<?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-01701624</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="2026-05-18T05:04:09+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Modeling longitudinal wave propagation in nonlinear viscoelastic solids with softening</title>
            <author role="aut">
              <persName>
                <forename type="first">Harold</forename>
                <surname>Berjamin</surname>
              </persName>
              <email type="md5">852d40361e70605e4e537a6b2632121a</email>
              <email type="domain">universityofgalway.ie</email>
              <idno type="idhal" notation="string">harold-berjamin</idno>
              <idno type="idhal" notation="numeric">171354</idno>
              <idno type="halauthorid" notation="string">27579-171354</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/B-1073-2017</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-6637-8485</idno>
              <idno type="IDREF">https://www.idref.fr/236847007</idno>
              <idno type="ARXIV">https://arxiv.org/a/berjamin_h_1</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=rbAjLQYAAAAJ</idno>
              <idno type="VIAF">https://viaf.org/viaf/258156563615623242064</idno>
              <affiliation ref="#struct-388661"/>
              <affiliation ref="#struct-136844"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Bruno</forename>
                <surname>Lombard</surname>
              </persName>
              <email type="md5">7297d2c66b4a3e887d6bf9b028d53d8e</email>
              <email type="domain">lma.cnrs-mrs.fr</email>
              <idno type="idhal" notation="numeric">830034</idno>
              <idno type="halauthorid" notation="string">104987-830034</idno>
              <affiliation ref="#struct-388661"/>
              <affiliation ref="#struct-136844"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Guillaume</forename>
                <surname>Chiavassa</surname>
              </persName>
              <email type="md5">d1aa67b11837e4a0a625b0770467b4fd</email>
              <email type="domain">ec-marseille.fr</email>
              <idno type="idhal" notation="numeric">939063</idno>
              <idno type="halauthorid" notation="string">246975-939063</idno>
              <affiliation ref="#struct-199963"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Nicolas</forename>
                <surname>Favrie</surname>
              </persName>
              <email type="md5">3c27a8f59e01059f21137fbc19484983</email>
              <email type="domain">univ-amu.fr</email>
              <idno type="idhal" notation="string">nicolas-favrie</idno>
              <idno type="idhal" notation="numeric">949729</idno>
              <idno type="halauthorid" notation="string">470222-949729</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-3788-2927</idno>
              <affiliation ref="#struct-949"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Bruno</forename>
                <surname>Lombard</surname>
              </persName>
              <email type="md5">7297d2c66b4a3e887d6bf9b028d53d8e</email>
              <email type="domain">lma.cnrs-mrs.fr</email>
            </editor>
            <funder ref="#projanr-42558"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2018-02-05 22:41:35</date>
              <date type="whenModified">2025-04-30 15:56:27</date>
              <date type="whenReleased">2018-02-14 11:24:53</date>
              <date type="whenProduced">2018</date>
              <date type="whenEndEmbargoed">2018-02-05</date>
              <ref type="file" target="https://hal.science/hal-01701624v1/document">
                <date notBefore="2018-02-05"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-01701624v1/file/Ijss1.pdf" id="file-1701624-1749459">
                <date notBefore="2018-02-05"/>
              </ref>
              <ref type="externalLink" target="https://hal.archives-ouvertes.fr/hal-01701624/file/Ijss1.pdf"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="102242">
                <persName>
                  <forename>Bruno</forename>
                  <surname>Lombard</surname>
                </persName>
                <email type="md5">7297d2c66b4a3e887d6bf9b028d53d8e</email>
                <email type="domain">lma.cnrs-mrs.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01701624</idno>
            <idno type="halUri">https://hal.science/hal-01701624</idno>
            <idno type="halBibtex">berjamin:hal-01701624</idno>
            <idno type="halRefHtml">&lt;i&gt;International Journal of Solids and Structures&lt;/i&gt;, 2018, 141-142, pp.35-44. &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.ijsolstr.2018.02.009"&gt;&amp;#x27E8;10.1016/j.ijsolstr.2018.02.009&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">International Journal of Solids and Structures, 2018, 141-142, pp.35-44. &amp;#x27E8;10.1016/j.ijsolstr.2018.02.009&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1701624-1749459"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="LMA_UPR7051">Laboratoire de Mécanique et d'Acoustique</idno>
