A transition scheme from diffusive to discrete crack topologies at finite strain during the course of a staggered iterative procedure
This study presents a novel transition scheme that can trace an actual crack path as closely as possible and stably update its explicit crack tip even in a large deformation regime. The crack initiation and propagation processes are determined from an energy minimization problem with respect to the...
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Veröffentlicht in: | International journal for numerical methods in engineering 2023-03, Vol.124 (6), p.1405-1433 |
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creator | Han, Jike Shintaku, Yuichi Moriguchi, Shuji Terada, Kenjiro |
description | This study presents a novel transition scheme that can trace an actual crack path as closely as possible and stably update its explicit crack tip even in a large deformation regime. The crack initiation and propagation processes are determined from an energy minimization problem with respect to the displacement field and crack phase‐field, and the predicted path represented by a diffuse crack topology is replaced by a discrete path by applying the finite cover method. By developing a technique for determining explicit crack tips, the crack topology is updated from diffusive to discrete intermittently during the course of the staggered iterative procedure. Therefore, even a curved crack path that evolves significantly within a single time increment can be explicitly captured. Additionally, to stably update an explicit crack tip within the finite strain framework, we introduce a stabilization technique. Specifically, pseudo‐stiffness is applied to severely damaged elements around the discrete crack path to prevent excessively large deformations, and the corrector of the displacement increment in the global Newton–Raphson iterative procedure is intentionally diminished so that the discrete crack opens in a gradual and stable manner. After describing the individual techniques devised in the proposed scheme for achieving these features based on their algorithmic aspects, we present several representative numerical examples to demonstrate the performance and capability of the developed approach. |
doi_str_mv | 10.1002/nme.7169 |
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The crack initiation and propagation processes are determined from an energy minimization problem with respect to the displacement field and crack phase‐field, and the predicted path represented by a diffuse crack topology is replaced by a discrete path by applying the finite cover method. By developing a technique for determining explicit crack tips, the crack topology is updated from diffusive to discrete intermittently during the course of the staggered iterative procedure. Therefore, even a curved crack path that evolves significantly within a single time increment can be explicitly captured. Additionally, to stably update an explicit crack tip within the finite strain framework, we introduce a stabilization technique. Specifically, pseudo‐stiffness is applied to severely damaged elements around the discrete crack path to prevent excessively large deformations, and the corrector of the displacement increment in the global Newton–Raphson iterative procedure is intentionally diminished so that the discrete crack opens in a gradual and stable manner. After describing the individual techniques devised in the proposed scheme for achieving these features based on their algorithmic aspects, we present several representative numerical examples to demonstrate the performance and capability of the developed approach.</description><identifier>ISSN: 0029-5981</identifier><identifier>EISSN: 1097-0207</identifier><identifier>DOI: 10.1002/nme.7169</identifier><language>eng</language><publisher>Hoboken, USA: John Wiley & Sons, Inc</publisher><subject>Crack initiation ; crack phase‐field ; Crack propagation ; Crack tips ; Deformation ; finite cover method ; finite strain ; Iterative methods ; staggered iterative procedure ; Stiffness ; strong discontinuity ; Topology</subject><ispartof>International journal for numerical methods in engineering, 2023-03, Vol.124 (6), p.1405-1433</ispartof><rights>2022 The Authors. published by John Wiley & Sons Ltd.</rights><rights>2022. 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The crack initiation and propagation processes are determined from an energy minimization problem with respect to the displacement field and crack phase‐field, and the predicted path represented by a diffuse crack topology is replaced by a discrete path by applying the finite cover method. By developing a technique for determining explicit crack tips, the crack topology is updated from diffusive to discrete intermittently during the course of the staggered iterative procedure. Therefore, even a curved crack path that evolves significantly within a single time increment can be explicitly captured. Additionally, to stably update an explicit crack tip within the finite strain framework, we introduce a stabilization technique. Specifically, pseudo‐stiffness is applied to severely damaged elements around the discrete crack path to prevent excessively large deformations, and the corrector of the displacement increment in the global Newton–Raphson iterative procedure is intentionally diminished so that the discrete crack opens in a gradual and stable manner. After describing the individual techniques devised in the proposed scheme for achieving these features based on their algorithmic aspects, we present several representative numerical examples to demonstrate the performance and capability of the developed approach.