Söhngen 2017a - Revision history

https://www.scipedia.com/wd/index.php?action=history&feed=atom&title=S%C3%B6hngen_2017a Söhngen 2017a - Revision history 2026-04-07T08:18:30Z Revision history for this page on the wiki MediaWiki 1.27.0-wmf.10 https://www.scipedia.com/wd/index.php?title=S%C3%B6hngen_2017a&diff=80636&oldid=prev Scipediacontent at 14:31, 5 April 2018 2018-04-05T14:31:10Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 14:31, 5 April 2018</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l456" >Line 456:</td> <td colspan="2" class="diff-lineno">Line 456:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Though the specimen exhibits mainly pure shear as expected it can be seen that also other strain states are induced.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Though the specimen exhibits mainly pure shear as expected it can be seen that also other strain states are induced.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The afore-mentioned alternating shear loading of the specimen is depicted in&nbsp;fig:specimen_load. Starting off with the initial unloaded configuration the speckle patterns for  the three peak loading values (<math display="inline">|F_{\mathrm{x/y}}|=\<del class="diffchange diffchange-inline">SI{8}</del>{kN}</math>, <math display="inline">|F_{\mathrm{x/y}}|=\<del class="diffchange diffchange-inline">SI{9}</del>{kN}</math> and <math display="inline">|F_{\mathrm{x/y}}|=<del class="diffchange diffchange-inline">\SI</del>{<del class="diffchange diffchange-inline">10</del>}{kN}</math>) are shown.  The deformation state can be judged by the elliptic deformation of the originally circular bore in the middle.  For the loading a linear force rate of <math display="inline">|\dot{F}_{\mathrm{x/y}}| = <del class="diffchange diffchange-inline">\SI</del>{<del class="diffchange diffchange-inline">100</del>}{N/s}</math> is chosen. <del class="diffchange diffchange-inline">  </del><div id='img-3'></div></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The afore-mentioned alternating shear loading of the specimen is depicted in&nbsp;fig:specimen_load. Starting off with the initial unloaded configuration the speckle patterns for  the three peak loading values (<math display="inline">|F_{\mathrm{x/y}}|=<ins class="diffchange diffchange-inline">8 </ins>\<ins class="diffchange diffchange-inline">mbox</ins>{kN}</math>, <math display="inline">|F_{\mathrm{x/y}}|=<ins class="diffchange diffchange-inline">9 </ins>\<ins class="diffchange diffchange-inline">mbox</ins>{kN}</math> and <math display="inline">|F_{\mathrm{x/y}}|=<ins class="diffchange diffchange-inline">1x10^</ins>{<ins class="diffchange diffchange-inline">1</ins>} <ins class="diffchange diffchange-inline">\mbox</ins>{kN}</math>) are shown.  The deformation state can be judged by the elliptic deformation of the originally circular bore in the middle.  For the loading a linear force rate of <math display="inline">|\dot{F}_{\mathrm{x/y}}| = <ins class="diffchange diffchange-inline">1x10^</ins>{<ins class="diffchange diffchange-inline">2</ins>} <ins class="diffchange diffchange-inline">\mbox</ins>{N/s}</math> is chosen. <div id='img-3'></div></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>  </table>