            <idno type="stamp" n="EC-MARSEILLE">Ecole Centrale de Marseille</idno>
            <idno type="stamp" n="M2P2">Mécanique Modélisation et Procédés Propres</idno>
            <idno type="stamp" n="IUSTI">Institut Universitaire des Systèmes Thermiques Industriels</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="PEIRESC">Fédération Fabri de Peiresc</idno>
            <idno type="stamp" n="IMI-AMU">Institut Mécanique et Ingénierie</idno>
            <idno type="stamp" n="CENTRALE-MEDITERRANEE">Centrale Méditerranée</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">Modeling longitudinal wave propagation in nonlinear viscoelastic solids with softening</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Harold</forename>
                    <surname>Berjamin</surname>
                  </persName>
                  <email type="md5">852d40361e70605e4e537a6b2632121a</email>
                  <email type="domain">universityofgalway.ie</email>
                  <idno type="idhal" notation="string">harold-berjamin</idno>
                  <idno type="idhal" notation="numeric">171354</idno>
                  <idno type="halauthorid" notation="string">27579-171354</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/B-1073-2017</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-6637-8485</idno>
                  <idno type="IDREF">https://www.idref.fr/236847007</idno>
                  <idno type="ARXIV">https://arxiv.org/a/berjamin_h_1</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=rbAjLQYAAAAJ</idno>
                  <idno type="VIAF">https://viaf.org/viaf/258156563615623242064</idno>
                  <affiliation ref="#struct-388661"/>
                  <affiliation ref="#struct-136844"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Bruno</forename>
                    <surname>Lombard</surname>
                  </persName>
                  <email type="md5">7297d2c66b4a3e887d6bf9b028d53d8e</email>
                  <email type="domain">lma.cnrs-mrs.fr</email>
                  <idno type="idhal" notation="numeric">830034</idno>
                  <idno type="halauthorid" notation="string">104987-830034</idno>
                  <affiliation ref="#struct-388661"/>
                  <affiliation ref="#struct-136844"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Guillaume</forename>
                    <surname>Chiavassa</surname>
                  </persName>
                  <email type="md5">d1aa67b11837e4a0a625b0770467b4fd</email>
                  <email type="domain">ec-marseille.fr</email>
                  <idno type="idhal" notation="numeric">939063</idno>
                  <idno type="halauthorid" notation="string">246975-939063</idno>
                  <affiliation ref="#struct-199963"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Nicolas</forename>
                    <surname>Favrie</surname>
                  </persName>
                  <email type="md5">3c27a8f59e01059f21137fbc19484983</email>
                  <email type="domain">univ-amu.fr</email>
                  <idno type="idhal" notation="string">nicolas-favrie</idno>
                  <idno type="idhal" notation="numeric">949729</idno>
                  <idno type="halauthorid" notation="string">470222-949729</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-3788-2927</idno>
                  <affiliation ref="#struct-949"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">14714</idno>
                <idno type="issn">0020-7683</idno>
                <title level="j">International Journal of Solids and Structures</title>
                <imprint>
                  <publisher>Elsevier</publisher>
                  <biblScope unit="volume">141-142</biblScope>
                  <biblScope unit="pp">35-44</biblScope>
                  <date type="datePub">2018</date>
                  <date type="dateEpub">2018</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1016/j.ijsolstr.2018.02.009</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">viscoelasticity</term>
                <term xml:lang="en">Nonlinear acoustics</term>
                <term xml:lang="en">softening</term>
              </keywords>
              <classCode scheme="classification">PACS: 43.25.+y, 43.25.Dc, 02.70.Bf</classCode>
