Date
2022-01-03Metadata
Show full item record
Aufsatz
A Critical Review on the Complex Potentials in Linear Elastic Fracture Mechanics
Abstract
Introducing a crack in an elastic plate is challenging from the mathematical point of view and relevant within an engineering context of evaluating strength and reliability of structures. Accordingly, a multitude of associated works is available to date, emanating from both applied mathematics and mechanics communities. Although considering the same problem, the given complex potentials prove to be different, revealing various inconsistencies in terms of resulting stresses and displacements. Essential information on crack near-tip fields and crack opening displacements is nonetheless available, while intuitive adaption is required to obtain the full-field solutions. Investigating the cause of prevailing deficiencies inevitably leads to a critical review of classical works by Muskhelishvili or Westergaard. Complex potentials of the mixed-mode loaded Griffith crack, sparing restrictive assumptions or limitations of validity, are finally provided, allowing for rigorous mathematical treatment. The entity of stresses and displacements in the whole plate is finally illustrated and the distributions in the crack plane are given explicitly.
Sponsorship
Gefördert im Rahmen des Projekts DEALCitation
@article{doi:10.17170/kobra-202201255611,
author={Scheel, Johannes and Wallenta, Daniel and Ricoeur, Andreas},
title={A Critical Review on the Complex Potentials in Linear Elastic Fracture Mechanics},
journal={Journal of Elasticity},
year={2022}
}
0500 Oax
0501 Text $btxt$2rdacontent
0502 Computermedien $bc$2rdacarrier
1100 2022$n2022
1500 1/eng
2050 ##0##http://hdl.handle.net/123456789/13761
3000 Scheel, Johannes
3010 Wallenta, Daniel
3010 Ricoeur, Andreas
4000 A Critical Review on the Complex Potentials in Linear Elastic Fracture Mechanics / Scheel, Johannes
4030
4060 Online-Ressource
4085 ##0##=u http://nbn-resolving.de/http://hdl.handle.net/123456789/13761=x R
4204 \$dAufsatz
4170
5550 {{Rissbildung}}
5550 {{Bruchmechanik}}
5550 {{Gleichung}}
5550 {{Mathematisches Modell}}
7136 ##0##http://hdl.handle.net/123456789/13761
<resource xsi:schemaLocation="http://datacite.org/schema/kernel-2.2 http://schema.datacite.org/meta/kernel-2.2/metadata.xsd"> 2022-04-19T09:48:06Z 2022-04-19T09:48:06Z 2022-01-03 doi:10.17170/kobra-202201255611 http://hdl.handle.net/123456789/13761 Gefördert im Rahmen des Projekts DEAL eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ complex potentials Westergaard stress function Griffith crack Kolosov´s equations crack fields 660 510 530 A Critical Review on the Complex Potentials in Linear Elastic Fracture Mechanics Aufsatz Introducing a crack in an elastic plate is challenging from the mathematical point of view and relevant within an engineering context of evaluating strength and reliability of structures. Accordingly, a multitude of associated works is available to date, emanating from both applied mathematics and mechanics communities. Although considering the same problem, the given complex potentials prove to be different, revealing various inconsistencies in terms of resulting stresses and displacements. Essential information on crack near-tip fields and crack opening displacements is nonetheless available, while intuitive adaption is required to obtain the full-field solutions. Investigating the cause of prevailing deficiencies inevitably leads to a critical review of classical works by Muskhelishvili or Westergaard. Complex potentials of the mixed-mode loaded Griffith crack, sparing restrictive assumptions or limitations of validity, are finally provided, allowing for rigorous mathematical treatment. The entity of stresses and displacements in the whole plate is finally illustrated and the distributions in the crack plane are given explicitly. open access Scheel, Johannes Wallenta, Daniel Ricoeur, Andreas doi:10.1007/s10659-021-09873-1 Rissbildung Bruchmechanik Gleichung Mathematisches Modell publishedVersion eissn:1573-2681 Issue 1-2 Journal of Elasticity 291-308 Volume 147 false </resource>
The following license files are associated with this item:
Except where otherwise noted, this item's license is described as Namensnennung 4.0 International