<?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-00111620</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="2026-05-25T08:01:57+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">On the stability of strain-rate dependent solids. I-Structural examples</title>
            <author role="aut">
              <persName>
                <forename type="first">Patrick</forename>
                <surname>Massin</surname>
              </persName>
              <email type="md5">1c58b080ec6a8b901e04232d3fbeaefe</email>
              <email type="domain">edf.fr</email>
              <idno type="idhal" notation="string">patrick-massin</idno>
              <idno type="idhal" notation="numeric">5725</idno>
              <idno type="halauthorid" notation="string">556927-5725</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-9196-8639</idno>
              <idno type="IDREF">https://www.idref.fr/115123555</idno>
              <affiliation ref="#struct-302313"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Nicolas</forename>
                <surname>Triantafyllidis</surname>
              </persName>
              <email type="md5">1f99a5059f0f510d3bc89a5b53b046dc</email>
              <email type="domain">polytechnique.edu</email>
              <idno type="idhal" notation="numeric">1037608</idno>
              <idno type="halauthorid" notation="string">172906-1037608</idno>
              <affiliation ref="#struct-24332"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Yves</forename>
                <surname>Leroy</surname>
              </persName>
              <idno type="halauthorid">2527333-0</idno>
              <affiliation ref="#struct-1167"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Mathias</forename>
                <surname>Legrand</surname>
              </persName>
              <email type="md5">ffcb48ad643d28bacba8c1287c93bce7</email>
              <email type="domain">ec-nantes.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2024-04-15 10:18:58</date>
              <date type="whenModified">2025-12-18 16:20:03</date>
              <date type="whenReleased">2024-04-16 15:04:09</date>
              <date type="whenProduced">1999</date>
              <date type="whenEndEmbargoed">2024-04-15</date>
              <ref type="file" target="https://hal.science/hal-00111620v1/document">
                <date notBefore="2024-04-15"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00111620v1/file/Massin1999.pdf" id="file-4546276-3940619">
                <date notBefore="2024-04-15"/>
              </ref>
              <ref type="externalLink" target="https://api.istex.fr/ark:/67375/6H6-P94142L7-L/fulltext.pdf?sid=hal"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="109149">
                <persName>
                  <forename>Mathias</forename>
                  <surname>Legrand</surname>
                </persName>
                <email type="md5">ffcb48ad643d28bacba8c1287c93bce7</email>
                <email type="domain">ec-nantes.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00111620</idno>
            <idno type="halUri">https://hal.science/hal-00111620</idno>
            <idno type="halBibtex">massin:hal-00111620</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of the Mechanics and Physics of Solids&lt;/i&gt;, 1999, 47, pp.1737-1779. &lt;a target="_blank" href="https://dx.doi.org/10.1016/S0022-5096(98)00117-3"&gt;&amp;#x27E8;10.1016/S0022-5096(98)00117-3&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Journal of the Mechanics and Physics of Solids, 1999, 47, pp.1737-1779. &amp;#x27E8;10.1016/S0022-5096(98)00117-3&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4546276-3940619"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="X">École polytechnique</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="X-LMS" corresp="X">Laboratoire de Mécanique des Solides (LMS)</idno>
            <idno type="stamp" n="X-DEP-MECA">Département de mécanique de l’École polytechnique </idno>
            <idno type="stamp" n="EDF">EDF</idno>
            <idno type="stamp" n="DEPARTEMENT-DE-MATHEMATIQUES">Collection du Département de Mathématiques</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">On the stability of strain-rate dependent solids. I-Structural examples</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Patrick</forename>
                    <surname>Massin</surname>
                  </persName>
                  <email type="md5">1c58b080ec6a8b901e04232d3fbeaefe</email>
                  <email type="domain">edf.fr</email>
                  <idno type="idhal" notation="string">patrick-massin</idno>
                  <idno type="idhal" notation="numeric">5725</idno>
                  <idno type="halauthorid" notation="string">556927-5725</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-9196-8639</idno>
                  <idno type="IDREF">https://www.idref.fr/115123555</idno>
                  <affiliation ref="#struct-302313"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Nicolas</forename>
                    <surname>Triantafyllidis</surname>
                  </persName>
                  <email type="md5">1f99a5059f0f510d3bc89a5b53b046dc</email>
                  <email type="domain">polytechnique.edu</email>
                  <idno type="idhal" notation="numeric">1037608</idno>
                  <idno type="halauthorid" notation="string">172906-1037608</idno>
                  <affiliation ref="#struct-24332"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Yves</forename>
                    <surname>Leroy</surname>
                  </persName>
                  <idno type="halauthorid">2527333-0</idno>
                  <affiliation ref="#struct-1167"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">6561</idno>
                <idno type="issn">0022-5096</idno>
