Traction Laws - Revision history

http://osupdocs.forestry.oregonstate.edu/index.php?action=history&feed=atom&title=Traction_Laws Traction Laws - Revision history 2026-05-22T03:35:45Z Revision history for this page on the wiki MediaWiki 1.36.2 http://osupdocs.forestry.oregonstate.edu/index.php?title=Traction_Laws&diff=26141&oldid=prev Nairnj: /* References */ 2026-03-29T17:19:13Z

<p><span dir="auto"><span class="autocomment">References</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:19, 29 March 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l87">Line 87:</td> <td colspan="2" class="diff-lineno">Line 87:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><ref name='CRAMP'>J. A. Nairn, "Material Point Method Calculations with Explicit Cracks," <i>Computer Modeling in Engineering &amp; Sciences</i>, <b>4</b>, 649-664 (2003). ([http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/MPMCracks.pdf See PDF])</ref></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><ref name='CRAMP'>J. A. Nairn, "Material Point Method Calculations with Explicit Cracks," <i>Computer Modeling in Engineering &amp; Sciences</i>, <b>4</b>, 649-664 (2003). ([http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/MPMCracks.pdf See PDF])</ref></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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><ref name="mixedmode">J. A. Nairn and Y. E. Aimene "A re-evaluation of mixed-mode cohesive zone modeling based on strength concepts instead of traction laws" <del style="font-weight: bold; text-decoration: none;">submitted </del>(2021).</ref></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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><ref name="mixedmode">J. A. Nairn and Y. E. Aimene<ins style="font-weight: bold; text-decoration: none;">, </ins>"A re-evaluation of mixed-mode cohesive zone modeling based on strength concepts instead of traction laws"<ins style="font-weight: bold; text-decoration: none;">, ''Engineering Fracture Mechanics'', '''248''', 107704 </ins>(2021). <ins style="font-weight: bold; text-decoration: none;">([https://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/StrengthCZM.pdf See PDF])</ins></ref></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><ref name="czm">J. A. Nairn, "Analytical and Numerical Modeling of R Curves for Cracks with Bridging Zones" <i>Int. J. Fracture</i>, <b>155</b>, 167-181 (2009). ([http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/JBridging.pdf See PDF])</ref></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><ref name="czm">J. A. Nairn, "Analytical and Numerical Modeling of R Curves for Cracks with Bridging Zones" <i>Int. J. Fracture</i>, <b>155</b>, 167-181 (2009). ([http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/JBridging.pdf See PDF])</ref></div></td></tr> </table>

Nairnj http://osupdocs.forestry.oregonstate.edu/index.php?title=Traction_Laws&diff=7580&oldid=prev Nairnj: /* Fracture Mechanics J Integral */ 2021-01-03T18:20:03Z

<p><span dir="auto"><span class="autocomment">Fracture Mechanics J Integral</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:20, 3 January 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l53">Line 53:</td> <td colspan="2" class="diff-lineno">Line 53:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Fracture Mechanics J Integral ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Fracture Mechanics J Integral ===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 total J Integral for a crack with a cohesive zone is equal to the reported <tt>G</tt> for each debonding event.<ref name="rice"/> Unfortunately, this J integral is only equal to energy release rate when the crack growth is "self-similar crack growth."<ref name="rice"/> When modeling crack growth with cohesive zones, "self-similar crack growth" requires the cohesive damage length to remain constant. Thus J integral is equal to energy release rate if, and only if, the cohesive damage length remains constant. Whenever it is not constant, J integral still exists, but the method in the previous section has to be used instead to find energy release.<ref name="mixedmode"/></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 total J Integral for a crack with a cohesive zone is equal to the reported <tt>G</tt> for each debonding event.<ref name="rice"/> Unfortunately, this J integral is only equal to energy release rate when the crack growth is "self-similar crack growth."<ref name="rice"/> When modeling crack growth with cohesive zones, "self-similar crack growth" requires the cohesive damage length to remain constant. Thus J integral is equal to energy release rate if, and only if, the cohesive damage length remains constant. Whenever it is not constant, J integral still exists, but the method in the previous section has to be used instead to find energy release.<ref name="mixedmode"/> <ins style="font-weight: bold; text-decoration: none;">Furthermore, mode mixity during non-self-similar crack growth must use the mode I and mode II energy release found by the general methods and not rely on the report <tt>GI(%)</tt>.</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Traction Law Materials ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Traction Law Materials ==</div></td></tr> </table>

Nairnj http://osupdocs.forestry.oregonstate.edu/index.php?title=Traction_Laws&diff=7579&oldid=prev Nairnj: /* Fracture Mechanics J Integral */ 2021-01-03T18:18:13Z

