Modeling complex crack problems using the numerical manifold method
In the numerical manifold method, there are two kinds of covers, namely mathematical cover and physical cover. Mathematical covers are independent of the physical domain of the problem, over which weight functions are defined. Physical covers are the intersection of the mathematical covers and the p...
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| Veröffentlicht in: | International journal of fracture 2009-03, Vol.156 (1), p.21-35 |
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| creator | Ma, G. W. An, X. M. Zhang, H. H. Li, L. X. |
| description | In the numerical manifold method, there are two kinds of covers, namely mathematical cover and physical cover. Mathematical covers are independent of the physical domain of the problem, over which weight functions are defined. Physical covers are the intersection of the mathematical covers and the physical domain, over which cover functions with unknowns to be determined are defined. With these two kinds of covers, the method is quite suitable for modeling discontinuous problems. In this paper, complex crack problems such as multiple branched and intersecting cracks are studied to exhibit the advantageous features of the numerical manifold method. Complex displacement discontinuities across crack surfaces are modeled by different cover functions in a natural and straightforward manner. For the crack tip singularity, the asymptotic near tip field is incorporated to the cover function of the singular physical cover. By virtue of the domain form of the interaction integral, the mixed mode stress intensity factors are evaluated for three typical examples. The excellent results show that the numerical manifold method is prominent in modeling the complex crack problems. |
| doi_str_mv | 10.1007/s10704-009-9342-7 |
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For the crack tip singularity, the asymptotic near tip field is incorporated to the cover function of the singular physical cover. By virtue of the domain form of the interaction integral, the mixed mode stress intensity factors are evaluated for three typical examples. The excellent results show that the numerical manifold method is prominent in modeling the complex crack problems.</description><identifier>ISSN: 0376-9429</identifier><identifier>EISSN: 1573-2673</identifier><identifier>DOI: 10.1007/s10704-009-9342-7</identifier><identifier>CODEN: IJFRAP</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Asymptotic properties ; Automotive Engineering ; Characterization and Evaluation of Materials ; Chemistry and Materials Science ; Civil Engineering ; Classical Mechanics ; Crack tips ; Cracks ; Discontinuity ; Exact sciences and technology ; Fracture mechanics ; Fracture mechanics (crack, fatigue, damage...) ; Fundamental areas of phenomenology (including applications) ; Manifolds ; Materials Science ; Mathematical analysis ; Mathematical models ; Mechanical Engineering ; Original Paper ; Physics ; Singularities ; Solid mechanics ; Stress intensity factors ; Structural and continuum mechanics ; Weight function ; Weighting functions</subject><ispartof>International journal of fracture, 2009-03, Vol.156 (1), p.21-35</ispartof><rights>Springer Science+Business Media B.V. 2009</rights><rights>2009 INIST-CNRS</rights><rights>International Journal of Fracture is a copyright of Springer, (2009). 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W.</creatorcontrib><creatorcontrib>An, X. M.</creatorcontrib><creatorcontrib>Zhang, H. H.</creatorcontrib><creatorcontrib>Li, L. X.</creatorcontrib><title>Modeling complex crack problems using the numerical manifold method</title><title>International journal of fracture</title><addtitle>Int J Fract</addtitle><description>In the numerical manifold method, there are two kinds of covers, namely mathematical cover and physical cover. Mathematical covers are independent of the physical domain of the problem, over which weight functions are defined. Physical covers are the intersection of the mathematical covers and the physical domain, over which cover functions with unknowns to be determined are defined. With these two kinds of covers, the method is quite suitable for modeling discontinuous problems. In this paper, complex crack problems such as multiple branched and intersecting cracks are studied to exhibit the advantageous features of the numerical manifold method. Complex displacement discontinuities across crack surfaces are modeled by different cover functions in a natural and straightforward manner. For the crack tip singularity, the asymptotic near tip field is incorporated to the cover function of the singular physical cover. By virtue of the domain form of the interaction integral, the mixed mode stress intensity factors are evaluated for three typical examples. The excellent results show that the numerical manifold method is prominent in modeling the complex crack problems.