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<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>Equivalent Stresses and Strains</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3" colspan = "2"><table class = "DocThemeIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "header"><p class = "abstract">
<span class = "shortdesc">
The equivalent stresses are the main input for the shape optimization controller
algorithm. All values, whether nodal, from gauss points or elements, are interpolated to
the nodes. Most equivalent stresses are only allowed in the objective function by
controller-based shape optimization. Some measures are also available for sensitivity-based optimizations.
</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-terms-dresps-stressstrain-equStress__tso-c-usr-terms-equStress-contactStrainMeas" id = "toc_rg" title = "">Contact and Strain Measures</a></li><li><a href = "#tso-c-usr-terms-dresps-stressstrain-equStress__tso-c-usr-terms-equStress-anaType-Stress" id = "toc_rg" title = "">Analysis Types: Any Analysis Type with Stress Output or Fatigue Result</a></li><li><a href = "#tso-c-usr-terms-dresps-stressstrain-equStress__tso-c-usr-terms-equStress-anaType-Strain" id = "toc_rg" title = "">Analysis Types: Any Analysis Type with Contact and Strain Output</a></li></ul>
</p></td></tr></table></td></tr></table>




<div class = "body conbody">
<table class = "table" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620"><caption/><colgroup><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>Parameter Name</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><p>Formula</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_1</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow></msub></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_2</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msub></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_3</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></msub></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_11</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">11</mn></mrow></msub></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_22</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">22</mn></mrow></msub></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_33</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">33</mn></mrow></msub></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_12</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">12</mn></mrow></msub></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_23</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">23</mn></mrow></msub></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_13</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">13</mn></mrow></msub></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_ABS_123</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mtext class = "- topic/foreign ">max </mtext><mfenced open = "(" close = ")" separators = "," class = "- topic/foreign "><mrow class = "- topic/foreign "><mfenced open = "|" close = "|" separators = "" class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow></msub></mfenced></mrow><mrow class = "- topic/foreign "><mfenced open = "|" close = "|" separators = "" class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msub></mfenced></mrow><mrow class = "- topic/foreign "><mfenced open = "|" close = "|" separators = "" class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></msub></mfenced></mrow></mfenced></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_ABS_3</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mfenced open = "|" close = "|" separators = "" class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></msub></mfenced></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_BELTRAMI</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><msqrt class = "- topic/foreign "><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><mo class = "- topic/foreign ">-</mo><mn class = "- topic/foreign ">2</mn><mi class = "- topic/foreign ">ν</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><mo class = "- topic/foreign ">)</mo></msqrt></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_DRUCKER_PRAGER</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mo class = "- topic/foreign ">{</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ν</mi><mo class = "- topic/foreign ">-</mo><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn><mi class = "- topic/foreign ">ν</mi></mrow></mfrac><mo class = "- topic/foreign ">+</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">ν</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn><mi class = "- topic/foreign ">ν</mi></mrow></mfrac><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">}</mo><msqrt class = "- topic/foreign "><mfrac class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn><mn class = "- topic/foreign ">2</mn></mfrac><mo class = "- topic/foreign ">{</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><mo class = "- topic/foreign ">-</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><msup class = "- topic/foreign "><mo class = "- topic/foreign ">)</mo><mn class = "- topic/foreign ">2</mn></msup><mo class = "- topic/foreign ">+</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><mo class = "- topic/foreign ">-</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><msup class = "- topic/foreign "><mo class = "- topic/foreign ">)</mo><mn class = "- topic/foreign ">2</mn></msup><mo class = "- topic/foreign ">+</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><mo class = "- topic/foreign ">-</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><msup class = "- topic/foreign "><mo class = "- topic/foreign ">)</mo><mn class = "- topic/foreign ">2</mn></msup><mo class = "- topic/foreign ">}</mo></msqrt></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_KUHN</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">ν</mi></mrow><mn class = "- topic/foreign ">3</mn></mfrac><mo class = "- topic/foreign ">{</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><mo class = "- topic/foreign ">-</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><msup class = "- topic/foreign "><mo class = "- topic/foreign ">)</mo><mn class = "- topic/foreign ">2</mn></msup><mo class = "- topic/foreign ">+</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><mo class = "- topic/foreign ">-</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><msup class = "- topic/foreign "><mo class = "- topic/foreign ">)</mo><mn class = "- topic/foreign ">2</mn></msup><mo class = "- topic/foreign ">+</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><mo class = "- topic/foreign ">-</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><msup class = "- topic/foreign "><mo class = "- topic/foreign ">)</mo><mn class = "- topic/foreign ">2</mn></msup><mo class = "- topic/foreign ">}</mo><mo class = "- topic/foreign ">+</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn><mo class = "- topic/foreign ">-</mo><mn class = "- topic/foreign ">2</mn><mi class = "- topic/foreign ">ν</mi></mrow><mn class = "- topic/foreign ">3</mn></mfrac><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><msup class = "- topic/foreign "><mo class = "- topic/foreign ">)</mo><mn class = "- topic/foreign ">3</mn></msup></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><mo class = "- topic/foreign ">|</mo></mrow></mfrac></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_MARIOTTE</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mi class = "- topic/foreign ">max</mi><mo class = "- topic/foreign ">{</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><mo class = "- topic/foreign ">-</mo><mi class = "- topic/foreign ">ν</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">,</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><mo class = "- topic/foreign ">-</mo><mi class = "- topic/foreign ">ν</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">,</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">3</mn></msub><mo class = "- topic/foreign ">-</mo><mi class = "- topic/foreign ">ν</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">1</mn></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi><mn class = "- topic/foreign ">2</mn></msub><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">}</mo> </math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_MISES</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><p> <span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><mrow class = "- topic/foreign "><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></mfrac><mo class = "- topic/foreign ">{</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">}</mo></mrow></mrow></msqrt></mrow></math></span></p></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_SIGNED_MISES</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">sgn(1,</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">11</mn></mrow></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">22</mn></mrow></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">33</mn></mrow></msub><mo class = "- topic/foreign ">)</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">vM</mn></mrow></msub></mrow></math></span></p></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_SANDEL</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msqrt class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">−</mo><mn class = "- topic/foreign ">2</mn><mi class = "- topic/foreign ">ν</mi><mrow class = "- topic/foreign "><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn><mo class = "- topic/foreign ">−</mo><mi class = "- topic/foreign ">ν</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn><mo class = "- topic/foreign ">+</mo><mn class = "- topic/foreign ">2</mn><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ν</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></mfrac><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow></msub><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msub><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></msub><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow></msub><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></msqrt></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_SAUTER</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mroot class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">|</mo></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></msub><mo class = "- topic/foreign ">|</mo></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">|</mo></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow></msup></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow></mroot></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__1"><p>SIG_TRESCA</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938620__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mtext class = "- topic/foreign ">max</mtext><mfenced open = "(" close = ")" separators = "," class = "- topic/foreign "><mrow class = "- topic/foreign "><mfenced open = "|" close = "|" separators = "" class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">-</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msub></mfenced></mrow><mrow class = "- topic/foreign "><mfenced open = "|" close = "|" separators = "" class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">-</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></msub></mfenced></mrow><mrow class = "- topic/foreign "><mfenced open = "|" close = "|" separators = "" class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></msub><mo class = "- topic/foreign ">-</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow></msub></mfenced></mrow></mfenced></math></span></td>
</tr>
</tbody></table>