<p><span dir="auto"><span class="autocomment">Fracture Mechanics J Integral</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:18, 3 January 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l53">Line 53:</td> <td colspan="2" class="diff-lineno">Line 53:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Fracture Mechanics J Integral ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Fracture Mechanics J Integral ===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 J Integral for a crack with a cohesive zone is equal to the reported <tt>G</tt> for each debonding event.<ref name="rice"/> Unfortunately, this J integral is only equal to energy release rate when the crack growth is "self-similar crack growth."<ref name="rice"/> When modeling crack growth with cohesive zones, "self-similar crack growth" requires the cohesive damage length to remain constant. Thus J integral is equal to energy release rate if, and only if, the cohesive damage length remains constant. Whenever it is not constant, J integral still exists, but the method in the previous section has to be used instead to find energy release.<ref name="mixedmode"/></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 <ins style="font-weight: bold; text-decoration: none;">total </ins>J Integral for a crack with a cohesive zone is equal to the reported <tt>G</tt> for each debonding event.<ref name="rice"/> Unfortunately, this J integral is only equal to energy release rate when the crack growth is "self-similar crack growth."<ref name="rice"/> When modeling crack growth with cohesive zones, "self-similar crack growth" requires the cohesive damage length to remain constant. Thus J integral is equal to energy release rate if, and only if, the cohesive damage length remains constant. Whenever it is not constant, J integral still exists, but the method in the previous section has to be used instead to find energy release.<ref name="mixedmode"/></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Traction Law Materials ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Traction Law Materials ==</div></td></tr> </table>

Nairnj http://osupdocs.forestry.oregonstate.edu/index.php?title=Traction_Laws&diff=7578&oldid=prev Nairnj: /* Fracture Mechanics J Integral */ 2021-01-03T18:17:56Z

<p><span dir="auto"><span class="autocomment">Fracture Mechanics J Integral</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:17, 3 January 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l53">Line 53:</td> <td colspan="2" class="diff-lineno">Line 53:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Fracture Mechanics J Integral ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Fracture Mechanics J Integral ===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 J Integral for a crack with a cohesive zone is equal to the reported <tt>G</tt> for each debonding event.<ref name="rice"/> Unfortunately, this J integral is only equal to energy release rate when the crack growth <del style="font-weight: bold; text-decoration: none;">for </del>"self-similar crack growth."<ref name="rice"/> When modeling crack growth with cohesive zones, "self-similar crack growth" <del style="font-weight: bold; text-decoration: none;">required </del>the cohesive damage length to remain constant. Thus J integral is equal to energy release rate if, and only if, the cohesive damage length remains constant. Whenever it is not constant, J integral still exists, but the method in the previous section has to be used instead to find energy release.<ref name="mixedmode"/></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 J Integral for a crack with a cohesive zone is equal to the reported <tt>G</tt> for each debonding event.<ref name="rice"/> Unfortunately, this J integral is only equal to energy release rate when the crack growth <ins style="font-weight: bold; text-decoration: none;">is </ins>"self-similar crack growth."<ref name="rice"/> When modeling crack growth with cohesive zones, "self-similar crack growth" <ins style="font-weight: bold; text-decoration: none;">requires </ins>the cohesive damage length to remain constant. Thus J integral is equal to energy release rate if, and only if, the cohesive damage length remains constant. Whenever it is not constant, J integral still exists, but the method in the previous section has to be used instead to find energy release.<ref name="mixedmode"/></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Traction Law Materials ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Traction Law Materials ==</div></td></tr> </table>

Nairnj http://osupdocs.forestry.oregonstate.edu/index.php?title=Traction_Laws&diff=7577&oldid=prev Nairnj: /* Fracture Mechanics J Integral */ 2021-01-03T18:17:00Z

<p><span dir="auto"><span class="autocomment">Fracture Mechanics J Integral</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:17, 3 January 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l53">Line 53:</td> <td colspan="2" class="diff-lineno">Line 53:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Fracture Mechanics J Integral ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Fracture Mechanics J Integral ===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 J Integral for a crack with a cohesive zone is equal to the <del style="font-weight: bold; text-decoration: none;">report </del><tt>G</tt> <del style="font-weight: bold; text-decoration: none;">reported </del>for each debonding event.<ref name="rice"/> Unfortunately, this J integral is only equal to energy release rate when the crack growth <del style="font-weight: bold; text-decoration: none;">is </del>"self-similar crack growth."<ref name="rice"/> When <del style="font-weight: bold; text-decoration: none;">model </del>crack growth with cohesive zones, J integral is equal to energy release <del style="font-weight: bold; text-decoration: none;">only </del>if, and only if, the cohesive damage length remains constant. Whenever it is not constant, J integral still exists, but the method in the previous section has to be used instead to find energy release.<name <del style="font-weight: bold; text-decoration: none;">ref</del>="mixedmode"/></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 J Integral for a crack with a cohesive zone is equal to the <ins style="font-weight: bold; text-decoration: none;">reported </ins><tt>G</tt> for each debonding event.<ref name="rice"/> Unfortunately, this J integral is only equal to energy release rate when the crack growth <ins style="font-weight: bold; text-decoration: none;">for </ins>"self-similar crack growth."<ref name="rice"/> When <ins style="font-weight: bold; text-decoration: none;">modeling </ins>crack growth with cohesive zones, <ins style="font-weight: bold; text-decoration: none;">"self-similar crack growth" required the cohesive damage length to remain constant. Thus </ins>J integral is equal to energy release <ins style="font-weight: bold; text-decoration: none;">rate </ins>if, and only if, the cohesive damage length remains constant. Whenever it is not constant, J integral still exists, but the method in the previous section has to be used instead to find energy release.<<ins style="font-weight: bold; text-decoration: none;">ref </ins>name="mixedmode"/></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Traction Law Materials ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Traction Law Materials ==</div></td></tr> </table>

