<?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-00833490</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="2026-05-01T21:29:42+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Symbolic and numerical solution of the axisymmetric indentation problem for a multilayered elastic coating</title>
            <author role="aut">
              <persName>
                <forename type="first">Andrei</forename>
                <surname>Constantinescu</surname>
              </persName>
              <email type="md5">89eca3858219599db930c164b7ae7c90</email>
              <email type="domain">polytechnique.edu</email>
              <idno type="idhal" notation="string">andrei-constantinescu</idno>
              <idno type="idhal" notation="numeric">5596</idno>
              <idno type="halauthorid" notation="string">5001-5596</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-4702-4256</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=CuYlVDMAAAAJ&amp;hl=de&amp;oi=ao</idno>
              <idno type="IDREF">https://www.idref.fr/074120239</idno>
              <affiliation ref="#struct-1167"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Alexander</forename>
                <forename type="middle">M.</forename>
                <surname>Korsunsky</surname>
              </persName>
              <email type="md5">2f1b0cea8dd2b1b023edc006e8453e9b</email>
              <email type="domain">eng.ox.ac.uk</email>
              <idno type="idhal" notation="numeric">1544745</idno>
              <idno type="halauthorid" notation="string">431172-1544745</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-3558-5198</idno>
              <affiliation ref="#struct-74670"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Olivier</forename>
                <surname>Pison</surname>
              </persName>
              <idno type="halauthorid">1380506-0</idno>
              <affiliation ref="#struct-1167"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Abdelbacet</forename>
                <surname>Oueslati</surname>
              </persName>
              <idno type="halauthorid">172084-0</idno>
              <affiliation ref="#struct-1252"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Andrei</forename>
                <surname>Constantinescu</surname>
              </persName>
              <email type="md5">89eca3858219599db930c164b7ae7c90</email>
              <email type="domain">polytechnique.edu</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2013-06-12 19:09:10</date>
              <date type="whenModified">2025-07-04 11:58:58</date>
              <date type="whenReleased">2013-06-12 19:09:10</date>
              <date type="whenProduced">2013-03-18</date>
              <ref type="externalLink" target="https://doi.org/10.1016/j.ijsolstr.2013.04.017"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="120310">
                <persName>
                  <forename>Andrei</forename>
                  <surname>Constantinescu</surname>
                </persName>
                <email type="md5">89eca3858219599db930c164b7ae7c90</email>
                <email type="domain">polytechnique.edu</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00833490</idno>
            <idno type="halUri">https://polytechnique.hal.science/hal-00833490</idno>
            <idno type="halBibtex">constantinescu:hal-00833490</idno>
            <idno type="halRefHtml">&lt;i&gt;International Journal of Solids and Structures&lt;/i&gt;, 2013, 50 (18), pp.2798-2807. &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.ijsolstr.2013.04.017"&gt;&amp;#x27E8;10.1016/j.ijsolstr.2013.04.017&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">International Journal of Solids and Structures, 2013, 50 (18), pp.2798-2807. &amp;#x27E8;10.1016/j.ijsolstr.2013.04.017&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </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="PARISTECH">ParisTech</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">Symbolic and numerical solution of the axisymmetric indentation problem for a multilayered elastic coating</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Andrei</forename>
                    <surname>Constantinescu</surname>
                  </persName>
                  <email type="md5">89eca3858219599db930c164b7ae7c90</email>
                  <email type="domain">polytechnique.edu</email>
                  <idno type="idhal" notation="string">andrei-constantinescu</idno>
                  <idno type="idhal" notation="numeric">5596</idno>
                  <idno type="halauthorid" notation="string">5001-5596</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-4702-4256</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=CuYlVDMAAAAJ&amp;hl=de&amp;oi=ao</idno>
                  <idno type="IDREF">https://www.idref.fr/074120239</idno>
                  <affiliation ref="#struct-1167"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Alexander</forename>
                    <forename type="middle">M.</forename>
                    <surname>Korsunsky</surname>
                  </persName>
                  <email type="md5">2f1b0cea8dd2b1b023edc006e8453e9b</email>
                  <email type="domain">eng.ox.ac.uk</email>
                  <idno type="idhal" notation="numeric">1544745</idno>
                  <idno type="halauthorid" notation="string">431172-1544745</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-3558-5198</idno>
                  <affiliation ref="#struct-74670"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Olivier</forename>
