Consistent tangent operators for implicit non-local models of integral type
•Consistent linearisation of non-local implicit models of the integral type is discussed.•Closed-form analytical expressions are derived for a J2 plasticity and a Lemaitre-based non-local damage models.•The structure of the consistent tangent operators is discussed and the corresponding assembly pro...
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| Veröffentlicht in: | Computers & structures 2014-08, Vol.141, p.59-73 |
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| container_title | Computers & structures |
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| creator | Andrade, F.X.C. Andrade Pires, F.M. Cesar de Sa, J.M.A. |
| description | •Consistent linearisation of non-local implicit models of the integral type is discussed.•Closed-form analytical expressions are derived for a J2 plasticity and a Lemaitre-based non-local damage models.•The structure of the consistent tangent operators is discussed and the corresponding assembly procedure is described.•Numerical examples demonstrate that the quadratic rate of convergence of the Newton-Raphson method is successfully achieved.
This work is concerned with the consistent linearisation of non-local models of the integral type whenever the non-local variable is an implicit function of the other constitutive variables. The general framework for the derivation of consistent non-local tangent operators is initially presented for elasto-plastic materials. Then, closed-form analytical expressions are established for a J2 hybrid local/non-local plasticity model and the Lemaitre-based non-local model. The structure of the consistent tangent operators is discussed and the corresponding assembly procedure is described. The numerical results show the efficiency of the approach and demonstrate that quadratic rates of convergence are successfully achieved. |
| doi_str_mv | 10.1016/j.compstruc.2014.05.007 |
| format | Article |
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This work is concerned with the consistent linearisation of non-local models of the integral type whenever the non-local variable is an implicit function of the other constitutive variables. The general framework for the derivation of consistent non-local tangent operators is initially presented for elasto-plastic materials. Then, closed-form analytical expressions are established for a J2 hybrid local/non-local plasticity model and the Lemaitre-based non-local model. The structure of the consistent tangent operators is discussed and the corresponding assembly procedure is described. The numerical results show the efficiency of the approach and demonstrate that quadratic rates of convergence are successfully achieved.</description><identifier>ISSN: 0045-7949</identifier><identifier>EISSN: 1879-2243</identifier><identifier>DOI: 10.1016/j.compstruc.2014.05.007</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>Consistent tangent operator ; Convergence ; Derivation ; Exact solutions ; Integrals ; Mathematical analysis ; Mathematical models ; Newton–Raphson method ; Non-local formulation ; Operators ; Tangents</subject><ispartof>Computers & structures, 2014-08, Vol.141, p.59-73</ispartof><rights>2014 Elsevier Ltd</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c381t-543860bcb0c56f3eac57cf6e6065ed1ba3dd24357d6816b1a8d0b254de7569733</citedby><cites>FETCH-LOGICAL-c381t-543860bcb0c56f3eac57cf6e6065ed1ba3dd24357d6816b1a8d0b254de7569733</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0045794914001217$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27903,27904,65308</link.rule.ids></links><search><creatorcontrib>Andrade, F.X.C.</creatorcontrib><creatorcontrib>Andrade Pires, F.M.</creatorcontrib><creatorcontrib>Cesar de Sa, J.M.A.</creatorcontrib><title>Consistent tangent operators for implicit non-local models of integral type</title><title>Computers & structures</title><description>•Consistent linearisation of non-local implicit models of the integral type is discussed.•Closed-form analytical expressions are derived for a J2 plasticity and a Lemaitre-based non-local damage models.•The structure of the consistent tangent operators is discussed and the corresponding assembly procedure is described.•Numerical examples demonstrate that the quadratic rate of convergence of the Newton-Raphson method is successfully achieved.