Nairnj http://osupdocs.forestry.oregonstate.edu/index.php?title=Traction_Laws&diff=7576&oldid=prev Nairnj: /* Fracture Mechanics Energy Release Rate */ 2021-01-03T18:14:01Z

<p><span dir="auto"><span class="autocomment">Fracture Mechanics Energy Release Rate</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:14, 3 January 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l49">Line 49:</td> <td colspan="2" class="diff-lineno">Line 49:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* If the cohesive zone is modeling microcracks or microvoids that are not visible during experiments, the experiments likely correspond to the "Debonded Crack Length" (''i.e.'', the crack length not counting any with a still-bonded cohesive zone and a plotting option in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* If the cohesive zone is modeling microcracks or microvoids that are not visible during experiments, the experiments likely correspond to the "Debonded Crack Length" (''i.e.'', the crack length not counting any with a still-bonded cohesive zone and a plotting option in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]).</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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>* If the cohesive zone is modeling a visible process, such as fiber bridging in composite or wood crack growth, the experiment might be closer to sum of "Debonded Crack Length" and "Cohesive Damage Length" (''i.e.'', the crack length <del style="font-weight: bold; text-decoration: none;">include </del>a process zone defined as any cohesive zones beyond their elastic limit and the sum or two plotting options in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]). Note that the [[Cubic Traction Law]] has no elastic regime, which means <del style="font-weight: bold; text-decoration: none;">is </del>its cohesive damage length will include all cohesive zones after any finite deformation occurs. It is therefore better to avoid the [[Cubic Traction Law]] when modeling needs to determine the cohesive damage length.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>* If the cohesive zone is modeling a visible process, such as fiber bridging in composite or wood crack growth, the experiment might be closer to sum of "Debonded Crack Length" and "Cohesive Damage Length" (''i.e.'', the crack length <ins style="font-weight: bold; text-decoration: none;">including </ins>a process zone defined as any cohesive zones beyond their elastic limit and the sum or two plotting options in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]). Note that the [[Cubic Traction Law]] has no elastic regime, which means its cohesive damage length will include all cohesive zones after any finite deformation occurs. It is therefore better to avoid the [[Cubic Traction Law]] when modeling needs to determine the cohesive damage length.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Fracture Mechanics J Integral ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Fracture Mechanics J Integral ===</div></td></tr> </table>

Nairnj http://osupdocs.forestry.oregonstate.edu/index.php?title=Traction_Laws&diff=7575&oldid=prev Nairnj: /* Fracture Mechanics Energy Release Rate */ 2021-01-03T18:13:03Z

<p><span dir="auto"><span class="autocomment">Fracture Mechanics Energy Release Rate</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:13, 3 January 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l49">Line 49:</td> <td colspan="2" class="diff-lineno">Line 49:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* If the cohesive zone is modeling microcracks or microvoids that are not visible during experiments, the experiments likely correspond to the "Debonded Crack Length" (''i.e.'', the crack length not counting any with a still-bonded cohesive zone and a plotting option in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* If the cohesive zone is modeling microcracks or microvoids that are not visible during experiments, the experiments likely correspond to the "Debonded Crack Length" (''i.e.'', the crack length not counting any with a still-bonded cohesive zone and a plotting option in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]).</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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>* If the cohesive zone is modeling a visible process, such as fiber bridging in <del style="font-weight: bold; text-decoration: none;">composites </del>or wood crack growth, the experiment might be closer to sum of "Debonded Crack Length" and "Cohesive Damage Length" (''i.e.'', the crack length include a process zone defined as any cohesive zones beyond their elastic limit and the sum or two plotting options in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]). Note that the [[Cubic Traction Law]] has no elastic regime, which means is its cohesive damage length will include all cohesive zones after any finite deformation occurs. It is therefore better to avoid the [[Cubic Traction Law]] when modeling needs to determine the cohesive damage length.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>* If the cohesive zone is modeling a visible process, such as fiber bridging in <ins style="font-weight: bold; text-decoration: none;">composite </ins>or wood crack growth, the experiment might be closer to sum of "Debonded Crack Length" and "Cohesive Damage Length" (''i.e.'', the crack length include a process zone defined as any cohesive zones beyond their elastic limit and the sum or two plotting options in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]). Note that the [[Cubic Traction Law]] has no elastic regime, which means is its cohesive damage length will include all cohesive zones after any finite deformation occurs. It is therefore better to avoid the [[Cubic Traction Law]] when modeling needs to determine the cohesive damage length.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Fracture Mechanics J Integral ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Fracture Mechanics J Integral ===</div></td></tr> </table>

