Lattice Boltzmann simulation of antiplane shear loading of a stationary crack
In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional...
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| Veröffentlicht in: | Computational mechanics 2018-11, Vol.62 (5), p.1059-1069 |
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| creator | Schlüter, Alexander Kuhn, Charlotte Müller, Ralf |
| description | In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by Guangwu (J Comput Phys 161(1):61–69,
2000
) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu’s work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated. |
| doi_str_mv | 10.1007/s00466-018-1550-4 |
| format | Article |
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2000
) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu’s work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated.</description><identifier>ISSN: 0178-7675</identifier><identifier>EISSN: 1432-0924</identifier><identifier>DOI: 10.1007/s00466-018-1550-4</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Antiplane deformation ; Boundary conditions ; Classical and Continuum Physics ; Computational Science and Engineering ; Computer simulation ; Elastic deformation ; Engineering ; Finite element method ; Original Paper ; Partial differential equations ; Shear deformation ; Theoretical and Applied Mechanics ; Wave equations</subject><ispartof>Computational mechanics, 2018-11, Vol.62 (5), p.1059-1069</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2018</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-5f983108d722ad34b14378567a8275f5c1c75c23eeadec60ec4a553e27326073</citedby><cites>FETCH-LOGICAL-c316t-5f983108d722ad34b14378567a8275f5c1c75c23eeadec60ec4a553e27326073</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00466-018-1550-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00466-018-1550-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Schlüter, Alexander</creatorcontrib><creatorcontrib>Kuhn, Charlotte</creatorcontrib><creatorcontrib>Müller, Ralf</creatorcontrib><title>Lattice Boltzmann simulation of antiplane shear loading of a stationary crack</title><title>Computational mechanics</title><addtitle>Comput Mech</addtitle><description>In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by Guangwu (J Comput Phys 161(1):61–69,
2000
) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu’s work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated.</description><subject>Antiplane deformation</subject><subject>Boundary conditions</subject><subject>Classical and Continuum Physics</subject><subject>Computational Science and Engineering</subject><subject>Computer simulation</subject><subject>Elastic deformation</subject><subject>Engineering</subject><subject>Finite element method</subject><subject>Original Paper</subject><subject>Partial differential equations</subject><subject>Shear deformation</subject><subject>Theoretical and Applied Mechanics</subject><subject>Wave equations</subject><issn>0178-7675</issn><issn>1432-0924</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kLtOAzEQRS0EEiHwAXSWqA3jt1NCxEsKoklvGa83bNjYwXYK-Ho2WSQqqinm3Dujg9AlhWsKoG8KgFCKADWESglEHKEJFZwRmDFxjCZAtSFaaXmKzkpZA1BpuJygl4WrtfMB36W-fm9cjLh0m13vapciTi12sXbb3sWAy3twGffJNV1cHVa41APn8hf22fmPc3TSur6Ei985RcuH--X8iSxeH5_ntwviOVWVyHZmOAXTaMZcw8Xb8Kk2UmlnmJat9NRr6RkPwTXBKwheOCl5YJozBZpP0dVYu83pcxdKteu0y3G4aBnlzADjmg8UHSmfUyk5tHabu83wq6Vg99LsKM0O0uxemhVDho2ZMrBxFfJf8_-hH5dkblg</recordid><startdate>20181101</startdate><enddate>20181101</enddate><creator>Schlüter, Alexander</creator><creator>Kuhn, Charlotte</creator><creator>Müller, Ralf</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20181101</creationdate><title>Lattice Boltzmann simulation of antiplane shear loading of a stationary crack</title><author>Schlüter, Alexander ; Kuhn, Charlotte ; Müller, Ralf</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-5f983108d722ad34b14378567a8275f5c1c75c23eeadec60ec4a553e27326073</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Antiplane deformation</topic><topic>Boundary conditions</topic><topic>Classical and Continuum Physics</topic><topic>Computational Science and Engineering</topic><topic>Computer simulation</topic><topic>Elastic deformation</topic><topic>Engineering</topic><topic>Finite element method</topic><topic>Original Paper</topic><topic>Partial differential equations</topic><topic>Shear deformation</topic><topic>Theoretical and Applied Mechanics</topic><topic>Wave equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Schlüter, Alexander</creatorcontrib><creatorcontrib>Kuhn, Charlotte</creatorcontrib><creatorcontrib>Müller, Ralf</creatorcontrib><collection>CrossRef</collection><jtitle>Computational mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Schlüter, Alexander</au><au>Kuhn, Charlotte</au><au>Müller, Ralf</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Lattice Boltzmann simulation of antiplane shear loading of a stationary crack</atitle><jtitle>Computational mechanics</jtitle><stitle>Comput Mech</stitle><date>2018-11-01</date><risdate>2018</risdate><volume>62</volume><issue>5</issue><spage>1059</spage><epage>1069</epage><pages>1059-1069</pages><issn>0178-7675</issn><eissn>1432-0924</eissn><abstract>In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by Guangwu (J Comput Phys 161(1):61–69,
2000
) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu’s work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00466-018-1550-4</doi><tpages>11</tpages></addata></record> |
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| subjects | Antiplane deformation Boundary conditions Classical and Continuum Physics Computational Science and Engineering Computer simulation Elastic deformation Engineering Finite element method Original Paper Partial differential equations Shear deformation Theoretical and Applied Mechanics Wave equations |
| title | Lattice Boltzmann simulation of antiplane shear loading of a stationary crack |
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