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      <div class="title_refTopic" id="xps10_pagetitle">MATHE </div>
      <hr noshade="true">
      <h4 class="refClassification">Hyperelastic Material Properties (SOLs 601 and 701 only) </h4>
      <p class="para_refTopic">Specifies hyperelastic (rubber-like) material properties for advanced nonlinear analysis. </p>
      <div class="title_refCategory">Format 1 (default): Generalized Mooney-Rivlin model (Model = Mooney) </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
            </colgroup>
            <thead>
               <tr>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">1 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">2 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">3 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">4 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">5 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">6 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">7 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">8 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">9 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">10 </p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MATHE </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Model </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">K </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">RHO </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">TEXP </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C10 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C01 </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C20 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C11 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C02 </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C30 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C21 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C12 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C03 </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Format 2: Ogden model or Hyperfoam model (Model = Ogden or foam) </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
            </colgroup>
            <thead>
               <tr>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">1 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">2 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">3 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">4 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">5 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">6 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">7 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">8 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">9 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">10 </p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MATHE </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Model </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">K </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">RHO </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">TEXP </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MU1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ALPHA1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">BETA1 </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MU2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ALPHA2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">BETA2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MU3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ALPHA3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">BETA3 </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MU4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ALPHA4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">BETA4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MU5 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ALPHA5 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">BETA5 </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MU6 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ALPHA6 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">BETA6 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MU7 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ALPHA7 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">BETA7 </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MU8 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ALPHA8 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">BETA8 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MU9 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ALPHA9 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">BETA9 </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Format 3: Arruda-Boyce model (Model = Aboyce) </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
            </colgroup>
            <thead>
               <tr>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">1 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">2 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">3 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">4 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">5 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">6 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">7 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">8 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">9 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">10 </p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MATHE </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Model </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">K </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">RHO </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">TEXP </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">NKT </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">N </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Fields:</div>
      <div class="refCategoryContent">
         <table cellpadding="9" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="16*">
               <col span="1" width="84*">
            </colgroup>
            <thead>
               <tr>
                  <th align="left" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Field </b></p>
                  </th>
                  <th align="left" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Contents </b></p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Material identification number (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Model </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Hyperelastic material model type (Character; Default = Mooney) </p>
                     <p class="para_td">Mooney: Generalized Mooney-Rivlin model </p>
                     <p class="para_td">Ogden: Ogden model </p>
                     <p class="para_td">Foam: Hyperfoam model </p>
                     <p class="para_td">Aboyce: Arruda-Boyce model </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">K </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Specifies a bulk modulus. Not used in hyperfoam material. See Remark 7. (Real &gt; 0.0; Default = automatically set for nearly incompressible condition). </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">RHO </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Mass density in reference configuration. (Real; Default = 0.0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Texp </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Coefficient of thermal expansion. See Remark 8. (Real; Default = 0.0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Cij </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Material constants related to distortional deformation for generalized Monney-Rivlin model. See Remark 3. (Real; Default = 1.0 for C10 and C01, = 0.0 for other constants). </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Muk </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Coefficients &mu;<sub class="subscript">k</sub> of the strain energy function for Ogden or hyperfoam material. See Remarks 4 and 5. (Real; Default = 0.0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Alphak </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Coefficients &alpha;<sub class="subscript">k</sub> of the strain energy function for Ogden or hyperfoam material. See Remarks 4 and 5. (Real; Default = 0.0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Betak </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Coefficients &beta;<sub class="subscript">k</sub> of the strain energy function for hyperfoam material. These fields are unused for the Ogden model. See Remark 5. (Real; Default = 0.0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">NKT </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Material constant for Arruda-Boyce strain energy model. See Remark 6. (Real &gt; 0; Default = 1.0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">N </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Material constant representing the number of statistical links of the chain for Arruda-Boyce model. See Remark 6. (Real &gt; 0; Default = 1.0) </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Remarks: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li>
               <p class="para_item">Model = Foam or Aboyce is not supported for SOL 701. </p>
            </li>
            <li>
               <p class="para_item">Minimum input lines: 1 for Mooney or Aboyce, 2 for Ogden or foam. </p>
            </li>
            <li>
               <p class="para_item">The generalized Mooney-Rivlin strain energy function may be expressed as follows: </p>
               <p class="para_item"><img align="bottom" src="graphics/bulkmno-equ10.gif" border="0"></p>
               <p class="para_item">with </p>
               <p class="para_item"><img align="bottom" src="graphics/bulkmno-equ11.gif" border="0"></p>
               <p class="para_item"><img align="bottom" src="graphics/bulkmno-ufig01.gif" border="0"> 
               </p>
               <p class="para_item">is the deviatoric stretch ratio defined as </p>
               <p class="para_item"><img align="bottom" src="graphics/bulkmno-equ12.gif" border="0">, 
               </p>
               <p class="para_item">and K and J are the bulk modulus and volume ratio, respectively. </p>
               <p class="para_item">For small strains, the shear modulus G is realted to the Mooney-Rivlin constants by G = 2(C<sub class="subscript">10</sub>+C<sub class="subscript">01</sub>). 
