A local strain-based implementation strategy for the extended peridynamic model with bond rotation
The conventional grid displacements-based implementation of the extended peridynamic model with bond rotation may give rise to some difficulty in predicting non-uniform deformation field, essentially due to the existence of local rigid rotation in solid. This paper presents a novel alternative local...
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Veröffentlicht in: | Computer methods in applied mechanics and engineering 2020-01, Vol.358, p.112625, Article 112625 |
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creator | Li, Wei-Jian Zhu, Qi-Zhi Ni, Tao |
description | The conventional grid displacements-based implementation of the extended peridynamic model with bond rotation may give rise to some difficulty in predicting non-uniform deformation field, essentially due to the existence of local rigid rotation in solid. This paper presents a novel alternative local strain-based implementation technique for handling the numerical issue. The key is to formulate the relative displacement between particles in terms of the strain tensor approximated locally rather than the direct use of displacements at peridynamic particles. It is critically proved that bond stretch is independent of the rigid rotation tensor. Local strain is thus required only for approximating local shear deformation. The model is currently implemented for static problems in a hybrid manner and in a finite element/peridynamics coupling framework, the latter allowing direct and correct imposition of boundary conditions. To illustrate the performance of the proposed method in numerical accuracy and computational efficiency, various examples are performed with varying Poisson’s ratio and comparisons with the results from finite element analysis are presented.
•A novel hybrid implementation method for the peridynamic model with bond rotation.•Shear displacement measured via local strain to eliminate the influence of rigid rotation.•FEM/PD coupling for direct and correct imposition of boundary conditions.•Validation and simulation with a large range of the values of Poisson’s ratio. |
doi_str_mv | 10.1016/j.cma.2019.112625 |
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•A novel hybrid implementation method for the peridynamic model with bond rotation.•Shear displacement measured via local strain to eliminate the influence of rigid rotation.•FEM/PD coupling for direct and correct imposition of boundary conditions.•Validation and simulation with a large range of the values of Poisson’s ratio.</description><identifier>ISSN: 0045-7825</identifier><identifier>EISSN: 1879-2138</identifier><identifier>DOI: 10.1016/j.cma.2019.112625</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Boundary conditions ; Displacement ; Extended peridynamic model (XPDM) ; Finite element method ; Finite element/peridynamic coupling ; Local strain ; Mathematical analysis ; Mathematical models ; Numerical implementation ; Poisson's ratio ; Rotation ; Shear deformation ; Solid materials ; Strain ; Tensors</subject><ispartof>Computer methods in applied mechanics and engineering, 2020-01, Vol.358, p.112625, Article 112625</ispartof><rights>2019 Elsevier B.V.</rights><rights>Copyright Elsevier BV Jan 1, 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-954ec561ce00dc9eb476c60f99dcccbc215ad1bf5df6fa82212c6456853a4c83</citedby><cites>FETCH-LOGICAL-c325t-954ec561ce00dc9eb476c60f99dcccbc215ad1bf5df6fa82212c6456853a4c83</cites><orcidid>0000-0003-2749-4998 ; 0000-0002-8454-8246</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.cma.2019.112625$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Li, Wei-Jian</creatorcontrib><creatorcontrib>Zhu, Qi-Zhi</creatorcontrib><creatorcontrib>Ni, Tao</creatorcontrib><title>A local strain-based implementation strategy for the extended peridynamic model with bond rotation</title><title>Computer methods in applied mechanics and engineering</title><description>The conventional grid displacements-based implementation of the extended peridynamic model with bond rotation may give rise to some difficulty in predicting non-uniform deformation field, essentially due to the existence of local rigid rotation in solid. This paper presents a novel alternative local strain-based implementation technique for handling the numerical issue. The key is to formulate the relative displacement between particles in terms of the strain tensor approximated locally rather than the direct use of displacements at peridynamic particles. It is critically proved that bond stretch is independent of the rigid rotation tensor. Local strain is thus required only for approximating local shear deformation. The model is currently implemented for static problems in a hybrid manner and in a finite element/peridynamics coupling framework, the latter allowing direct and correct imposition of boundary conditions. To illustrate the performance of the proposed method in numerical accuracy and computational efficiency, various examples are performed with varying Poisson’s ratio and comparisons with the results from finite element analysis are presented.