</description><subject>Crack initiation</subject><subject>crack phase‐field</subject><subject>Crack propagation</subject><subject>Crack tips</subject><subject>Deformation</subject><subject>finite cover method</subject><subject>finite strain</subject><subject>Iterative methods</subject><subject>staggered iterative procedure</subject><subject>Stiffness</subject><subject>strong discontinuity</subject><subject>Topology</subject><issn>0029-5981</issn><issn>1097-0207</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>24P</sourceid><sourceid>WIN</sourceid><recordid>eNp1kMtOwzAQRS0EEqUg8QmW2LBJsZ2nl1XFSyqwgbXlJOPUpYmL7YD6Afw3U8qW1WjmnrkzuoRccjbjjImboYdZyQt5RCacyTJhgpXHZIKSTHJZ8VNyFsKaMc5zlk7I95xGr4dgo3UDDc0KeqDGu5621pgx2E-g0WETGg8RaON1846Trdu4zkKgOlJjB4tSQCM70Hb0duhoXCHsRh-AOkM1qrrrwENLkfU67o233jWAPJyTE6M3AS7-6pS83d2-Lh6S5cv942K-TJo0lzLhZZrXLKuhFrVkooRC6ExqznRViBwlbjgHzUC30kjcqTJeZQAmNRmIQqRTcnXwxcsfI4So1vjigCeVKEshmUwrhtT1gWq8C8GDUVtve-13ijO1D1lhyGofMqLJAf2yG9j9y6nnp9tf_geoin-v</recordid><startdate>20230330</startdate><enddate>20230330</enddate><creator>Han, Jike</creator><creator>Shintaku, Yuichi</creator><creator>Moriguchi, Shuji</creator><creator>Terada, Kenjiro</creator><general>John Wiley & Sons, Inc</general><general>Wiley Subscription Services, Inc</general><scope>24P</scope><scope>WIN</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><orcidid>https://orcid.org/0000-0001-6799-2233</orcidid><orcidid>https://orcid.org/0000-0003-0721-8355</orcidid><orcidid>https://orcid.org/0000-0003-1742-5948</orcidid><orcidid>https://orcid.org/0000-0002-7535-7202</orcidid></search><sort><creationdate>20230330</creationdate><title>A transition scheme from diffusive to discrete crack topologies at finite strain during the course of a staggered iterative procedure</title><author>Han, Jike ; Shintaku, Yuichi ; Moriguchi, Shuji ; Terada, Kenjiro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3599-1735b04beb2b9027e62a49a10a86255b01f11ea0ead9f9c3584184eef3f4e2623</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Crack initiation</topic><topic>crack phase‐field</topic><topic>Crack propagation</topic><topic>Crack tips</topic><topic>Deformation</topic><topic>finite cover method</topic><topic>finite strain</topic><topic>Iterative methods</topic><topic>staggered iterative procedure</topic><topic>Stiffness</topic><topic>strong discontinuity</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Han, Jike</creatorcontrib><creatorcontrib>Shintaku, Yuichi</creatorcontrib><creatorcontrib>Moriguchi, Shuji</creatorcontrib><creatorcontrib>Terada, Kenjiro</creatorcontrib><collection>Wiley Online Library Open Access</collection><collection>Wiley Online Library Free Content</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>Han, Jike</au><au>Shintaku, Yuichi</au><au>Moriguchi, Shuji</au><au>Terada, Kenjiro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A transition scheme from diffusive to discrete crack topologies at finite strain during the course of a staggered iterative procedure</atitle><jtitle>International journal for numerical methods in engineering</jtitle><date>2023-03-30</date><risdate>2023</risdate><volume>124</volume><issue>6</issue><spage>1405</spage><epage>1433</epage><pages>1405-1433</pages><issn>0029-5981</issn><eissn>1097-0207</eissn><abstract>This study presents a novel transition scheme that can trace an actual crack path as closely as possible and stably update its explicit crack tip even in a large deformation regime. 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Specifically, pseudo‐stiffness is applied to severely damaged elements around the discrete crack path to prevent excessively large deformations, and the corrector of the displacement increment in the global Newton–Raphson iterative procedure is intentionally diminished so that the discrete crack opens in a gradual and stable manner. After describing the individual techniques devised in the proposed scheme for achieving these features based on their algorithmic aspects, we present several representative numerical examples to demonstrate the performance and capability of the developed approach.</abstract><cop>Hoboken, USA</cop><pub>John Wiley & Sons, Inc</pub><doi>10.1002/nme.7169</doi><tpages>29</tpages><orcidid>https://orcid.org/0000-0001-6799-2233</orcidid><orcidid>https://orcid.org/0000-0003-0721-8355</orcidid><orcidid>https://orcid.org/0000-0003-1742-5948</orcidid><orcidid>https://orcid.org/0000-0002-7535-7202</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Crack initiation crack phase‐field Crack propagation Crack tips Deformation finite cover method finite strain Iterative methods staggered iterative procedure Stiffness strong discontinuity Topology |
title | A transition scheme from diffusive to discrete crack topologies at finite strain during the course of a staggered iterative procedure |
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