A surface Cauchy-Born model for nanoscale materials
We present an energy‐based continuum model for the analysis of nanoscale materials where surface effects are expected to contribute significantly to the mechanical response. The approach adopts principles utilized in Cauchy–Born constitutive modelling in that the strain energy density of the continu...
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| Veröffentlicht in: | International journal for numerical methods in engineering 2006-12, Vol.68 (10), p.1072-1095 |
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| container_end_page | 1095 |
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| container_title | International journal for numerical methods in engineering |
| container_volume | 68 |
| creator | Park, Harold S. Klein, Patrick A. Wagner, Gregory J. |
| description | We present an energy‐based continuum model for the analysis of nanoscale materials where surface effects are expected to contribute significantly to the mechanical response. The approach adopts principles utilized in Cauchy–Born constitutive modelling in that the strain energy density of the continuum is derived from an underlying crystal structure and interatomic potential. The key to the success of the proposed method lies in decomposing the potential energy of the material into bulk (volumetric) and surface area components. In doing so, the method naturally satisfies a variational formulation in which the bulk volume and surface area contribute independently to the overall system energy. Because the surface area to volume ratio increases as the length scale of a body decreases, the variational form naturally allows the surface energy to become important at small length scales; this feature allows the accurate representation of size and surface effects on the mechanical response. Finite element simulations utilizing the proposed approach are compared against fully atomistic simulations for verification and validation. Copyright © 2006 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/nme.1754 |
| format | Article |
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The approach adopts principles utilized in Cauchy–Born constitutive modelling in that the strain energy density of the continuum is derived from an underlying crystal structure and interatomic potential. The key to the success of the proposed method lies in decomposing the potential energy of the material into bulk (volumetric) and surface area components. In doing so, the method naturally satisfies a variational formulation in which the bulk volume and surface area contribute independently to the overall system energy. Because the surface area to volume ratio increases as the length scale of a body decreases, the variational form naturally allows the surface energy to become important at small length scales; this feature allows the accurate representation of size and surface effects on the mechanical response. Finite element simulations utilizing the proposed approach are compared against fully atomistic simulations for verification and validation. Copyright © 2006 John Wiley & Sons, Ltd.</description><identifier>ISSN: 0029-5981</identifier><identifier>EISSN: 1097-0207</identifier><identifier>DOI: 10.1002/nme.1754</identifier><identifier>CODEN: IJNMBH</identifier><language>eng</language><publisher>Chichester, UK: John Wiley & Sons, Ltd</publisher><subject>Cauchy-Born ; Continuums ; Cross-disciplinary physics: materials science; rheology ; Energy density ; Exact sciences and technology ; Fundamental areas of phenomenology (including applications) ; Materials science ; Mathematical models ; Nanocomposites ; Nanomaterials ; nanoscale materials ; Nanoscale materials and structures: fabrication and characterization ; Nanostructure ; Physics ; Simulation ; Solid mechanics ; Static elasticity (thermoelasticity...) ; Structural and continuum mechanics ; Surface area ; surface elasticity ; surface stress</subject><ispartof>International journal for numerical methods in engineering, 2006-12, Vol.68 (10), p.1072-1095</ispartof><rights>Copyright © 2006 John Wiley & Sons, Ltd.</rights><rights>2006 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c4314-4909a5b6c6c545695a28384d75477921d988717a9bbcbf023e4ef476e048539d3</citedby><cites>FETCH-LOGICAL-c4314-4909a5b6c6c545695a28384d75477921d988717a9bbcbf023e4ef476e048539d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnme.1754$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnme.1754$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18287597$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Park, Harold S.</creatorcontrib><creatorcontrib>Klein, Patrick A.</creatorcontrib><creatorcontrib>Wagner, Gregory J.</creatorcontrib><title>A surface Cauchy-Born model for nanoscale materials</title><title>International journal for numerical methods in engineering</title><addtitle>Int. J. Numer. Meth. Engng</addtitle><description>We present an energy‐based continuum model for the analysis of nanoscale materials where surface effects are expected to contribute significantly to the mechanical response. The approach adopts principles utilized in Cauchy–Born constitutive modelling in that the strain energy density of the continuum is derived from an underlying crystal structure and interatomic potential. The key to the success of the proposed method lies in decomposing the potential energy of the material into bulk (volumetric) and surface area components. In doing so, the method naturally satisfies a variational formulation in which the bulk volume and surface area contribute independently to the overall system energy. Because the surface area to volume ratio increases as the length scale of a body decreases, the variational form naturally allows the surface energy to become important at small length scales; this feature allows the accurate representation of size and surface effects on the mechanical response. Finite element simulations utilizing the proposed approach are compared against fully atomistic simulations for verification and validation. Copyright © 2006 John Wiley & Sons, Ltd.