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      <div class="title_refTopic" id="xps10_pagetitle">MAT1 </div>
      <hr noshade="true">
      <h4 class="refClassification">Isotropic Material Property Definition </h4>
      <p class="para_refTopic">Defines the material properties for linear isotropic materials. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="10*">
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            <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">
                     <p class="para_td">MAT1 </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">E </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">G </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">NU </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">A </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">TREF </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">GE </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">ST </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">SC </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">SS </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MCSID </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>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Example: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
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            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1">
                     <p class="para_td">MAT1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">17 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">3.+7 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.33 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">4.28 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">6.5-6 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">5.37+2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.23 </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">20.+4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">15.+4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">12.+4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1003 </p>
                  </td>
                  <td align="center" 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>
                  <td align="center" 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>
                  <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="18.89*">
               <col span="1" width="81.11*">
            </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">E </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Young&rsquo;s modulus.  (Real &ge; 0.0 or blank) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">G </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Shear modulus.  (Real &ge; 0.0 or blank) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">NU </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Poisson&rsquo;s ratio.  (-1.0 &lt; Real &le; 0.5 or blank) </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.  See Remark 5. (Real) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">A </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Thermal expansion coefficient.  (Real) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">TREF </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Reference temperature for the calculation of thermal loads, or a temperature-dependent thermal expansion coefficient.  See Remarks 9 and 10. (Real; Default = 0.0 if A is specified.) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">GE </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Structural element damping coefficient.  See Remarks 8, 9, and 4. (Real) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">ST, SC, SS </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Stress limits for tension, compression, and shear are optionally supplied, used only to compute margins of safety in certain elements; and have no effect on the computational procedures.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/08ref24356_1.html');return(false);">Parameters</a> for more information.  (Real &ge; 0.0 or blank) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MCSID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Material coordinate system identification number.  Used only for PARAM,CURV processing.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/08ref24356_1.html');return(false);">Parameters</a> for more information. (Integer &ge; 0 or blank) 
                     </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">The material identification number must be unique for all MAT1, MAT2, MAT3, and MAT9 entries. </p>
            </li>
            <li>
               <p class="para_item">The following rules apply when E, G, or NU are blank.</p>
               <ul>
                  <li>
                     <p class="para_item">E and G may not both be blank. </p>
                  </li>
                  <li>
                     <p class="para_item">If NU and E, or NU and G, are both blank, then both are set to 0.0. </p>
                  </li>
                  <li>
                     <p class="para_item">If only one E, G, or NU is blank, then it will be computed from the equation:  E = 2 · (1 + NU) · G.  If this is not desired, then the MAT2 entry is recommended.  If E, G, or NU are made temperature dependent by the MATT1 entry, then the equation is applied to the initial values only.</p>
                  </li>
               </ul>
               <table border="0">
                  <tr>
                     <td valign="top" align="left"><img align="left" src="../graphics/note.gif" alt="Note" title="Note"></td>
                     <td valign="bottom" align="left" width="100%">
                        <div class="para_note">
                           <p class="para_note_body">Note: These rules are always validated at the beginning of the solution, even when a MATS1 entry is used.</p>
                        </div>
                     </td>
                  </tr>
               </table>
            </li>
            <li>
               <p class="para_item">If values are specified for all of the properties E, G, and NU, then it is recommended that the following relationship be satisfied:</p>
               <p align="center"><img align="bottom" src="graphics/bulkmno-equ01.gif"></p>
               <p class="para_item">If this relationship is not desired, then the MAT2 entry is recommended.</p>
               <p class="para_item">It should also be noted that some of the properties are not applied in the stiffness formulation of certain elements as indicated in <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/17topic_2.html#ref46322');return(false);">Table 16-1</a>.  Therefore, it is recommended that only the applicable properties be specified for a given element. 
               </p><a name="ref46322"></a><div class="title_tableWrapper">Table 16-1. Material Property Usage Versus Element Types </div>
               <table border="1" cellpadding="9" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="25.30*">
                     <col span="1" width="22.94*">
                     <col span="1" width="27.30*">
                     <col span="1" width="24.46*">
                  </colgroup>
                  <thead>
                     <tr>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Element Entry </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">E </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">NU </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">G </b></p>
                        </th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">CROD </p>
                           <p class="para_td">CBEAM </p>
                           <p class="para_td">CBAR </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">Extension and Bending </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">Not Used </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">Torsion Transverse Shear </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">CQUADi</p>
                           <p class="para_td">CTRIAi</p>
                           <p class="para_td">CCONEAX </p>
                        </td>
                        <td align="center" colspan="2" rowspan="1">
                           <p class="para_td">Membrane, including In-plane Shear, and Bending </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">Transverse Shear </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">CSHEAR </p>
                        </td>
                        <td align="center" colspan="2" rowspan="1">
                           <p class="para_td">Not Used </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">Shear </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">CRAC2D </p>
                        </td>
                        <td align="center" colspan="2" rowspan="1">
                           <p class="para_td">All Terms </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">Not Used </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">CHEXA</p>
                           <p class="para_td">CPENTA</p>
                           <p class="para_td">CTETRA</p>
                           <p class="para_td">CRAC3D </p>
                        </td>
                        <td align="center" colspan="2" rowspan="1">
                           <p class="para_td">All Terms </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">Not Used </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">CTRIAX6 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">Radial, Axial, Circumferential </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">All Coupled Ratios </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">Shear </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br></li>
            <li><a name="refdOiHi16clori"></a><p class="para_item">MAT1 materials may be made temperature-dependent by use of the MATT1 entry.  In SOL 106, linear and nonlinear elastic material properties in the residual structure will be updated as prescribed under the TEMPERATURE Case Control command. </p>
            </li>
            <li>
               <p class="para_item">The mass density RHO will be used to compute mass for all structural elements automatically. </p>
            </li>
            <li>
               <p class="para_item">Weight density may be used in field 6 if the value 1/g is entered on the PARAM,WTMASS entry, where g is the acceleration of gravity (see <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/08ref24356_1.html');return(false);">Parameters</a> for more information). 
