<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-03311689</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-02T16:14:23+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Homogenized strain gradient remodeling model for trabecular bone microstructures</title>
            <author role="aut">
              <persName>
                <forename type="first">Zineeddine</forename>
                <surname>Louna</surname>
              </persName>
              <idno type="halauthorid">2260427-0</idno>
              <affiliation ref="#struct-92874"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Ibrahim</forename>
                <surname>Goda</surname>
              </persName>
              <idno type="idhal" notation="numeric">780011</idno>
              <idno type="halauthorid" notation="string">1093419-780011</idno>
              <idno type="IDREF">https://www.idref.fr/186391978</idno>
              <affiliation ref="#struct-455400"/>
              <affiliation ref="#struct-189611"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jean-François</forename>
                <surname>Ganghoffer</surname>
              </persName>
              <email type="md5">9a9cd077b4cced6275680cc27a4a4124</email>
              <email type="domain">univ-lorraine.fr</email>
              <idno type="idhal" notation="string">jean-francois-ganghoffer</idno>
              <idno type="idhal" notation="numeric">744089</idno>
              <idno type="halauthorid" notation="string">408886-744089</idno>
              <idno type="IDREF">https://www.idref.fr/074174452</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-7947-0587</idno>
              <affiliation ref="#struct-178323"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Jean-François</forename>
                <surname>GANGHOFFER</surname>
              </persName>
              <email type="md5">9a9cd077b4cced6275680cc27a4a4124</email>
              <email type="domain">univ-lorraine.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2021-08-02 06:50:07</date>
              <date type="whenModified">2026-04-01 03:19:23</date>
              <date type="whenReleased">2021-08-02 06:50:07</date>
              <date type="whenProduced">2019-09</date>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="464326">
                <persName>
                  <forename>Jean-François</forename>
                  <surname>GANGHOFFER</surname>
                </persName>
                <email type="md5">9a9cd077b4cced6275680cc27a4a4124</email>
                <email type="domain">univ-lorraine.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03311689</idno>
            <idno type="halUri">https://hal.univ-lorraine.fr/hal-03311689</idno>
            <idno type="halBibtex">louna:hal-03311689</idno>
            <idno type="halRefHtml">&lt;i&gt;Continuum Mechanics and Thermodynamics&lt;/i&gt;, 2019, 31 (5), pp.1339-1367. &lt;a target="_blank" href="https://dx.doi.org/10.1007/s00161-019-00746-6"&gt;&amp;#x27E8;10.1007/s00161-019-00746-6&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Continuum Mechanics and Thermodynamics, 2019, 31 (5), pp.1339-1367. &amp;#x27E8;10.1007/s00161-019-00746-6&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-TOURS">Université François Rabelais</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="ENSAM">Arts et Métiers Sciences et Technologies</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="LMPT">Laboratoire de Mathématiques et Physique Théorique</idno>
            <idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno>
            <idno type="stamp" n="LEM3-UL">LEM3 - Laboratoire d'étude des Microstructures et de Mécanique des Matériaux</idno>
            <idno type="stamp" n="IDP">Institut Denis Poisson</idno>
            <idno type="stamp" n="TEST3-HALCNRS">TEST3-HALCNRS</idno>
            <idno type="stamp" n="HESAM">Hesam</idno>
            <idno type="stamp" n="HESAM-ENSAM" corresp="HESAM">Ecole Nationale Supérieure d'Arts et Métiers - Hesam</idno>
            <idno type="stamp" n="M4-UL">Pôle scientifique Matière, Matériaux, Métallurgie, Mécanique de l'Université de Lorraine</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Homogenized strain gradient remodeling model for trabecular bone microstructures</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Zineeddine</forename>
                    <surname>Louna</surname>
                  </persName>
                  <idno type="halauthorid">2260427-0</idno>
                  <affiliation ref="#struct-92874"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Ibrahim</forename>
                    <surname>Goda</surname>
                  </persName>
                  <idno type="idhal" notation="numeric">780011</idno>
                  <idno type="halauthorid" notation="string">1093419-780011</idno>
                  <idno type="IDREF">https://www.idref.fr/186391978</idno>
                  <affiliation ref="#struct-455400"/>
                  <affiliation ref="#struct-189611"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jean-François</forename>
                    <surname>Ganghoffer</surname>
                  </persName>
                  <email type="md5">9a9cd077b4cced6275680cc27a4a4124</email>
                  <email type="domain">univ-lorraine.fr</email>
                  <idno type="idhal" notation="string">jean-francois-ganghoffer</idno>
                  <idno type="idhal" notation="numeric">744089</idno>
                  <idno type="halauthorid" notation="string">408886-744089</idno>
                  <idno type="IDREF">https://www.idref.fr/074174452</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-7947-0587</idno>
                  <affiliation ref="#struct-178323"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">12121</idno>
                <idno type="issn">0935-1175</idno>
                <idno type="eissn">1432-0959</idno>