<div class = "section" id = "tso-c-usr-terms-dresps-stressstrain-equStress__tso-c-usr-terms-equStress-contactStrainMeas"><h2 class = "title sectiontitle">Contact and Strain Measures</h2>

<table class = "table" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851"><caption/><colgroup><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__1"><p>Parameter Name</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__2"><p>Formula</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__1"><p>ABQ_ND_PEEQ</p></td><td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__2"><p>PEEQ, see <span class = "ph">Abaqus</span> documentation</p></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__1"><p>SIG_CONTACT_PRESSURE</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__2"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow></math></span></p></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__1"><p>SIG_CONTACT_SHEAR</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">τ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">τ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__1"><p>SIG_CONTACT_SHEAR_X</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">τ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow></msub></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__1"><p>SIG_CONTACT_SHEAR_Y</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">τ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msub></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__1"><p>SIG_CONTACT_TOTAL</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">τ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">τ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__1"><p>STRAIN_ELASTIC</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">{</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></mfrac><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">[</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">11</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">22</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">33</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><mn class = "- topic/foreign ">2</mn><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">12</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">13</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">23</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">)</mo></mrow><mo class = "- topic/foreign ">]</mo></mrow><mo class = "- topic/foreign ">}</mo></mrow><mrow class = "- topic/foreign "><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></mfrac></mrow></msup></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__1"><p>STRAIN_PLASTIC</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">{</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></mfrac><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">[</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">11</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">22</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">33</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><mn class = "- topic/foreign ">2</mn><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">12</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">13</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">23</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">)</mo></mrow><mo class = "- topic/foreign ">]</mo></mrow><mo class = "- topic/foreign ">}</mo></mrow><mrow class = "- topic/foreign "><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></mfrac></mrow></msup></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__1"><p>STRAIN_TOTAL</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx938851__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">{</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></mfrac><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">[</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">11</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">22</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">33</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><mn class = "- topic/foreign ">2</mn><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">12</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">13</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">23</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">)</mo></mrow><mo class = "- topic/foreign ">]</mo></mrow><mo class = "- topic/foreign ">}</mo></mrow><mrow class = "- topic/foreign "><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></mfrac></mrow></msup></mrow></math></span></td>
</tr>
</tbody></table>
<table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"><p>
Elastic and plastic strain values (<code class = "ph codeph">TYPE = STRAIN_ELASTIC and TYPE =
STRAIN_PLASTIC</code>) are available only in a nonlinear analysis with plastic
materials. Using these DRESPs for linear analysis will result in an error.
</p></span></td></tr></table>

</div>


<div class = "section" id = "tso-c-usr-terms-dresps-stressstrain-equStress__tso-c-usr-terms-equStress-anaType-Stress"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle">Analysis Types: Any Analysis Type with Stress Output or Fatigue Result</h2>

