Non‐affine fiber kinematics in arterial mechanics: a continuum micromechanical investigation
There is growing experimental evidence for non‐affine deformations occurring in different types of fibrous soft tissues; meaning that the fiber orientations do not follow the macroscopic deformation gradient. Suitable mathematical modeling of this phenomenon is an open challenge, which we here tackl...
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| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Mechanik 2018-12, Vol.98 (12), p.2101-2121 |
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| creator | Morin, Claire Avril, Stéphane Hellmich, Christian |
| description | There is growing experimental evidence for non‐affine deformations occurring in different types of fibrous soft tissues; meaning that the fiber orientations do not follow the macroscopic deformation gradient. Suitable mathematical modeling of this phenomenon is an open challenge, which we here tackle in the framework of continuum micromechanics. From a rate‐based analogon of Eshelby's inhomogeneity problem, we derive strain and spin concentration tensors relating macroscopic strain rate tensors applied to the boundaries of a Representative Volume Element (RVE), to strain rates and spins within the tissue microstructure, in particular those associated with fiber rotations due to external mechanical loading. After presenting suitable algorithms for integrating the resulting rate‐type governing equations, a first relevance check of the novel modeling approach is undertaken, by comparison of model results to recent experiments performed on the adventitia layer of rabbit carotid tissue.
There is growing experimental evidence for non‐affine deformations occurring in different types of fibrous soft tissues; meaning that the fiber orientations do not follow the macroscopic deformation gradient. Suitable mathematical modeling of this phenomenon is an open challenge, which we here tackle in the framework of continuum micromechanics. From a rate‐based analogon of Eshelby's inhomogeneity problem, we derive strain and spin concentration tensors relating macroscopic strain rate tensors applied to the boundaries of a Representative Volume Element (RVE), to strain rates and spins within the tissue microstructure, in particular those associated with fiber rotations due to external mechanical loading. After presenting suitable algorithms for integrating the resulting rate‐type governing equations, a first relevance check of the novel modeling approach is undertaken, by comparison of model results to recent experiments performed on the adventitia layer of rabbit carotid tissue. |
| doi_str_mv | 10.1002/zamm.201700360 |
| format | Article |
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There is growing experimental evidence for non‐affine deformations occurring in different types of fibrous soft tissues; meaning that the fiber orientations do not follow the macroscopic deformation gradient. Suitable mathematical modeling of this phenomenon is an open challenge, which we here tackle in the framework of continuum micromechanics. From a rate‐based analogon of Eshelby's inhomogeneity problem, we derive strain and spin concentration tensors relating macroscopic strain rate tensors applied to the boundaries of a Representative Volume Element (RVE), to strain rates and spins within the tissue microstructure, in particular those associated with fiber rotations due to external mechanical loading. After presenting suitable algorithms for integrating the resulting rate‐type governing equations, a first relevance check of the novel modeling approach is undertaken, by comparison of model results to recent experiments performed on the adventitia layer of rabbit carotid tissue.</description><identifier>ISSN: 0044-2267</identifier><identifier>EISSN: 1521-4001</identifier><identifier>DOI: 10.1002/zamm.201700360</identifier><language>eng</language><publisher>Weinheim: Wiley Subscription Services, Inc</publisher><subject>Biomechanics ; Deformation ; Inhomogeneity ; Kinematics ; large fiber rotations ; large strain continuum micromechanics ; Mathematical analysis ; Mechanics ; Micromechanics ; Physics ; Soft tissues ; spin concentration tensor ; Strain rate ; Tensors</subject><ispartof>Zeitschrift für angewandte Mathematik und Mechanik, 2018-12, Vol.98 (12), p.2101-2121</ispartof><rights>2018 The Authors. Published by Wiley‐VCH Verlag GmbH & Co. KGaA</rights><rights>2018 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3910-e710bfdbc318522cc2ba92fb7d977020aabab1ea57690dc076c2e6cb06b53af3</citedby><cites>FETCH-LOGICAL-c3910-e710bfdbc318522cc2ba92fb7d977020aabab1ea57690dc076c2e6cb06b53af3</cites><orcidid>0000-0001-9813-3933 ; 0000-0002-8604-7736</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fzamm.201700360$$EPDF$$P50$$Gwiley$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fzamm.201700360$$EHTML$$P50$$Gwiley$$Hfree_for_read</linktohtml><link.rule.ids>230,314,777,781,882,1412,27905,27906,45555,45556</link.rule.ids><backlink>$$Uhttps://hal.science/hal-02004904$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Morin, Claire</creatorcontrib><creatorcontrib>Avril, Stéphane</creatorcontrib><creatorcontrib>Hellmich, Christian</creatorcontrib><title>Non‐affine fiber kinematics in arterial mechanics: a continuum micromechanical investigation</title><title>Zeitschrift für angewandte Mathematik und Mechanik</title><description>There is growing experimental evidence for non‐affine deformations occurring in different types of fibrous soft tissues; meaning that the fiber orientations do not follow the macroscopic deformation gradient. Suitable mathematical modeling of this phenomenon is an open challenge, which we here tackle in the framework of continuum micromechanics. From a rate‐based analogon of Eshelby's inhomogeneity problem, we derive strain and spin concentration tensors relating macroscopic strain rate tensors applied to the boundaries of a Representative Volume Element (RVE), to strain rates and spins within the tissue microstructure, in particular those associated with fiber rotations due to external mechanical loading. After presenting suitable algorithms for integrating the resulting rate‐type governing equations, a first relevance check of the novel modeling approach is undertaken, by comparison of model results to recent experiments performed on the adventitia layer of rabbit carotid tissue.
There is growing experimental evidence for non‐affine deformations occurring in different types of fibrous soft tissues; meaning that the fiber orientations do not follow the macroscopic deformation gradient. Suitable mathematical modeling of this phenomenon is an open challenge, which we here tackle in the framework of continuum micromechanics. From a rate‐based analogon of Eshelby's inhomogeneity problem, we derive strain and spin concentration tensors relating macroscopic strain rate tensors applied to the boundaries of a Representative Volume Element (RVE), to strain rates and spins within the tissue microstructure, in particular those associated with fiber rotations due to external mechanical loading. After presenting suitable algorithms for integrating the resulting rate‐type governing equations, a first relevance check of the novel modeling approach is undertaken, by comparison of model results to recent experiments performed on the adventitia layer of rabbit carotid tissue.</description><subject>Biomechanics</subject><subject>Deformation</subject><subject>Inhomogeneity</subject><subject>Kinematics</subject><subject>large fiber rotations</subject><subject>large strain continuum micromechanics</subject><subject>Mathematical analysis</subject><subject>Mechanics</subject><subject>Micromechanics</subject><subject>Physics</subject><subject>Soft tissues</subject><subject>spin concentration tensor</subject><subject>Strain rate</subject><subject>Tensors</subject><issn>0044-2267</issn><issn>1521-4001</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>24P</sourceid><sourceid>WIN</sourceid><recordid>eNqFkL1OwzAUhS0EEqWwMkdiYki5dv5qtqoCitTCwsSAde061CVxipMUlYlH4Bl5ElwFysh0r46_c3R9CDmlMKAA7OIdy3LAgGYAUQp7pEcTRsMYgO6THkAch4yl2SE5qusleJXTqEee7ir79fGJeW6sDnIjtQte_FpiY1QdGBuga7QzWASlVgu0Xr0MMFCVbYxt2zIojXLV75vHjF3rujHPPqCyx-Qgx6LWJz-zTx6urx7Gk3B6f3M7Hk1DFXEKoc4oyHwuVUSHCWNKMYmc5TKb8ywDBogSJdWYZCmHuYIsVUynSkIqkwjzqE_Ou9gFFmLlTIluIyo0YjKaiq3mMyDmEK-pZ886duWq19afKpZV66y_TjCaxPGQUxp5atBR_nN17XS-i6UgtnWLbd1iV7c38M7wZgq9-YcWj6PZ7M_7DUhThfo</recordid><startdate>201812</startdate><enddate>201812</enddate><creator>Morin, Claire</creator><creator>Avril, Stéphane</creator><creator>Hellmich, Christian</creator><general>Wiley Subscription Services, Inc</general><general>Wiley-VCH Verlag</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><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0001-9813-3933</orcidid><orcidid>https://orcid.org/0000-0002-8604-7736</orcidid></search><sort><creationdate>201812</creationdate><title>Non‐affine