The Effects of Surface Elasticity on an Elastic Solid With Mode-III Crack: Complete Solution
We examined the effects of surface elasticity in a classical mode-III crack problem arising in the antiplane shear deformations of a linearly elastic solid. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. Complex variable methods are us...
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Veröffentlicht in: | Journal of applied mechanics 2010-03, Vol.77 (2), p.021011 (7)-021011 (7) |
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creator | Kim, C. I Schiavone, P Ru, C.-Q |
description | We examined the effects of surface elasticity in a classical mode-III crack problem arising in the antiplane shear deformations of a linearly elastic solid. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. Complex variable methods are used to obtain an exact solution valid everywhere in the domain of interest (including at the crack tip) by reducing the problem to a Cauchy singular integro-differential equation of the first order. Finally, we adapt classical collocation methods to obtain numerical solutions, which demonstrate several interesting phenomena in the case when the solid incorporates a traction-free crack face and is subjected to uniform remote loading. In particular, we note that, in contrast to the classical result from linear elastic fracture mechanics, the stresses at the (sharp) crack tip remain finite. |
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I ; Schiavone, P ; Ru, C.-Q</creator><creatorcontrib>Kim, C. I ; Schiavone, P ; Ru, C.-Q</creatorcontrib><description>We examined the effects of surface elasticity in a classical mode-III crack problem arising in the antiplane shear deformations of a linearly elastic solid. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. Complex variable methods are used to obtain an exact solution valid everywhere in the domain of interest (including at the crack tip) by reducing the problem to a Cauchy singular integro-differential equation of the first order. Finally, we adapt classical collocation methods to obtain numerical solutions, which demonstrate several interesting phenomena in the case when the solid incorporates a traction-free crack face and is subjected to uniform remote loading. In particular, we note that, in contrast to the classical result from linear elastic fracture mechanics, the stresses at the (sharp) crack tip remain finite.</description><identifier>ISSN: 0021-8936</identifier><identifier>EISSN: 1528-9036</identifier><identifier>DOI: 10.1115/1.3177000</identifier><language>eng</language><publisher>ASME</publisher><subject>Complex variables ; Elastic deformation ; Elasticity ; Exact solutions ; Fracture mechanics ; Mathematical analysis ; Mathematical models ; Shear deformation</subject><ispartof>Journal of applied mechanics, 2010-03, Vol.77 (2), p.021011 (7)-021011 (7)</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a282t-eadcd858da4b0c346db953f293fe90392d223013465d15d6bef5322ad1aed00d3</citedby><cites>FETCH-LOGICAL-a282t-eadcd858da4b0c346db953f293fe90392d223013465d15d6bef5322ad1aed00d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925,38520</link.rule.ids></links><search><creatorcontrib>Kim, C. I</creatorcontrib><creatorcontrib>Schiavone, P</creatorcontrib><creatorcontrib>Ru, C.-Q</creatorcontrib><title>The Effects of Surface Elasticity on an Elastic Solid With Mode-III Crack: Complete Solution</title><title>Journal of applied mechanics</title><addtitle>J. Appl. Mech</addtitle><description>We examined the effects of surface elasticity in a classical mode-III crack problem arising in the antiplane shear deformations of a linearly elastic solid. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. Complex variable methods are used to obtain an exact solution valid everywhere in the domain of interest (including at the crack tip) by reducing the problem to a Cauchy singular integro-differential equation of the first order. Finally, we adapt classical collocation methods to obtain numerical solutions, which demonstrate several interesting phenomena in the case when the solid incorporates a traction-free crack face and is subjected to uniform remote loading. In particular, we note that, in contrast to the classical result from linear elastic fracture mechanics, the stresses at the (sharp) crack tip remain finite.</description><subject>Complex variables</subject><subject>Elastic deformation</subject><subject>Elasticity</subject><subject>Exact solutions</subject><subject>Fracture mechanics</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Shear deformation</subject><issn>0021-8936</issn><issn>1528-9036</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNo10D1PwzAQBmALgUQpDMwsHmFI8UfsOGwoKhCpiKFFLEiW6w81JYmL7Qz996RqmU66e3S6ewG4xWiGMWaPeEZxUSCEzsAEMyKyElF-DiYIEZyJkvJLcBXjdgRM8HwCvlcbC-fOWZ0i9A4uh-CUHlutiqnRTdpD30PV_zfg0reNgV9N2sB3b2xW1zWsgtI_T7Dy3a61yR7MkBrfX4MLp9pob051Cj5f5qvqLVt8vNbV8yJTRJCUWWW0EUwYla-Rpjk365JRR0rq7Hh-SQwhFOFxwAxmhq-tY5QQZbCyBiFDp-D-uHcX_O9gY5JdE7VtW9VbP0SJiaBcUFQWI304Uh18jME6uQtNp8JeYiQPCUosTwmO9u5oVeys3Poh9OMXMudlwTn9A2sGano</recordid><startdate>20100301</startdate><enddate>20100301</enddate><creator>Kim, C. I</creator><creator>Schiavone, P</creator><creator>Ru, C.-Q</creator><general>ASME</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>KR7</scope></search><sort><creationdate>20100301</creationdate><title>The Effects of Surface Elasticity on an Elastic Solid With Mode-III Crack: Complete Solution</title><author>Kim, C. I ; Schiavone, P ; Ru, C.-Q</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a282t-eadcd858da4b0c346db953f293fe90392d223013465d15d6bef5322ad1aed00d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Complex variables</topic><topic>Elastic deformation</topic><topic>Elasticity</topic><topic>Exact solutions</topic><topic>Fracture mechanics</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Shear deformation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kim, C. I</creatorcontrib><creatorcontrib>Schiavone, P</creatorcontrib><creatorcontrib>Ru, C.-Q</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>Journal of applied mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kim, C. I</au><au>Schiavone, P</au><au>Ru, C.-Q</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Effects of Surface Elasticity on an Elastic Solid With Mode-III Crack: Complete Solution</atitle><jtitle>Journal of applied mechanics</jtitle><stitle>J. Appl. Mech</stitle><date>2010-03-01</date><risdate>2010</risdate><volume>77</volume><issue>2</issue><spage>021011 (7)</spage><epage>021011 (7)</epage><pages>021011 (7)-021011 (7)</pages><issn>0021-8936</issn><eissn>1528-9036</eissn><abstract>We examined the effects of surface elasticity in a classical mode-III crack problem arising in the antiplane shear deformations of a linearly elastic solid. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. Complex variable methods are used to obtain an exact solution valid everywhere in the domain of interest (including at the crack tip) by reducing the problem to a Cauchy singular integro-differential equation of the first order. Finally, we adapt classical collocation methods to obtain numerical solutions, which demonstrate several interesting phenomena in the case when the solid incorporates a traction-free crack face and is subjected to uniform remote loading. In particular, we note that, in contrast to the classical result from linear elastic fracture mechanics, the stresses at the (sharp) crack tip remain finite.</abstract><pub>ASME</pub><doi>10.1115/1.3177000</doi></addata></record> |
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subjects | Complex variables Elastic deformation Elasticity Exact solutions Fracture mechanics Mathematical analysis Mathematical models Shear deformation |
title | The Effects of Surface Elasticity on an Elastic Solid With Mode-III Crack: Complete Solution |
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