za podmínek rovinné deformace, na 2D modelu kontinua.cs
dc.formattextcs
dc.format.extent28-48cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationMechanics of Materials. 2016, vol. 95, issue 1, p. 28-48.en
dc.identifier.doi10.1016/j.mechmat.2015.12.007cs
dc.identifier.issn0167-6636cs
dc.identifier.other120700cs
dc.identifier.urihttp://hdl.handle.net/11012/203138
dc.language.isoencs
dc.publisherElseviercs
dc.relation.ispartofMechanics of Materialscs
dc.relation.urihttps://www.sciencedirect.com/science/article/pii/S0167663615002781cs
dc.rightsCreative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/0167-6636/cs
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/cs
dc.subjectCeramic materialen
dc.subjectFoam materialen
dc.subjectGradient elasticityen
dc.subjectStress concentrationsen
dc.subjectFinite elementsen
dc.subjectNumerical algorithmsen
dc.subjectKeramické materiály
dc.subjectPěnové materiály
dc.subjectGradientní elasticita
dc.subjectKoncentrace napětí
dc.subjectKonečné prvky
dc.subjectNumerické algoritmy
dc.titleNovel approach to FE solution of crack problems in the Laplacian-based gradient elasticityen
dc.title.alternativeNový přístup k řešení problémů lomové mechaniky využitím gradientní elasticitycs
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-120700en
sync.item.dbtypeVAVen
sync.item.insts2021.12.09 13:55:01en
sync.item.modts2021.12.09 12:14:15en
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. NCK energetika - sekce lomové mechanikycs
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