Study of the influence of small defects near a singular point in antiplane elasticity by an asymptotic method
We consider a domain made of a linear elastic material which contains an angular point. A small defect, like a cavity or a crack, is located in the neighborhood of the tip of the wedge. In order to study its influence both on the local and global responses of the body, we use a matched asymptotic e...
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| Format: | Article |
| Language: | English |
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Publishing House for Science and Technology
2018-03-01
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| Series: | Vietnam Journal of Mechanics |
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| Online Access: | https://vjs.ac.vn/index.php/vjmech/article/view/9341 |
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| author | Dang Thi Bach Tuyet Laurence Halpern Jean-Jacques Marigo |
| author_facet | Dang Thi Bach Tuyet Laurence Halpern Jean-Jacques Marigo |
| author_sort | Dang Thi Bach Tuyet |
| collection | DOAJ |
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We consider a domain made of a linear elastic material which contains an angular point. A small defect, like a cavity or a crack, is located in the neighborhood of the tip of the wedge. In order to study its influence both on the local and global responses of the body, we use a matched asymptotic expansion method. After the general construction of the matched asymptotic expansions for an arbitrary defect, we develop the method in the particular case where the defect is a small crack. The numerical results obtained from the method are finally compared with those given by the classical finite element method. All the analysis is made in an antiplane setting in order to make easier the calculations.
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| format | Article |
| id | doaj-art-0d7937f5786348e6b96a1c02ca4ab69c |
| institution | DOAJ |
| issn | 0866-7136 2815-5882 |
| language | English |
| publishDate | 2018-03-01 |
| publisher | Publishing House for Science and Technology |
| record_format | Article |
| series | Vietnam Journal of Mechanics |
| spelling | doaj-art-0d7937f5786348e6b96a1c02ca4ab69c2025-08-20T03:04:46ZengPublishing House for Science and TechnologyVietnam Journal of Mechanics0866-71362815-58822018-03-0140110.15625/0866-7136/9341Study of the influence of small defects near a singular point in antiplane elasticity by an asymptotic methodDang Thi Bach Tuyet0Laurence Halpern1Jean-Jacques Marigo2Laboratoire de Mecanique des Solides, Ecole Polytechnique, F-Palaiseau, FranceLAGA, Universite Paris XIII, F-Villetaneuse, FranceLaboratoire de Mecanique des Solides, Ecole Polytechnique, F-Palaiseau, France We consider a domain made of a linear elastic material which contains an angular point. A small defect, like a cavity or a crack, is located in the neighborhood of the tip of the wedge. In order to study its influence both on the local and global responses of the body, we use a matched asymptotic expansion method. After the general construction of the matched asymptotic expansions for an arbitrary defect, we develop the method in the particular case where the defect is a small crack. The numerical results obtained from the method are finally compared with those given by the classical finite element method. All the analysis is made in an antiplane setting in order to make easier the calculations. https://vjs.ac.vn/index.php/vjmech/article/view/9341brittle fracturecohesive modelasymptotic methodssingularities |
| spellingShingle | Dang Thi Bach Tuyet Laurence Halpern Jean-Jacques Marigo Study of the influence of small defects near a singular point in antiplane elasticity by an asymptotic method Vietnam Journal of Mechanics brittle fracture cohesive model asymptotic methods singularities |
| title | Study of the influence of small defects near a singular point in antiplane elasticity by an asymptotic method |
| title_full | Study of the influence of small defects near a singular point in antiplane elasticity by an asymptotic method |
| title_fullStr | Study of the influence of small defects near a singular point in antiplane elasticity by an asymptotic method |
| title_full_unstemmed | Study of the influence of small defects near a singular point in antiplane elasticity by an asymptotic method |
| title_short | Study of the influence of small defects near a singular point in antiplane elasticity by an asymptotic method |
| title_sort | study of the influence of small defects near a singular point in antiplane elasticity by an asymptotic method |
| topic | brittle fracture cohesive model asymptotic methods singularities |
| url | https://vjs.ac.vn/index.php/vjmech/article/view/9341 |
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