This work is concerned with the consistent linearisation of non-local models of the integral type whenever the non-local variable is an implicit function of the other constitutive variables. The general framework for the derivation of consistent non-local tangent operators is initially presented for elasto-plastic materials. Then, closed-form analytical expressions are established for a J2 hybrid local/non-local plasticity model and the Lemaitre-based non-local model. The structure of the consistent tangent operators is discussed and the corresponding assembly procedure is described. The numerical results show the efficiency of the approach and demonstrate that quadratic rates of convergence are successfully achieved.</description><subject>Consistent tangent operator</subject><subject>Convergence</subject><subject>Derivation</subject><subject>Exact solutions</subject><subject>Integrals</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Newton–Raphson method</subject><subject>Non-local formulation</subject><subject>Operators</subject><subject>Tangents</subject><issn>0045-7949</issn><issn>1879-2243</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNqNkEtLxDAUhYMoOI7-Brt003rTvNqlDL5QcKPrkCa3kqFtapIR_Pd2GHGrqwOXcz4uHyGXFCoKVF5vKxvGOeW4s1UNlFcgKgB1RFa0UW1Z15wdkxUAF6VqeXtKzlLaAoDkACvytAlT8injlItspvd9hhmjySGmog-x8OM8eOtzMYWpHII1QzEGh0MqQl_4KeN7XE75a8ZzctKbIeHFT67J293t6-ahfH65f9zcPJeWNTSXgrNGQmc7sEL2DI0VyvYSJUiBjnaGObc8LZSTDZUdNY2DrhbcoRKyVYytydWBO8fwscOU9eiTxWEwE4Zd0lQq1TaMAv9HtQZgii_YNVGHqo0hpYi9nqMfTfzSFPTetN7qX9N6b1qD0IvpZXlzWC5S8NNj1Ml6nCw6H9Fm7YL_k_ENUcmMRg</recordid><startdate>20140801</startdate><enddate>20140801</enddate><creator>Andrade, F.X.C.</creator><creator>Andrade Pires, F.M.</creator><creator>Cesar de Sa, J.M.A.</creator><general>Elsevier Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</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>20140801</creationdate><title>Consistent tangent operators for implicit non-local models of integral type</title><author>Andrade, F.X.C. ; Andrade Pires, F.M. ; Cesar de Sa, J.M.A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c381t-543860bcb0c56f3eac57cf6e6065ed1ba3dd24357d6816b1a8d0b254de7569733</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Consistent tangent operator</topic><topic>Convergence</topic><topic>Derivation</topic><topic>Exact solutions</topic><topic>Integrals</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Newton–Raphson method</topic><topic>Non-local formulation</topic><topic>Operators</topic><topic>Tangents</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Andrade, F.X.C.</creatorcontrib><creatorcontrib>Andrade Pires, F.M.</creatorcontrib><creatorcontrib>Cesar de Sa, J.M.A.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems 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>Computers & structures</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Andrade, F.X.C.</au><au>Andrade Pires, F.M.</au><au>Cesar de Sa, J.M.A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Consistent tangent operators for implicit non-local models of integral type</atitle><jtitle>Computers & structures</jtitle><date>2014-08-01</date><risdate>2014</risdate><volume>141</volume><spage>59</spage><epage>73</epage><pages>59-73</pages><issn>0045-7949</issn><eissn>1879-2243</eissn><abstract>•Consistent linearisation of non-local implicit models of the integral type is discussed.•Closed-form analytical expressions are derived for a J2 plasticity and a Lemaitre-based non-local damage models.•The structure of the consistent tangent operators is discussed and the corresponding assembly procedure is described.•Numerical examples demonstrate that the quadratic rate of convergence of the Newton-Raphson method is successfully achieved.
This work is concerned with the consistent linearisation of non-local models of the integral type whenever the non-local variable is an implicit function of the other constitutive variables. The general framework for the derivation of consistent non-local tangent operators is initially presented for elasto-plastic materials. Then, closed-form analytical expressions are established for a J2 hybrid local/non-local plasticity model and the Lemaitre-based non-local model. The structure of the consistent tangent operators is discussed and the corresponding assembly procedure is described. The numerical results show the efficiency of the approach and demonstrate that quadratic rates of convergence are successfully achieved.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.compstruc.2014.05.007</doi><tpages>15</tpages></addata></record> |
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| source | Elsevier ScienceDirect Journals |
| subjects | Consistent tangent operator Convergence Derivation Exact solutions Integrals Mathematical analysis Mathematical models Newton–Raphson method Non-local formulation Operators Tangents |
| title | Consistent tangent operators for implicit non-local models of integral type |
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