                <title level="j">Journal of the Mechanics and Physics of Solids</title>
                <imprint>
                  <publisher>Elsevier</publisher>
                  <biblScope unit="volume">47</biblScope>
                  <biblScope unit="pp">1737-1779</biblScope>
                  <date type="datePub">1999</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1016/S0022-5096(98)00117-3</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Bucking</term>
                <term xml:lang="en">Structures</term>
                <term xml:lang="en">Beams and columns</term>
                <term xml:lang="en">Elastic-viscoplastic material</term>
                <term xml:lang="en">Stability and bifurcation</term>
              </keywords>
              <classCode scheme="halDomain" n="spi.meca">Engineering Sciences [physics]/Mechanics [physics.med-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 linear stability criterion for strain-rate sensitive solids and structures is proposed and validated with the help of two versions of Shanleys column, the first with two discrete supports and the second with a continuous distribution of supports. Linear stability transition is defined by the change in sign of the second derivative with respect to time of the columns angular position evaluated at the onset of perturbation. This criterion pertains to the initiation of instabilities but is not expected to provide information on their long term development. Two parameters influence linear stability: the dimensionless number T, defined as the ratio of the relaxation time of the viscous support to the characteristic loading time, and the perturbation size. It is found that the critical load of principal equilibria, defined for a straight column and a zero value of T, is the classical reduced modulus load, in agreement with existing stability criteria for rate-independent models based on maximum dissipation. For arbitrary values of T, two critical loads are identified at the linear stability transition. The first is named the rate-dependent tangent modulus load and is valid for perturbations sufficiently small to prevent initial unloading. That load coincides with the classical tangent modulus load for T tending to zero and is, surprisingly, a decreasing function of that dimensionless number. The second critical load is termed the rate-dependent reduced modulus load, and is applicable to columns that are partly unloaded at the onset of perturbation. This critical load approaches the classical reduced modulus load in the limit of T tending to zero, is a decreasing function of T, and depends on the imperfection size. Similar results are found for the second model, with a new insight on the role of the unloading zone extent in determining the critical load in the singular limit of T equal to zero. The proposed stability criterion is validated by comparing its predictions with the outcome of nonlinear perturbation analyses and of imperfection sensitivity studies. It is shown, in particular, that an imperfection evolves according to our stability predictions as long as the relative difference between the irreversible displacements of the supports can be disregarded. A generalization of the proposed linear stability criterion to viscoplastic continua is finally sketched.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="institution" xml:id="struct-302313" status="VALID">
          <idno type="IdRef">026436965</idno>
          <idno type="ISNI">0000000122985443</idno>
          <idno type="ROR">https://ror.org/03wb8xz10</idno>
          <idno type="Wikidata">Q274591</idno>
          <orgName>EDF – Électricité de France</orgName>
          <orgName type="acronym">EDF [E.D.F.]</orgName>
          <date type="start">1946-04-08</date>
          <desc>
            <address>
              <addrLine>22-30 – 22 avenue de Wagram – 75008 Paris – France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.edf.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-24332" status="VALID">
          <idno type="IdRef">02643198X</idno>
          <idno type="ROR">https://ror.org/00jmfr291</idno>
          <idno type="Wikidata">Q230492</idno>
          <orgName>Université du Michigan = University of Michigan [Ann Arbor]</orgName>
          <orgName type="acronym">UMich</orgName>
          <desc>
            <address>
              <addrLine>500 Church Street Ann Arbor, MI 48109-1090</addrLine>
              <country key="US"/>
            </address>
            <ref type="url">http://www.umich.edu/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-1167" status="VALID">
          <idno type="IdRef">077600649</idno>
          <idno type="ISNI">0000000122879755</idno>
          <idno type="RNSR">199719346W</idno>
          <idno type="ROR">https://ror.org/00xd1ek73</idno>
          <idno type="Wikidata">Q30262303</idno>
          <orgName>Laboratoire de Mécanique des Solides</orgName>
          <orgName type="acronym">LMS</orgName>
          <date type="start">1997-01-01</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://lms.ip-paris.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300340" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7649" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300340" status="VALID">
          <idno type="IdRef">027309320</idno>
          <idno type="ISNI">0000000121581279</idno>
          <idno type="ROR">https://ror.org/05hy3tk52</idno>
          <idno type="Wikidata">Q273626</idno>
          <orgName>École polytechnique</orgName>
          <orgName type="acronym">X</orgName>
          <date type="start">1794-03-11</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.polytechnique.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.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>
    </back>
  </text>
</TEI>