              <classCode scheme="halDomain" n="spi.acou">Engineering Sciences [physics]/Acoustics [physics.class-ph]</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>A model for longitudinal wave propagation in rocks and concrete is presented. Such materials are known to soften under a dynamic loading, i.e. the speed of sound diminishes with forcing amplitudes. Also known as slow dynamics, the softening of the material is not instantaneous. Based on continuum mechanics with internal variables of state, a new formulation is proposed, which accounts for nonlinear Zener viscoelasticity and softening. A finite-volume method using Roe linearization is developed for the system of partial differential equations so-obtained. The method is used to carry out resonance simulations, and its performance is assessed in the linear viscoelastic case. Qualitative agreement with experimental results of nonlinear ultrasound spectroscopy (NRUS) and dynamic acousto-elastic testing (DAET) is obtained.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-388661" status="VALID">
          <orgName>Ondes et Imagerie</orgName>
          <orgName type="acronym">O&amp;I</orgName>
          <desc>
            <address>
              <addrLine>Laboratoire de Mécanique et d’AcoustiqueCNRS - UMR 70314 impasse Nikola Tesla13453 Marseille Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lma.cnrs-mrs.fr/spip/spip.php?page=team&amp;id_mot=16</ref>
          </desc>
          <listRelation>
            <relation active="#struct-136844" type="direct"/>
            <relation name="UMR7031" active="#struct-198056" type="indirect"/>
            <relation name="UMR7031" active="#struct-300415" type="indirect"/>
            <relation name="UMR7031" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-136844" status="VALID">
          <idno type="IdRef">026390604</idno>
          <idno type="RNSR">199617659S</idno>
          <idno type="ROR">https://ror.org/03787ar02</idno>
          <orgName>Laboratoire de Mécanique et d'Acoustique [Marseille]</orgName>
          <orgName type="acronym">LMA</orgName>
          <date type="start">1941-01-01</date>
          <desc>
            <address>
              <addrLine>4 impasse Nikola TeslaCS 4000613453 Marseille Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lma.cnrs-mrs.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR7031" active="#struct-198056" type="direct"/>
            <relation name="UMR7031" active="#struct-300415" type="direct"/>
            <relation name="UMR7031" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-199963" status="VALID">
          <idno type="IdRef">184417139</idno>
          <idno type="RNSR">201220330A</idno>
          <idno type="ROR">01vrxpt40</idno>
          <orgName>Laboratoire de Mécanique, Modélisation et Procédés Propres</orgName>
          <orgName type="acronym">M2P2</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Technopôle de Château-Gombert, 38, rue Frédéric Joliot-Curie 13 451 Marseille cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.m2p2.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-198056" type="direct"/>
            <relation active="#struct-300415" type="direct"/>
            <relation name="UMR7340" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-949" status="VALID">
          <idno type="IdRef">035279028</idno>
          <idno type="RNSR">201220275R</idno>
          <idno type="ROR">04bgbbh33</idno>
          <orgName>Institut universitaire des systèmes thermiques industriels</orgName>
          <orgName type="acronym">IUSTI</orgName>
          <date type="start">2012</date>
          <desc>
            <address>
              <addrLine>Laboratoire IUSTITechnopôle de Château-Gombert5 rue Enrico Fermi13453 Marseille cedex 13FRANCE</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://iusti.univ-provence.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR7343" active="#struct-198056" type="direct"/>
            <relation name="UMR7343" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-198056" status="VALID">
          <idno type="IdRef">15863621X</idno>
          <idno type="ISNI">0000 0001 2176 4817</idno>
          <idno type="ROR">https://ror.org/035xkbk20</idno>
          <orgName>Aix Marseille Université</orgName>
          <orgName type="acronym">AMU</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Aix-Marseille UniversitéJardins du Pharo58 Boulevard Charles Livon13284 Marseille cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-amu.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300415" status="VALID">
          <idno type="ISNI">0000 0004 1762 2703</idno>
          <idno type="ROR">https://ror.org/040baw385</idno>
          <orgName>École Centrale de Marseille</orgName>
          <orgName type="acronym">ECM</orgName>
          <date type="start">2006-09-27</date>
          <desc>
            <address>
              <addrLine>Pôle de l'étoile - Technopole de Château-Gombert - 38 rue Frédéric Joliot-Curie - 13013 Marseille</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.centrale-marseille.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>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-42558" status="VALID">
          <idno type="anr">ANR-10-LABX-0092</idno>
          <orgName>MEC</orgName>
          <desc>Mechanics and Complexity</desc>
          <date type="start">2010</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>