<p>For all design responses from the table above (except <code class = "ph codeph">NEUBER</code>, <code class = "ph codeph">GLINKA</code> and <code class = "ph codeph">SIG_SIGNED_MISES </code>),
   the following table shows the allowed combinations between the strategy and
   the items <code class = "ph codeph">OBJ_FUNC</code> and <code class = "ph codeph">CONSTRAINT</code> with C for
   controller-based optimization and S for sensitivity-based optimization.</p>
<table class = "table" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105"><caption/><colgroup><col/><col/><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__1"/>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__2"><p>TOPO</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__3"><p>SHAPE</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__4"><p>BEAD</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__5"><p>SIZING</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__1"><p>OBJ_FUNC</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__2"/>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__3"><p>C</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__4"/>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__5"/>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__1"><p>CONSTRAINT</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__2"/>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__3"/>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__4"/>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939105__entry__5"/>
</tr>
</tbody></table>

<p>The equivalent stresses are the main input for the shape optimization
   controller algorithm. All values, whether nodal, from gauss points
   or elements, are interpolated to the nodes.</p>
<p>In addition, <code class = "ph codeph">SIG_1</code>, <code class = "ph codeph">SIG_3 </code>, and <code class = "ph codeph">SIG_MISES</code> are
            allowed for the following optimization types. <code class = "ph codeph">SIG_MISES</code> in only
            supported in optimization types with a <code class = "ph codeph">*</code>. </p>
<table class = "table" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106"><caption/><colgroup><col/><col/><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__1"/>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__2"><p>TOPO</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__3"><p>SHAPE</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__4"><p>BEAD</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__5"><p>SIZING</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__1"><p>OBJ_FUNC</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__2"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__3"><p>S*</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__4"><p>S*</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__5"><p>S</p></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__1"><p>CONSTRAINT</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__2"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__3"><p>S*</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__4"><p>S*</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939106__entry__5"><p>S</p></td>
</tr>
</tbody></table>
<p>The <code class = "ph codeph">NEUBER</code>, <code class = "ph codeph">GLINKA</code>, and <code class = "ph codeph">SIG_SIGNED_MISES</code>
            design responses are supported with the following optimization types. </p>
<table class = "table" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107"><caption/><colgroup><col/><col/><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__1"/>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__2"><p>TOPO</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__3"><p>SHAPE</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__4"><p>BEAD</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__5"><p>SIZING</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__1"><p>OBJ_FUNC</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__2"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__3"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__4"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__5"><p>S</p></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__1"><p>CONSTRAINT</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__2"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__3"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__4"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939107__entry__5"><p>S</p></td>
</tr>
</tbody></table>
<p>Typical optimization tasks:</p>
<ol class = "ol">
<li class = "li">Minimize maximal von Mises stress</li>
<li class = "li">Minimize maximal damage (fatigue analysis)</li>
</ol>
<p>Equivalent stresses are always read for <code class = "ph codeph">ALL_NODES</code> to give the user the most
appropriate output. This will give some warnings for nodes that do not have any
equivalent stress values. For example, nodes on elements that are not in contact
when evaluating <code class = "ph codeph">SIG_CONTACT_... </code>.</p>
</div>


<div class = "section" id = "tso-c-usr-terms-dresps-stressstrain-equStress__tso-c-usr-terms-equStress-anaType-Strain"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle">Analysis Types: Any Analysis Type with Contact and Strain Output</h2>

<p>For equivalent strain and contact measures,
the following table shows the allowed combinations between the strategy and
the items <code class = "ph codeph">OBJ_FUNC</code> and <code class = "ph codeph">CONSTRAINT</code> with C for
controller-based optimization and S for sensitivity-based optimization.</p>
<table class = "table" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108"><caption/><colgroup><col/><col/><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__1"/>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__2"><p>TOPO</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__3"><p>SHAPE</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__4"><p>BEAD</p></th>
<th class = "entry" id = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__5"><p>SIZING</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__1"><p>OBJ_FUNC</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__2"/>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__3"><p>C</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__4"/>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__5"/>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__1"><p>CONSTRAINT</p></td>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__2"/>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__3"/>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__4"/>
<td class = "entry" headers = "tso-c-usr-terms-dresps-stressstrain-equStress__xx939108__entry__5"/>
</tr>
</tbody></table>

<p>Typical optimization tasks:</p>
<ol class = "ol">
<li class = "li">Minimize maximal strain in a given region</li>
<li class = "li">Minimize contact pressure in a contact region</li>
</ol>
<p>Equivalent stresses are always read for <code class = "ph codeph">ALL_NODES</code> to give the user the most
appropriate output. This will give some warnings for nodes that do not have any
equivalent stress values. For example, nodes on elements that are not in contact
when evaluating <code class = "ph codeph">SIG_CONTACT_... </code>.</p>
<table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"><p>
Plastic strain values (<code class = "ph codeph">TYPE = STRAIN_PLASTIC</code>) are
calculated by <span class = "ph">Tosca Structure</span>
and might differ slightly from your solver results.</p>
</span></td></tr></table>

</div>

</div>

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