Time integration of a model for martensite detwinning and reorientation under nonproportional loading using Lagrange multipliers
[Display omitted] The paper presents a consistent integration scheme for a model of shape memory alloys that takes into account the processes of detwinning and reorientation of martensite. Lagrange multipliers are used to account for the saturation condition on the martensitic phase, which expresses...
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| Veröffentlicht in: | International journal of solids and structures 2012-10, Vol.49 (21), p.2951-2961 |
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| container_title | International journal of solids and structures |
| container_volume | 49 |
| creator | Zaki, Wael |
| description | [Display omitted]
The paper presents a consistent integration scheme for a model of shape memory alloys that takes into account the processes of detwinning and reorientation of martensite. Lagrange multipliers are used to account for the saturation condition on the martensitic phase, which expresses the requirement on the inelastic deformation of martensite not to exceed a material-specific value. A detailed procedure for implicit time integration of the constitutive equations is given, including a comprehensive derivation of a closed-form expression for the consistent tangent moduli. The equations are implemented into a commercial finite element software, which is used to simulate the response of martensitic SMA structures to complex loading. The results are shown to agree with experimental data taken from the literature. |
| doi_str_mv | 10.1016/j.ijsolstr.2012.05.038 |
| format | Article |
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The paper presents a consistent integration scheme for a model of shape memory alloys that takes into account the processes of detwinning and reorientation of martensite. Lagrange multipliers are used to account for the saturation condition on the martensitic phase, which expresses the requirement on the inelastic deformation of martensite not to exceed a material-specific value. A detailed procedure for implicit time integration of the constitutive equations is given, including a comprehensive derivation of a closed-form expression for the consistent tangent moduli. The equations are implemented into a commercial finite element software, which is used to simulate the response of martensitic SMA structures to complex loading. The results are shown to agree with experimental data taken from the literature.</description><identifier>ISSN: 0020-7683</identifier><identifier>EISSN: 1879-2146</identifier><identifier>DOI: 10.1016/j.ijsolstr.2012.05.038</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>Constitutive relationships ; Constrained optimization ; Exact solutions ; Lagrange multipliers ; Martensite ; Martensite reorientation ; Mathematical analysis ; Mathematical models ; Nonproportional loading ; Shape memory alloys ; Time integration</subject><ispartof>International journal of solids and structures, 2012-10, Vol.49 (21), p.2951-2961</ispartof><rights>2012 Elsevier Ltd</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c393t-865767cbe14b80298f553e15bbad3bc40e6a45426d8fa397581c92845dc3d6c03</citedby><cites>FETCH-LOGICAL-c393t-865767cbe14b80298f553e15bbad3bc40e6a45426d8fa397581c92845dc3d6c03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.ijsolstr.2012.05.038$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3536,27903,27904,45974</link.rule.ids></links><search><creatorcontrib>Zaki, Wael</creatorcontrib><title>Time integration of a model for martensite detwinning and reorientation under nonproportional loading using Lagrange multipliers</title><title>International journal of solids and structures</title><description>[Display omitted]
The paper presents a consistent integration scheme for a model of shape memory alloys that takes into account the processes of detwinning and reorientation of martensite. Lagrange multipliers are used to account for the saturation condition on the martensitic phase, which expresses the requirement on the inelastic deformation of martensite not to exceed a material-specific value. A detailed procedure for implicit time integration of the constitutive equations is given, including a comprehensive derivation of a closed-form expression for the consistent tangent moduli. The equations are implemented into a commercial finite element software, which is used to simulate the response of martensitic SMA structures to complex loading. The results are shown to agree with experimental data taken from the literature.</description><subject>Constitutive relationships</subject><subject>Constrained optimization</subject><subject>Exact solutions</subject><subject>Lagrange multipliers</subject><subject>Martensite</subject><subject>Martensite reorientation</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Nonproportional loading</subject><subject>Shape memory alloys</subject><subject>Time integration</subject><issn>0020-7683</issn><issn>1879-2146</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNqFkE9v3CAQxVGVSN0k_QoVx17sgDEY31JF_RNppVySM8IwXrHCsAHcqrd89GJtcs5lRhq9NzPvh9BXSlpKqLg9tu6Yo88ltR2hXUt4S5j8hHZUDmPT0V5coB0hHWkGIdlndJXzkRDSs5Hs0OuTWwC7UOCQdHEx4DhjjZdoweM5JrzoVCBkVwBbKH9dCC4csA4WJ4jJQShn2xosJBxiOKV4immbaY991HbTr3mre12PhAPgZfXFnbyDlG_Q5ax9hi9v_Ro9__zxdP-72T_-erj_vm8MG1lppOCDGMwEtJ8k6UY5c86A8mnSlk2mJyB0z_tOWDlrNg5cUjN2sufWMCsMYdfo23lv_e9lhVzU4rIB73WAuGZFKROM96NkVSrOUpNizglmdUqucvinKFEbcnVU78jVhlwRriryarw7G6EG-VPTqWwqIQPWJTBF2eg-WvEfImGRyA</recordid><startdate>20121015</startdate><enddate>20121015</enddate><creator>Zaki, Wael</creator><general>Elsevier Ltd</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>7TB</scope><scope>8BQ</scope><scope>8FD</scope><scope>FR3</scope><scope>JG9</scope><scope>KR7</scope></search><sort><creationdate>20121015</creationdate><title>Time integration of a model for martensite detwinning and reorientation under nonproportional loading using Lagrange multipliers</title><author>Zaki, Wael</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c393t-865767cbe14b80298f553e15bbad3bc40e6a45426d8fa397581c92845dc3d6c03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Constitutive relationships</topic><topic>Constrained optimization</topic><topic>Exact solutions</topic><topic>Lagrange multipliers</topic><topic>Martensite</topic><topic>Martensite reorientation</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Nonproportional loading</topic><topic>Shape memory alloys</topic><topic>Time integration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zaki, Wael</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Materials Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>International journal of solids and structures</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zaki, Wael</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Time integration of a model for martensite detwinning and reorientation under nonproportional loading using Lagrange multipliers</atitle><jtitle>International journal of solids and structures</jtitle><date>2012-10-15</date><risdate>2012</risdate><volume>49</volume><issue>21</issue><spage>2951</spage><epage>2961</epage><pages>2951-2961</pages><issn>0020-7683</issn><eissn>1879-2146</eissn><abstract>[Display omitted]
The paper presents a consistent integration scheme for a model of shape memory alloys that takes into account the processes of detwinning and reorientation of martensite. Lagrange multipliers are used to account for the saturation condition on the martensitic phase, which expresses the requirement on the inelastic deformation of martensite not to exceed a material-specific value. A detailed procedure for implicit time integration of the constitutive equations is given, including a comprehensive derivation of a closed-form expression for the consistent tangent moduli. The equations are implemented into a commercial finite element software, which is used to simulate the response of martensitic SMA structures to complex loading. The results are shown to agree with experimental data taken from the literature.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.ijsolstr.2012.05.038</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | International journal of solids and structures, 2012-10, Vol.49 (21), p.2951-2961 |
| issn | 0020-7683 1879-2146 |
| language | eng |
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| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Constitutive relationships Constrained optimization Exact solutions Lagrange multipliers Martensite Martensite reorientation Mathematical analysis Mathematical models Nonproportional loading Shape memory alloys Time integration |
| title | Time integration of a model for martensite detwinning and reorientation under nonproportional loading using Lagrange multipliers |
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