</description><subject>Cauchy-Born</subject><subject>Continuums</subject><subject>Cross-disciplinary physics: materials science; rheology</subject><subject>Energy density</subject><subject>Exact sciences and technology</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Materials science</subject><subject>Mathematical models</subject><subject>Nanocomposites</subject><subject>Nanomaterials</subject><subject>nanoscale materials</subject><subject>Nanoscale materials and structures: fabrication and characterization</subject><subject>Nanostructure</subject><subject>Physics</subject><subject>Simulation</subject><subject>Solid mechanics</subject><subject>Static elasticity (thermoelasticity...)</subject><subject>Structural and continuum mechanics</subject><subject>Surface area</subject><subject>surface elasticity</subject><subject>surface stress</subject><issn>0029-5981</issn><issn>1097-0207</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNp90DtPwzAUBWALgUQpSPyELCAWFz9jeyylFNRSFhCj5TiOCORR7EbQf4-rRnSC6Qz309HVAeAcoxFGiFw3tRthwdkBGGCkBEQEiUMwiCcFuZL4GJyE8I4QxhzRAaDjJHS-MNYlE9PZtw28aX2T1G3uqqRofdKYpg3WVC6pzdr50lThFBwVMdxZn0Pwcjd9ntzDxdPsYTJeQMsoZpAppAzPUptazniquCGSSpbH54RQBOdKSoGFUVlmswIR6pgrmEgdYpJTldMhuNz1rnz72bmw1nUZrKsq07i2C5qolGDKVYRX_0KMJMFSMCT31Po2BO8KvfJlbfwmIr0dUMcB9XbASC_6VrMdoPCmsWXYe0mk4EpEB3fuq6zc5s8-vXyc9r29L8Paff964z90Kqjg-nU507dzgVIsmZ7TH8CcihI</recordid><startdate>20061203</startdate><enddate>20061203</enddate><creator>Park, Harold S.</creator><creator>Klein, Patrick A.</creator><creator>Wagner, Gregory J.</creator><general>John Wiley & Sons, Ltd</general><general>Wiley</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20061203</creationdate><title>A surface Cauchy-Born model for nanoscale materials</title><author>Park, Harold S. ; Klein, Patrick A. ; Wagner, Gregory J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4314-4909a5b6c6c545695a28384d75477921d988717a9bbcbf023e4ef476e048539d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Cauchy-Born</topic><topic>Continuums</topic><topic>Cross-disciplinary physics: materials science; rheology</topic><topic>Energy density</topic><topic>Exact sciences and technology</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Materials science</topic><topic>Mathematical models</topic><topic>Nanocomposites</topic><topic>Nanomaterials</topic><topic>nanoscale materials</topic><topic>Nanoscale materials and structures: fabrication and characterization</topic><topic>Nanostructure</topic><topic>Physics</topic><topic>Simulation</topic><topic>Solid mechanics</topic><topic>Static elasticity (thermoelasticity...)</topic><topic>Structural and continuum mechanics</topic><topic>Surface area</topic><topic>surface elasticity</topic><topic>surface stress</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Park, Harold S.</creatorcontrib><creatorcontrib>Klein, Patrick A.</creatorcontrib><creatorcontrib>Wagner, Gregory J.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>International journal for numerical methods in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Park, Harold S.</au><au>Klein, Patrick A.</au><au>Wagner, Gregory J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A surface Cauchy-Born model for nanoscale materials</atitle><jtitle>International journal for numerical methods in engineering</jtitle><addtitle>Int. J. Numer. Meth. Engng</addtitle><date>2006-12-03</date><risdate>2006</risdate><volume>68</volume><issue>10</issue><spage>1072</spage><epage>1095</epage><pages>1072-1095</pages><issn>0029-5981</issn><eissn>1097-0207</eissn><coden>IJNMBH</coden><abstract>We present an energy‐based continuum model for the analysis of nanoscale materials where surface effects are expected to contribute significantly to the mechanical response. The approach adopts principles utilized in Cauchy–Born constitutive modelling in that the strain energy density of the continuum is derived from an underlying crystal structure and interatomic potential. The key to the success of the proposed method lies in decomposing the potential energy of the material into bulk (volumetric) and surface area components. In doing so, the method naturally satisfies a variational formulation in which the bulk volume and surface area contribute independently to the overall system energy. 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| ispartof | International journal for numerical methods in engineering, 2006-12, Vol.68 (10), p.1072-1095 |
| issn | 0029-5981 1097-0207 |
| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Cauchy-Born Continuums Cross-disciplinary physics: materials science rheology Energy density Exact sciences and technology Fundamental areas of phenomenology (including applications) Materials science Mathematical models Nanocomposites Nanomaterials nanoscale materials Nanoscale materials and structures: fabrication and characterization Nanostructure Physics Simulation Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Surface area surface elasticity surface stress |
| title | A surface Cauchy-Born model for nanoscale materials |
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