</description><subject>Asymptotic properties</subject><subject>Automotive Engineering</subject><subject>Characterization and Evaluation of Materials</subject><subject>Chemistry and Materials Science</subject><subject>Civil Engineering</subject><subject>Classical Mechanics</subject><subject>Crack tips</subject><subject>Cracks</subject><subject>Discontinuity</subject><subject>Exact sciences and technology</subject><subject>Fracture mechanics</subject><subject>Fracture mechanics (crack, fatigue, damage...)</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Manifolds</subject><subject>Materials Science</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mechanical Engineering</subject><subject>Original Paper</subject><subject>Physics</subject><subject>Singularities</subject><subject>Solid mechanics</subject><subject>Stress intensity factors</subject><subject>Structural and continuum mechanics</subject><subject>Weight function</subject><subject>Weighting functions</subject><issn>0376-9429</issn><issn>1573-2673</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp1kMtKxDAUhoMoOI4-gLuCCG6iae5ZyuANRtzoOmTS05mOvYxJC_r2pnRQEMzmEM53Pn5-hM5zcp0Tom5iThThmBCDDeMUqwM0y4VimErFDtGMMCWx4dQco5MYtySBSvMZWjx3BdRVu8581-xq-Mx8cP4924VuVUMTsyGOy34DWTs0ECrv6qxxbVV2dZE10G-64hQdla6OcLafc_R2f_e6eMTLl4enxe0Se85Fj71SWpJSOMOAOgAwGiQTTGumgBU-PRCgwbuVlNwlxnBGFVesLHX6sDm6mrwp3McAsbdNFT3UtWuhG6LNiaaUMilEQi_-oNtuCG1KZykVRlNJzUjlE-VDF2OA0u5C1bjwlVR2rNVOtdrUlh1rtSrdXO7NLqYuyuBaX8WfQ5oLypUe3XTiYlq1awi_Cf6XfwNldocP</recordid><startdate>20090301</startdate><enddate>20090301</enddate><creator>Ma, G. 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X.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c445t-c77860f5a93e2aeee98e63538837e3dcccce5e8ecab664ae2a94327473ff82a93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Asymptotic properties</topic><topic>Automotive Engineering</topic><topic>Characterization and Evaluation of Materials</topic><topic>Chemistry and Materials Science</topic><topic>Civil Engineering</topic><topic>Classical Mechanics</topic><topic>Crack tips</topic><topic>Cracks</topic><topic>Discontinuity</topic><topic>Exact sciences and technology</topic><topic>Fracture mechanics</topic><topic>Fracture mechanics (crack, fatigue, damage...)</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Manifolds</topic><topic>Materials Science</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mechanical Engineering</topic><topic>Original Paper</topic><topic>Physics</topic><topic>Singularities</topic><topic>Solid mechanics</topic><topic>Stress intensity factors</topic><topic>Structural and continuum mechanics</topic><topic>Weight function</topic><topic>Weighting functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ma, G. 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W.</au><au>An, X. M.</au><au>Zhang, H. H.</au><au>Li, L. X.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Modeling complex crack problems using the numerical manifold method</atitle><jtitle>International journal of fracture</jtitle><stitle>Int J Fract</stitle><date>2009-03-01</date><risdate>2009</risdate><volume>156</volume><issue>1</issue><spage>21</spage><epage>35</epage><pages>21-35</pages><issn>0376-9429</issn><eissn>1573-2673</eissn><coden>IJFRAP</coden><abstract>In the numerical manifold method, there are two kinds of covers, namely mathematical cover and physical cover. Mathematical covers are independent of the physical domain of the problem, over which weight functions are defined. Physical covers are the intersection of the mathematical covers and the physical domain, over which cover functions with unknowns to be determined are defined. With these two kinds of covers, the method is quite suitable for modeling discontinuous problems. In this paper, complex crack problems such as multiple branched and intersecting cracks are studied to exhibit the advantageous features of the numerical manifold method. Complex displacement discontinuities across crack surfaces are modeled by different cover functions in a natural and straightforward manner. For the crack tip singularity, the asymptotic near tip field is incorporated to the cover function of the singular physical cover. By virtue of the domain form of the interaction integral, the mixed mode stress intensity factors are evaluated for three typical examples. The excellent results show that the numerical manifold method is prominent in modeling the complex crack problems.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10704-009-9342-7</doi><tpages>15</tpages></addata></record> |
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| subjects | Asymptotic properties Automotive Engineering Characterization and Evaluation of Materials Chemistry and Materials Science Civil Engineering Classical Mechanics Crack tips Cracks Discontinuity Exact sciences and technology Fracture mechanics Fracture mechanics (crack, fatigue, damage...) Fundamental areas of phenomenology (including applications) Manifolds Materials Science Mathematical analysis Mathematical models Mechanical Engineering Original Paper Physics Singularities Solid mechanics Stress intensity factors Structural and continuum mechanics Weight function Weighting functions |
| title | Modeling complex crack problems using the numerical manifold method |
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