               </p>
               <p class="para_item">The model reduces to a Mooney-Rivlin material with only two constants (C10 and C01), and to a Neo-Hookean material with one constant (C10). </p>
            </li>
            <li>
               <p class="para_item">For the Ogden material model, the strain energy function is </p>
               <p align="center"><img align="bottom" src="graphics/bulkmno-equ13.gif"></p>
               <p class="para_item">where the &mu;<sub class="subscript">k</sub> and &alpha;<sub class="subscript">k</sub> are material constants.
               </p>
               <p class="para_item"> <img align="bottom" src="graphics/bulkmno-ufig01.gif" border="0"> is the deviatoric stretch ratio defined as 
               </p>
               <p class="para_item"><img align="bottom" src="graphics/bulkmno-equ14.gif" border="0">, 
               </p>
               <p class="para_item">and K and J are the bulk modulus and volume ratio, respectively. A two-term Ogden model can be made equivalent to a simple Mooney-Rivlin model by choosing &mu;<sub class="subscript">1</sub>=2C<sub class="subscript">10</sub>, &alpha;<sub class="subscript">1</sub>=2, &mu;<sub class="subscript">2</sub>=2C<sub class="subscript">01</sub>, &alpha;<sub class="subscript">2</sub>=−2. 
               </p>
               <p class="para_item">For small strains, the shear modulus G is related to the Ogden constants by </p>
               <p align="center"><img align="bottom" src="graphics/bulkmno-equ15.gif"></p>
            </li>
            <li>
               <p class="para_item">For the hyperfoam material model, the strain energy function is </p>
               <p align="center"><img align="bottom" src="graphics/bulkmno-equ16.gif"></p>
               <p class="para_item">where the &mu;<sub class="subscript">k</sub>, &alpha;<sub class="subscript">k</sub> and &beta;<sub class="subscript">k</sub> are material constants, and J is the volume ratio. 
               </p>
               <p class="para_item">For small strains, the shear modulus G and bulk modulus K are related to the hyperfoam constants by </p>
               <p align="center"><img align="bottom" src="graphics/bulkmno-equ17.gif"></p>
               <p class="para_item">These moduli must be greater than zero, hence we note that &beta;<sub class="subscript">k</sub> should be greater than -1/3. 
               </p>
               <p class="para_item">When all of the &beta;<sub class="subscript">k</sub> are equal to each other, then &beta; is related to the Poisson&rsquo;s ratio by 
               </p>
               <p class="para_item"><img align="bottom" src="graphics/bulkmno-equ18.gif" border="0">. 
               </p>
            </li>
            <li>
               <p class="para_item">For the Arruda-Boyce model, the strain energy function is </p>
               <p align="center"><img align="bottom" src="graphics/bulkmno-equ19.gif"></p>
               <p class="para_item">with </p>
               <p class="para_item"><img align="bottom" src="graphics/bulkmno-equ20.gif" border="0"></p>
               <p class="para_item"> where N<sub class="subscript">kt</sub> is a material constant and N is a material parameter representing the number of statistical links of the material chain. K and J are the bulk modulus and volume ratio, respectively. 
               </p>
               <p class="para_item">For small strains, the shear modulus G is equal to N<sub class="subscript">kt.</sub></p>
            </li>
            <li>
               <p class="para_item">Although the conventional Mooney-Rivlin, Ogden and Arruda-Boyce materials are fully incompresssible, the Mooney-Rivlin, Ogden and Arruda-Boyce material models in SOL 601/701 are compressible. Nearly incompressible materials may be simulated with a large value of K. </p>
               <p class="para_item">The default value of K is chosen so that the small-strain Poisson&rsquo;s ratio is 0.499. For the Mooney-Rivlin material, K=1000(C<sub class="subscript">10</sub>+C<sub class="subscript">01</sub>); for the Ogden material, 
               </p>
               <p class="para_item"><img align="bottom" src="graphics/bulkmno-equ21.gif" border="0">; 
               </p>
               <p class="para_item">for the Arruda-Boyce material, K=500N<sub class="subscript">kt</sub>. 
               </p>
            </li>
            <li>
               <p class="para_item">The thermal strain is computed by ϵ<sub class="subscript">th</sub>=&alpha; (T−T<sub class="subscript">0</sub>) where T<sub class="subscript">0</sub> is an initial temperature. ϵ<sub class="subscript">th</sub> is an engineering strain, thus, if the material is free to expand, 
               </p>
               <p align="left"><img align="bottom" src="graphics/bulkmno-equ22.gif"></p>
               <p class="para_item">where L(t) is the final length and L(0) is the initial length. </p>
            </li>
         </ol>
      </div>
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