fiber kinematics in arterial mechanics: a continuum micromechanical investigation</title><author>Morin, Claire ; Avril, Stéphane ; Hellmich, Christian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3910-e710bfdbc318522cc2ba92fb7d977020aabab1ea57690dc076c2e6cb06b53af3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Biomechanics</topic><topic>Deformation</topic><topic>Inhomogeneity</topic><topic>Kinematics</topic><topic>large fiber rotations</topic><topic>large strain continuum micromechanics</topic><topic>Mathematical analysis</topic><topic>Mechanics</topic><topic>Micromechanics</topic><topic>Physics</topic><topic>Soft tissues</topic><topic>spin concentration tensor</topic><topic>Strain rate</topic><topic>Tensors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Morin, Claire</creatorcontrib><creatorcontrib>Avril, Stéphane</creatorcontrib><creatorcontrib>Hellmich, Christian</creatorcontrib><collection>Wiley Online Library Open Access</collection><collection>Wiley 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><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Zeitschrift für angewandte Mathematik und Mechanik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Morin, Claire</au><au>Avril, Stéphane</au><au>Hellmich, Christian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Non‐affine fiber kinematics in arterial mechanics: a continuum micromechanical investigation</atitle><jtitle>Zeitschrift für angewandte Mathematik und Mechanik</jtitle><date>2018-12</date><risdate>2018</risdate><volume>98</volume><issue>12</issue><spage>2101</spage><epage>2121</epage><pages>2101-2121</pages><issn>0044-2267</issn><eissn>1521-4001</eissn><abstract>There is growing experimental evidence for non‐affine deformations occurring in different types of fibrous soft tissues; meaning that the fiber orientations do not follow the macroscopic deformation gradient. Suitable mathematical modeling of this phenomenon is an open challenge, which we here tackle in the framework of continuum micromechanics. From a rate‐based analogon of Eshelby's inhomogeneity problem, we derive strain and spin concentration tensors relating macroscopic strain rate tensors applied to the boundaries of a Representative Volume Element (RVE), to strain rates and spins within the tissue microstructure, in particular those associated with fiber rotations due to external mechanical loading. After presenting suitable algorithms for integrating the resulting rate‐type governing equations, a first relevance check of the novel modeling approach is undertaken, by comparison of model results to recent experiments performed on the adventitia layer of rabbit carotid tissue.
There is growing experimental evidence for non‐affine deformations occurring in different types of fibrous soft tissues; meaning that the fiber orientations do not follow the macroscopic deformation gradient. Suitable mathematical modeling of this phenomenon is an open challenge, which we here tackle in the framework of continuum micromechanics. From a rate‐based analogon of Eshelby's inhomogeneity problem, we derive strain and spin concentration tensors relating macroscopic strain rate tensors applied to the boundaries of a Representative Volume Element (RVE), to strain rates and spins within the tissue microstructure, in particular those associated with fiber rotations due to external mechanical loading. After presenting suitable algorithms for integrating the resulting rate‐type governing equations, a first relevance check of the novel modeling approach is undertaken, by comparison of model results to recent experiments performed on the adventitia layer of rabbit carotid tissue.</abstract><cop>Weinheim</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/zamm.201700360</doi><tpages>21</tpages><orcidid>https://orcid.org/0000-0001-9813-3933</orcidid><orcidid>https://orcid.org/0000-0002-8604-7736</orcidid><oa>free_for_read</oa></addata></record> |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Biomechanics Deformation Inhomogeneity Kinematics large fiber rotations large strain continuum micromechanics Mathematical analysis Mechanics Micromechanics Physics Soft tissues spin concentration tensor Strain rate Tensors |
| title | Non‐affine fiber kinematics in arterial mechanics: a continuum micromechanical investigation |
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