               </p>
            </li>
            <li>
               <p class="para_item">MCSID must be nonzero if PARAM,CURV is specified to calculate stresses or strains at grid points on plate and shell elements only. </p>
            </li>
            <li>
               <p class="para_item">To obtain the damping coefficient GE, multiply the critical damping ratio <em>C/C</em><sub class="subscript">o</sub>, by 2.0. 
               </p>
            </li>
            <li>
               <p class="para_item">TREF and GE are ignored if the MAT1 entry is referenced by a PCOMP entry. </p>
            </li>
            <li>
               <p class="para_item">TREF is used in two different ways: </p>
               <ul>
                  <li>
                     <p class="para_item">In nonlinear static analysis (SOL 106), TREF is used only for the calculation of a temperature-dependent thermal expansion coefficient.  The reference temperature for the calculation of thermal loads is obtained from the TEMPERATURE(INITIAL) set selection. </p><a name="ref79799"></a><div class="figure">
                        <p align="center"><img align="bottom" src="graphics/bulkmno-fig01.gif"></p>
                     </div>
                     <div class="title_figure">Figure. Use of TREF in Calculation of Thermal Loads </div>
                     <p class="para_item">ϵ<em><sub class="subscript">T</sub></em> = <em>A</em>(<em>T</em>) · (<em>T</em>−<em>TREF</em>)−<em>A</em>(<em>T</em><sub class="subscript">0</sub>) · (<em>T</em><sub class="subscript">0</sub>−<em>TREF</em>) 
                     </p>
                     <p class="para_item">where <em>T</em>is requested by the TEMPERATURE(LOAD) command and <em>T</em><sub class="subscript">0</sub> is requested by the TEMPERATURE(INITIAL) command. 
                     </p>
                     <table border="0">
                        <tr>
                           <td valign="top" align="left"><img align="left" src="../graphics/note.gif" alt="Note" title="Note"></td>
                           <td valign="bottom" align="left" width="100%">
                              <div class="para_note">
                                 <ol type="a" start="1">
                                    <li>
                                       <p class="para_note_body">A is a secant quantity. </p>
                                    </li>
                                    <li>
                                       <p class="para_note_body">TREF is obtained from the same source as the other material properties; e.g., ASTM, etc.  </p>
                                    </li>
                                    <li>
                                       <p class="para_note_body">If <em>A</em>(<em>T</em>) constant, then ϵ<em><sub class="subscript">T</sub></em> = <em>A</em> · (<em>T</em>−<em>T</em><sub class="subscript">0</sub>) 
                                       </p>
                                       <ul>
                                          <li>
                                             <p class="para_note_body">In all SOLs except 106, TREF is used only as the reference temperature for the calculation of thermal loads.  TEMPERATURE(INITIAL) may be used for this purpose, but TREF must be blank. </p>
                                          </li>
                                       </ul>
                                    </li>
                                    <li>
                                       <p class="para_note_body">If PARAM,W4 is not specified, GE is ignored in transient analysis.  See <b class="uiTerm">Parameters</b>. 
                                       </p>
                                    </li>
                                 </ol>
                              </div>
                           </td>
                        </tr>
                     </table>
                  </li>
               </ul>
            </li>
         </ol>
      </div>
      <div class="title_refCategory">Remarks related to SOLs 601 and 701: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li>
               <p class="para_item">GE, ST, SC, SS, and MCSID are ignored. </p>
            </li>
            <li>
               <p class="para_item">RHO is always used as mass density regardless of PARAM,WTMASS entry. </p>
            </li>
            <li>
               <p class="para_item">TREF is used only used when MAT1 is made temperature dependent by use of the MATT1 entry. </p>
            </li>
            <li>
               <p class="para_item">For CQUADi and CTRIAi elements, the transverse shear modulus is equal to the in-plane shear modulus. </p>
            </li>
            <li>
               <p class="para_item">E and NU may not be both blank. </p>
            </li>
         </ol>
      </div>
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