Scipediacontent https://www.scipedia.com/wd/index.php?title=S%C3%B6hngen_2017a&diff=80633&oldid=prev Scipediacontent at 14:30, 5 April 2018 2018-04-05T14:30:02Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 14:30, 5 April 2018</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l515" >Line 515:</td> <td colspan="2" class="diff-lineno">Line 515:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|+ style="font-size: 75%;" |<span id='table-3'></span>Table. 3 Initial and identified parameters of the mixed hardening formulation for DP600</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|+ style="font-size: 75%;" |<span id='table-3'></span>Table. 3 Initial and identified parameters of the mixed hardening formulation for DP600</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <del class="diffchange diffchange-inline">  </del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <ins class="diffchange diffchange-inline">  </ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| <math>\sigma _0</math>in MPa  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| <math>\sigma _0</math>in MPa  </div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| <math>\sigma _\infty </math>in MPa  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| <math>\sigma _\infty </math>in MPa  </div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l521" >Line 521:</td> <td colspan="2" class="diff-lineno">Line 521:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| <math>k_2</math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| <math>k_2</math></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <del class="diffchange diffchange-inline">  </del>Set 1  </div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <ins class="diffchange diffchange-inline"> </ins>Set 1  </div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num</del>{<del class="diffchange diffchange-inline">350</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">3.5x10^</ins>{<ins class="diffchange diffchange-inline">2</ins>}</math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num</del>{<del class="diffchange diffchange-inline">1500</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">1.5x10^</ins>{<ins class="diffchange diffchange-inline">3</ins>}</math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num</del>{<del class="diffchange diffchange-inline">1000</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">1x10^</ins>{<ins class="diffchange diffchange-inline">3</ins>}</math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num</del>{<del class="diffchange diffchange-inline">10</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">1x10^</ins>{<ins class="diffchange diffchange-inline">1</ins>}</math></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| Set 2  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| Set 2  </div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num</del>{<del class="diffchange diffchange-inline">350</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">3.5x10^</ins>{<ins class="diffchange diffchange-inline">2</ins>}</math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num</del>{<del class="diffchange diffchange-inline">1500</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">1.5x10^</ins>{<ins class="diffchange diffchange-inline">3</ins>}</math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num</del>{<del class="diffchange diffchange-inline">5000</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">5x10^</ins>{<ins class="diffchange diffchange-inline">3</ins>}</math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num</del>{<del class="diffchange diffchange-inline">100</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">1x10^</ins>{<ins class="diffchange diffchange-inline">2</ins>}</math></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| Set 3  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| Set 3  </div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num</del>{<del class="diffchange diffchange-inline">400</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">4x10^</ins>{<ins class="diffchange diffchange-inline">2</ins>}</math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num</del>{<del class="diffchange diffchange-inline">3000</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">3x10^</ins>{<ins class="diffchange diffchange-inline">3</ins>}</math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num</del>{<del class="diffchange diffchange-inline">1000</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">1x10^</ins>{<ins class="diffchange diffchange-inline">3</ins>}</math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num</del>{<del class="diffchange diffchange-inline">100</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">1x10^</ins>{<ins class="diffchange diffchange-inline">2</ins>}</math></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|    <del class="diffchange diffchange-inline">round-mode=places,round-precision=1 </del>Mean of optimization  </div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|    Mean of optimization  </div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num=round-mode=places,round-precision=1,scientific-notation=fixed</del></math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">2.6322x10^{2}</ins></math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num=round-mode=places,round-precision=1,scientific-notation=fixed</del></math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math><ins class="diffchange diffchange-inline">8.217x10^{2}</ins></math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num=round-mode=places,round-precision=</del>1<del class="diffchange diffchange-inline">,scientific-notation=fixed</del></math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math>1<ins class="diffchange diffchange-inline">.74349x10^{4}</ins></math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num=round-mode=places,round-precision=</del>1<del class="diffchange diffchange-inline">,scientific-notation=fixed</del></math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math>1<ins class="diffchange diffchange-inline">.74102x10^{2}</ins></math></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| SD  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| SD  </div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num [round-mode=places,round-precision=1,output-exponent-marker=\mathrm{d}]{</del>3.<del class="diffchange diffchange-inline">309686449162612e</del>-<del class="diffchange diffchange-inline">02 </del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math>3.<ins class="diffchange diffchange-inline">30969x10^{</ins>-<ins class="diffchange diffchange-inline">2</ins>}</math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num [round-mode=places,round-precision=1,output-exponent-marker=\mathrm{d}]{</del>2.<del class="diffchange diffchange-inline">850874394615004e</del>-<del class="diffchange diffchange-inline">02</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math>2.<ins class="diffchange diffchange-inline">85087x10^{</ins>-<ins class="diffchange diffchange-inline">2</ins>}</math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num [retain-zero-exponent=true ,round-mode=places,round-precision=1,output-exponent-marker=\mathrm{d}]{</del>9.<del class="diffchange diffchange-inline">033307689867824e+00}</del></math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math>9.<ins class="diffchange diffchange-inline">03331</ins></math></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <math><del class="diffchange diffchange-inline">\num [round-mode=places,round-precision=1,output-exponent-marker=\mathrm{d}]{</del>5.<del class="diffchange diffchange-inline">515135165598587e</del>-<del class="diffchange diffchange-inline">02</del>}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <math>5.<ins class="diffchange diffchange-inline">51514x10^{</ins>-<ins class="diffchange diffchange-inline">2</ins>}</math></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Observing a relative SD of <math display="inline"><del class="diffchange diffchange-inline">\num [output-exponent-marker=\mathrm</del>{<del class="diffchange diffchange-inline">d}]{5.d</del>-4}</math> and less confirms the significance of the mean values and hence the global nature of the minimum. To fulfill the above- mentioned convergence criteria the Levenberg-Marquardt optimization of the three sets needs between 14 (Set 2) and 25 (Set 3) iterations. Thereby, the number of iterations  refer to the optimization algorithm itself and does not represent the total number of FE simulations which is greater due to the evaluation of the finite differences.  In fig:isotropic_hardening the isotropic hardening function for the initial values and the mean of the identified parameters is plotted vs. the equivalent plastic strain  (<math display="inline">\mathop{}\!\bar{\varepsilon }^{\mathrm{pl}}=\int _0^t \dot{\gamma } \mathop{}\!\mathrm{d}t</math>). The evolution of the backstress in loading direction w.r.t. <math display="inline">\mathop{}\!\bar{\varepsilon }^{\mathrm{pl}}</math> is depicted in fig:evolution_backstress.  As can be seen the kinematic hardening modulus <math display="inline">k_1</math> leads to an initially steep incline while the parameter <math display="inline">k_2</math> causes the increase in backstress to saturate with  advancing plastic strain for the identified parameters.  <div id='img-4a'></div></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Observing a relative SD of <math display="inline"><ins class="diffchange diffchange-inline">5x10^</ins>{-4}</math> and less confirms the significance of the mean values and hence the global nature of the minimum. To fulfill the above- mentioned convergence criteria the Levenberg-Marquardt optimization of the three sets needs between 14 (Set 2) and 25 (Set 3) iterations. Thereby, the number of iterations  refer to the optimization algorithm itself and does not represent the total number of FE simulations which is greater due to the evaluation of the finite differences.  In fig:isotropic_hardening the isotropic hardening function for the initial values and the mean of the identified parameters is plotted vs. the equivalent plastic strain  (<math display="inline">\mathop{}\!\bar{\varepsilon }^{\mathrm{pl}}=\int _0^t \dot{\gamma } \mathop{}\!\mathrm{d}t</math>). The evolution of the backstress in loading direction w.r.t. <math display="inline">\mathop{}\!\bar{\varepsilon }^{\mathrm{pl}}</math> is depicted in fig:evolution_backstress.  As can be seen the kinematic hardening modulus <math display="inline">k_1</math> leads to an initially steep incline while the parameter <math display="inline">k_2</math> causes the increase in backstress to saturate with  advancing plastic strain for the identified parameters.  <div id='img-4a'></div></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><div id='img-4'></div></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><div id='img-4'></div></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"</div></td></tr> </table>