                    <surname>Pison</surname>
                  </persName>
                  <idno type="halauthorid">1380506-0</idno>
                  <affiliation ref="#struct-1167"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Abdelbacet</forename>
                    <surname>Oueslati</surname>
                  </persName>
                  <idno type="halauthorid">172084-0</idno>
                  <affiliation ref="#struct-1252"/>
                </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">50</biblScope>
                  <biblScope unit="issue">18</biblScope>
                  <biblScope unit="pp">2798-2807</biblScope>
                  <date type="datePub">2013-03-18</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1016/j.ijsolstr.2013.04.017</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Mathematica</term>
                <term xml:lang="en">Transfer matrix</term>
                <term xml:lang="en">Integral equation</term>
                <term xml:lang="en">Multilayer</term>
                <term xml:lang="en">Indentation</term>
              </keywords>
              <classCode scheme="halDomain" n="spi.meca.mema">Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of materials [physics.class-ph]</classCode>
              <classCode scheme="halDomain" n="phys.meca.mema">Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph]</classCode>
              <classCode scheme="halDomain" n="spi.meca.solid">Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph]</classCode>
              <classCode scheme="halDomain" n="phys.meca.solid">Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph]</classCode>
              <classCode scheme="halDomain" n="phys.cond.cm-ms">Physics [physics]/Condensed Matter [cond-mat]/Materials Science [cond-mat.mtrl-sci]</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>This paper is concerned with a semi-analytical approach to the solution of the axisymmetric indentation problem for a multilayered elastic half-space. The stress and displacement fields for each layer and the substrate are derived in closed form by using the Papkovich-Neuber potentials and the Hankel transform. The bonded or sliding interface conditions between the sub-layers are handled by the use of the appropriate transfer matrix, and then the mixed boundary value problem is reduced to a Fredholm integral equation. Symbolic and numerical computations of the solution are implemented in the symbolic software Mathematica in the form of a fast and efficient numerical algorithm, allowing rapid determination of the load-displacement curves and composite elastic properties for an arbitrary rigid indenter shape. A series of results for different indenters (flat, conical, spherical and blunted conical punch shapes) and different multilayered composites is presented and discussed. The complete set of symbolic and numerical computations are provided as supplementary resources with the paper.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <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="laboratory" xml:id="struct-74670" status="VALID">
          <orgName>Department of Engineering Science</orgName>
          <desc>
            <address>
              <addrLine>Department of Engineering Science University of Oxford Parks Road OXFORD OX1 3PJ UK</addrLine>
              <country key="GB"/>
            </address>
            <ref type="url">http://www.eng.ox.ac.uk/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-302612" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1252" status="OLD">
          <idno type="IdRef">150645597</idno>
          <idno type="ISNI">0000 0004 0617 9507</idno>
          <idno type="RNSR">200212764V</idno>
          <orgName>Laboratoire de Mécanique de Lille - FRE 3723</orgName>
          <orgName type="acronym">LML</orgName>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <addrLine>Bâtiment M6 Bvd Paul Langevin -  59655 VILLENEUVE D ASCQ CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://lml.univ-lille1.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-92973" type="direct"/>
            <relation active="#struct-120930" type="direct"/>
            <relation name="FRE3723 / UMR8107" 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>
        <org type="institution" xml:id="struct-302612" status="VALID">
          <idno type="ROR">https://ror.org/052gg0110</idno>
          <orgName>University of Oxford</orgName>
          <desc>
            <address>
              <addrLine>Wellington Square, Oxford OX1 2JD</addrLine>
              <country key="GB"/>
            </address>
            <ref type="url">http://www.ox.ac.uk/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-92973" status="OLD">
          <idno type="IdRef">026404184</idno>
          <idno type="ROR">https://ror.org/0546v5182</idno>
          <orgName>Université de Lille, Sciences et Technologies</orgName>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <addrLine>Cité Scientifique - 59655 Villeneuve d'Ascq Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-lille1.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-120930" status="VALID">
          <idno type="IdRef">256304629</idno>
          <idno type="ISNI">0000000122034461</idno>
          <idno type="ROR">https://ror.org/01x441g73</idno>
          <orgName>Centrale Lille</orgName>
          <desc>
            <address>
              <addrLine>École Centrale de Lille - Cité Scientifique - CS 20048 59651 Villeneuve d'Ascq Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://centralelille.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>