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Mixed analytical–numerical relaxation in finite single-slip crystal plasticity

Antonio Orlando

Continuum Mechanics and Thermodynamics

Swansea University Author: Antonio Orlando

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DOI (Published version): 10.1007/s00161-008-0082-0

Published in: Continuum Mechanics and Thermodynamics
Published: 2008
URI: https://cronfa.swan.ac.uk/Record/cronfa5669
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first_indexed 2013-07-23T11:53:22Z
last_indexed 2018-02-09T04:32:10Z
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fullrecord <?xml version="1.0"?><rfc1807><datestamp>2011-10-01T00:00:00.0000000</datestamp><bib-version>v2</bib-version><id>5669</id><entry>2013-01-21</entry><title>Mixed analytical&#x2013;numerical relaxation in finite single-slip crystal plasticity</title><swanseaauthors><author><sid>f3c1efb651e09fd36c2892468765aa26</sid><firstname>Antonio</firstname><surname>Orlando</surname><name>Antonio Orlando</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2013-01-21</date><abstract/><type>Journal Article</type><journal>Continuum Mechanics and Thermodynamics</journal><volume></volume><journalNumber></journalNumber><paginationStart/><paginationEnd/><publisher/><placeOfPublication/><issnPrint/><issnElectronic/><keywords/><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2008</publishedYear><publishedDate>2008-12-31</publishedDate><doi>10.1007/s00161-008-0082-0</doi><url/><notes>The modeling of the finite elastoplastic behaviour of single crystals with one active slip systemleads to a nonconvex variational problem, whose minimization produces fine structures. The computation ofthe quasiconvex envelope of the energy density involves the solution of a nonconvex optimization problemand faces severe numerical difficulties from the presence of many local minima. In this paper, we consider astandard model problem in two dimensions and, by exploiting analytical relaxation results for limiting casesand the special structure of the problem at hand, we obtain a fast and efficient numerical relaxation algorithm.The effectiveness of our algorithm is demonstrated with numerical examples. The precision of the results isassessed by lower bounds from polyconvexity.</notes><college>COLLEGE NANME</college><CollegeCode>COLLEGE CODE</CollegeCode><institution>Swansea University</institution><apcterm/><lastEdited>2011-10-01T00:00:00.0000000</lastEdited><Created>2013-01-21T06:00:51.0000000</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Engineering and Applied Sciences - Uncategorised</level></path><authors><author><firstname>Antonio</firstname><surname>Orlando</surname><order>1</order></author></authors><documents/><OutputDurs/></rfc1807>
spelling 2011-10-01T00:00:00.0000000 v2 5669 2013-01-21 Mixed analytical–numerical relaxation in finite single-slip crystal plasticity f3c1efb651e09fd36c2892468765aa26 Antonio Orlando Antonio Orlando true false 2013-01-21 Journal Article Continuum Mechanics and Thermodynamics 31 12 2008 2008-12-31 10.1007/s00161-008-0082-0 The modeling of the finite elastoplastic behaviour of single crystals with one active slip systemleads to a nonconvex variational problem, whose minimization produces fine structures. The computation ofthe quasiconvex envelope of the energy density involves the solution of a nonconvex optimization problemand faces severe numerical difficulties from the presence of many local minima. In this paper, we consider astandard model problem in two dimensions and, by exploiting analytical relaxation results for limiting casesand the special structure of the problem at hand, we obtain a fast and efficient numerical relaxation algorithm.The effectiveness of our algorithm is demonstrated with numerical examples. The precision of the results isassessed by lower bounds from polyconvexity. COLLEGE NANME COLLEGE CODE Swansea University 2011-10-01T00:00:00.0000000 2013-01-21T06:00:51.0000000 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Antonio Orlando 1
title Mixed analytical–numerical relaxation in finite single-slip crystal plasticity
spellingShingle Mixed analytical–numerical relaxation in finite single-slip crystal plasticity
Antonio Orlando
title_short Mixed analytical–numerical relaxation in finite single-slip crystal plasticity
title_full Mixed analytical–numerical relaxation in finite single-slip crystal plasticity
title_fullStr Mixed analytical–numerical relaxation in finite single-slip crystal plasticity
title_full_unstemmed Mixed analytical–numerical relaxation in finite single-slip crystal plasticity
title_sort Mixed analytical–numerical relaxation in finite single-slip crystal plasticity
author_id_str_mv f3c1efb651e09fd36c2892468765aa26
author_id_fullname_str_mv f3c1efb651e09fd36c2892468765aa26_***_Antonio Orlando
author Antonio Orlando
author2 Antonio Orlando
format Journal article
container_title Continuum Mechanics and Thermodynamics
publishDate 2008
institution Swansea University
doi_str_mv 10.1007/s00161-008-0082-0
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
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published_date 2008-12-31T03:06:51Z
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