                <title level="j">Continuum Mechanics and Thermodynamics</title>
                <imprint>
                  <publisher>Springer Verlag</publisher>
                  <biblScope unit="volume">31</biblScope>
                  <biblScope unit="issue">5</biblScope>
                  <biblScope unit="pp">1339-1367</biblScope>
                  <date type="datePub">2019-09</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1007/s00161-019-00746-6</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">External and internal remodeling</term>
                <term xml:lang="en">Trabecular bone</term>
                <term xml:lang="en">Surface growth</term>
                <term xml:lang="en">Homogenized strain gradient growth model</term>
                <term xml:lang="en">Micromechanics</term>
              </keywords>
              <classCode scheme="halDomain" n="spi">Engineering Sciences [physics]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Constitutive models for bone remodeling are established from micromechanical analyses at the scale of individual trabeculae defining the representative unit cell (RUC), accounting for both first- and second-order deformation gradients. On the microscale, trabeculae undergo apposition of new bone modeled by a surface growth velocity field driven by a mechanical stimulus identified to the surface divergence of an Eshelby-like tensor. The static and evolutive first and second gradient effective properties of a periodic network of bone trabeculae are evaluated by numerical simulations with controlled imposed first and second displacement gradient rates over the RUC. The formulated effective growth constitutive law at the scale of the homogenized set of trabeculae relates the (average) first and second growth strain rates to the homogenized stress and hyperstress tensors. The constitutive model is identified relying on the framework of TIP (thermodynamics of irreversible processes), adopting a split of the kinematic and static tensors into their deviator and hydrostatic contributions. The obtained results quantify the strength and importance of strain gradient effects on the overall remodeling process.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="institution" xml:id="struct-92874" status="VALID">
          <orgName>Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger]</orgName>
          <orgName type="acronym">USTHB</orgName>
          <desc>
            <address>
              <addrLine>BP 32 EL Alia 16111 Bab Ezzouar,  Alger</addrLine>
              <country key="DZ"/>
            </address>
            <ref type="url">http://www.usthb.dz/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-455400" status="VALID">
          <orgName>Fayoum University</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>Qesm Al Fayoum, Al Fayoum, Fayoum</addrLine>
              <country key="EG"/>
            </address>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-189611" status="OLD">
          <orgName>Laboratoire de Mathématiques et Physique Théorique</orgName>
          <orgName type="acronym">LMPT</orgName>
          <date type="start">2012-01-01</date>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <addrLine>Avenue Monge Parc de Grandmont - 37200 Tours</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lmpt.univ-tours.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300298" type="direct"/>
            <relation name="UMR7350" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-178323" status="VALID">
          <idno type="IdRef">153083956</idno>
          <idno type="ISNI">0000000417588568</idno>
          <idno type="RNSR">201119725X</idno>
          <idno type="IdUnivLorraine">[UL]RTC--</idno>
          <idno type="ROR">https://ror.org/01nyrrx14</idno>
          <orgName>Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux</orgName>
          <orgName type="acronym">LEM3</orgName>
          <date type="start">2011-01-01</date>
          <desc>
            <address>
              <addrLine>F-57070 Metz</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lem3.univ-lorraine.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-413289" type="direct"/>
            <relation name="UMR7239" active="#struct-441569" type="direct"/>
            <relation active="#struct-1003434" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300298" status="VALID">
          <idno type="IdRef">026404478</idno>
          <idno type="ISNI">0000000121608742</idno>
          <idno type="ROR">https://ror.org/02wwzvj46</idno>
          <orgName>Université de Tours</orgName>
          <orgName type="acronym">UT</orgName>
          <date type="start">1970-12-17</date>
          <desc>
            <address>
              <addrLine>60 rue du Plat d'Étain, 37020 Tours cedex 1</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tours.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-413289" status="VALID">
          <idno type="IdRef">157040569</idno>
          <idno type="IdUnivLorraine">[UL]100--</idno>
          <idno type="ROR">https://ror.org/04vfs2w97</idno>
          <orgName>Université de Lorraine</orgName>
          <orgName type="acronym">UL</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-lorraine.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-1003434" status="VALID">
          <idno type="IdRef">02637515X</idno>
          <idno type="ISNI">0000000121946047</idno>
          <idno type="ROR">https://ror.org/018pp1107</idno>
          <idno type="Wikidata">Q2570220</idno>
          <orgName>Arts et Métiers Sciences et Technologies</orgName>
          <date type="start">2020-03-04</date>
          <desc>
            <address>
              <addrLine>151 boulevard de l'Hôpital 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://artsetmetiers.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>