Scipediacontent https://www.scipedia.com/wd/index.php?title=S%C3%B6hngen_2017a&diff=65090&oldid=prev Bsoehngen at 13:47, 28 August 2017 2017-08-28T13:47:49Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 13:47, 28 August 2017</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l441" >Line 441:</td> <td colspan="2" class="diff-lineno">Line 441:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|[[Image:draft_Söhngen_975815040-FEmesh.png|400px|Finite element mesh of specimen (dots mark optimization nodes)]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|[[Image:draft_Söhngen_975815040-FEmesh.png|400px|Finite element mesh of specimen (dots mark optimization nodes)]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|- style="text-align: center; font-size: 75%;"</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|- style="text-align: center; font-size: 75%;"</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| (a) Dimensions of the cruciform specimen in <math>\<del class="diffchange diffchange-inline">SI{}</del>{mm}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| (a) Dimensions of the cruciform specimen in <math>\<ins class="diffchange diffchange-inline">mathrm</ins>{mm}</math></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|- style="text-align: center; font-size: 75%;"</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|- style="text-align: center; font-size: 75%;"</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| colspan="2" | '''Figure 1:''' Finite element mesh of specimen (dots mark optimization nodes)</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| colspan="2" | '''Figure 1:''' Finite element mesh of specimen (dots mark optimization nodes)</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l509" >Line 509:</td> <td colspan="2" class="diff-lineno">Line 509:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>For that identification the same cruciform specimen geometry was loaded with equi-biaxial tension. In the elastic region the material is assumed to behave isotropically with an elastic modulus of <math display="inline">E=<del class="diffchange diffchange-inline">\SI=scientific-notation=fixed</del></math> and a Poisson's ratio of <math display="inline">\nu = <del class="diffchange diffchange-inline">\num{</del>0.3<del class="diffchange diffchange-inline">}</del></math>. The optimization of the mixed hardening parameters is based on three different  initial values sets that are given in tab:DP600_kinematic_hard along with the mean and standard deviation (SD) of the three optimization runs.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>For that identification the same cruciform specimen geometry was loaded with equi-biaxial tension. In the elastic region the material is assumed to behave isotropically with an elastic modulus of <math display="inline">E=<ins class="diffchange diffchange-inline">210000</ins></math> and a Poisson's ratio of <math display="inline">\nu = 0.3</math>. The optimization of the mixed hardening parameters is based on three different  initial values sets that are given in tab:DP600_kinematic_hard along with the mean and standard deviation (SD) of the three optimization runs.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>  </table>

Bsoehngen https://www.scipedia.com/wd/index.php?title=S%C3%B6hngen_2017a&diff=50522&oldid=prev Scipediacontent at 14:50, 24 May 2017 2017-05-24T14:50:42Z

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