•A novel hybrid implementation method for the peridynamic model with bond rotation.•Shear displacement measured via local strain to eliminate the influence of rigid rotation.•FEM/PD coupling for direct and correct imposition of boundary conditions.•Validation and simulation with a large range of the values of Poisson’s ratio.</description><subject>Boundary conditions</subject><subject>Displacement</subject><subject>Extended peridynamic model (XPDM)</subject><subject>Finite element method</subject><subject>Finite element/peridynamic coupling</subject><subject>Local strain</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Numerical implementation</subject><subject>Poisson's ratio</subject><subject>Rotation</subject><subject>Shear deformation</subject><subject>Solid materials</subject><subject>Strain</subject><subject>Tensors</subject><issn>0045-7825</issn><issn>1879-2138</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE1PwzAMhiMEEmPwA7hF4tySpE3XiNM08SVN4rJ7lDouy9Q2I8mA_Xs6yhlffPD72NZDyC1nOWe8ut_l0JtcMK5yzkUl5BmZ8XqhMsGL-pzMGCtltqiFvCRXMe7YWDUXM9IsaefBdDSmYNyQNSaipa7fd9jjkExyfvidJXw_0tYHmrZI8TvhYMfgHoOzx8H0DmjvLXb0y6UtbfxgafATfk0uWtNFvPnrc7J5etysXrL12_PrarnOoBAyZUqWCLLigIxZUNiUiwoq1iplAaABwaWxvGmlbavW1EJwAVUpq1oWpoS6mJO7ae0--I8DxqR3_hCG8aIWhVALrkStxhSfUhB8jAFbvQ-uN-GoOdMnk3qnR5P6ZFJPJkfmYWJw_P7TYdARHA6A1gWEpK13_9A_s3R9Gw</recordid><startdate>20200101</startdate><enddate>20200101</enddate><creator>Li, Wei-Jian</creator><creator>Zhu, Qi-Zhi</creator><creator>Ni, Tao</creator><general>Elsevier B.V</general><general>Elsevier BV</general><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><orcidid>https://orcid.org/0000-0003-2749-4998</orcidid><orcidid>https://orcid.org/0000-0002-8454-8246</orcidid></search><sort><creationdate>20200101</creationdate><title>A local strain-based implementation strategy for the extended peridynamic model with bond rotation</title><author>Li, Wei-Jian ; Zhu, Qi-Zhi ; Ni, Tao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-954ec561ce00dc9eb476c60f99dcccbc215ad1bf5df6fa82212c6456853a4c83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Boundary conditions</topic><topic>Displacement</topic><topic>Extended peridynamic model (XPDM)</topic><topic>Finite element method</topic><topic>Finite element/peridynamic coupling</topic><topic>Local strain</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Numerical implementation</topic><topic>Poisson's ratio</topic><topic>Rotation</topic><topic>Shear deformation</topic><topic>Solid materials</topic><topic>Strain</topic><topic>Tensors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Wei-Jian</creatorcontrib><creatorcontrib>Zhu, Qi-Zhi</creatorcontrib><creatorcontrib>Ni, Tao</creatorcontrib><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>Computer methods in applied mechanics and engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Wei-Jian</au><au>Zhu, Qi-Zhi</au><au>Ni, Tao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A local strain-based implementation strategy for the extended peridynamic model with bond rotation</atitle><jtitle>Computer methods in applied mechanics and engineering</jtitle><date>2020-01-01</date><risdate>2020</risdate><volume>358</volume><spage>112625</spage><pages>112625-</pages><artnum>112625</artnum><issn>0045-7825</issn><eissn>1879-2138</eissn><abstract>The conventional grid displacements-based implementation of the extended peridynamic model with bond rotation may give rise to some difficulty in predicting non-uniform deformation field, essentially due to the existence of local rigid rotation in solid. This paper presents a novel alternative local strain-based implementation technique for handling the numerical issue. The key is to formulate the relative displacement between particles in terms of the strain tensor approximated locally rather than the direct use of displacements at peridynamic particles. It is critically proved that bond stretch is independent of the rigid rotation tensor. Local strain is thus required only for approximating local shear deformation. The model is currently implemented for static problems in a hybrid manner and in a finite element/peridynamics coupling framework, the latter allowing direct and correct imposition of boundary conditions. To illustrate the performance of the proposed method in numerical accuracy and computational efficiency, various examples are performed with varying Poisson’s ratio and comparisons with the results from finite element analysis are presented.
•A novel hybrid implementation method for the peridynamic model with bond rotation.•Shear displacement measured via local strain to eliminate the influence of rigid rotation.•FEM/PD coupling for direct and correct imposition of boundary conditions.•Validation and simulation with a large range of the values of Poisson’s ratio.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cma.2019.112625</doi><orcidid>https://orcid.org/0000-0003-2749-4998</orcidid><orcidid>https://orcid.org/0000-0002-8454-8246</orcidid></addata></record> |
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subjects | Boundary conditions Displacement Extended peridynamic model (XPDM) Finite element method Finite element/peridynamic coupling Local strain Mathematical analysis Mathematical models Numerical implementation Poisson's ratio Rotation Shear deformation Solid materials Strain Tensors |
title | A local strain-based implementation strategy for the extended peridynamic model with bond rotation |
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