Nairnj http://osupdocs.forestry.oregonstate.edu/index.php?title=Traction_Laws&diff=7574&oldid=prev Nairnj: /* Fracture Mechanics Energy Release Rate */ 2021-01-03T18:12:39Z

<p><span dir="auto"><span class="autocomment">Fracture Mechanics Energy Release Rate</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:12, 3 January 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l47">Line 47:</td> <td colspan="2" class="diff-lineno">Line 47:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When using cohesive zones to model experiments, the key challenge is to determine ''effective'' crack length by methods that correspond to the experimentally-measured crack length. Some options are:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When using cohesive zones to model experiments, the key challenge is to determine ''effective'' crack length by methods that correspond to the experimentally-measured crack length. Some options are:</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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>* If the cohesive zone is modeling microcracks or microvoids that are not visible during experiments, the experiments likely correspond to the "Debonded Crack Length" (''i.e.'', the crack length not counting any with <del style="font-weight: bold; text-decoration: none;">intact </del>cohesive zone and a plotting option in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>* If the cohesive zone is modeling microcracks or microvoids that are not visible during experiments, the experiments likely correspond to the "Debonded Crack Length" (''i.e.'', the crack length not counting any with <ins style="font-weight: bold; text-decoration: none;">a still-bonded </ins>cohesive zone and a plotting option in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]).</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* If the cohesive zone is modeling a visible process, such as fiber bridging in composites or wood crack growth, the experiment might be closer to sum of "Debonded Crack Length" and "Cohesive Damage Length" (''i.e.'', the crack length include a process zone defined as any cohesive zones beyond their elastic limit and the sum or two plotting options in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]). Note that the [[Cubic Traction Law]] has no elastic regime, which means is its cohesive damage length will include all cohesive zones after any finite deformation occurs. It is therefore better to avoid the [[Cubic Traction Law]] when modeling needs to determine the cohesive damage length.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* If the cohesive zone is modeling a visible process, such as fiber bridging in composites or wood crack growth, the experiment might be closer to sum of "Debonded Crack Length" and "Cohesive Damage Length" (''i.e.'', the crack length include a process zone defined as any cohesive zones beyond their elastic limit and the sum or two plotting options in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]). Note that the [[Cubic Traction Law]] has no elastic regime, which means is its cohesive damage length will include all cohesive zones after any finite deformation occurs. It is therefore better to avoid the [[Cubic Traction Law]] when modeling needs to determine the cohesive damage length.</div></td></tr> </table>

Nairnj http://osupdocs.forestry.oregonstate.edu/index.php?title=Traction_Laws&diff=7573&oldid=prev Nairnj: /* Fracture Mechanics Energy Release Rate */ 2021-01-03T18:11:43Z

<p><span dir="auto"><span class="autocomment">Fracture Mechanics Energy Release Rate</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:11, 3 January 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l47">Line 47:</td> <td colspan="2" class="diff-lineno">Line 47:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When using cohesive zones to model experiments, the key challenge is to determine ''effective'' crack length by methods that correspond to the experimentally-measured crack length. Some options are:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When using cohesive zones to model experiments, the key challenge is to determine ''effective'' crack length by methods that correspond to the experimentally-measured crack length. Some options are:</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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>* If the cohesive zone is modeling microcracks or microvoids that are not visible during experiments, the experiments <del style="font-weight: bold; text-decoration: none;">most close </del>correspond to the "Debonded Crack Length" (''i.e.'', the crack length not counting any with intact cohesive zone and a plotting option in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>* If the cohesive zone is modeling microcracks or microvoids that are not visible during experiments, the experiments <ins style="font-weight: bold; text-decoration: none;">likely </ins>correspond to the "Debonded Crack Length" (''i.e.'', the crack length not counting any with intact cohesive zone and a plotting option in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]).</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* If the cohesive zone is modeling a visible process, such as fiber bridging in composites or wood crack growth, the experiment might be closer to sum of "Debonded Crack Length" and "Cohesive Damage Length" (''i.e.'', the crack length include a process zone defined as any cohesive zones beyond their elastic limit and the sum or two plotting options in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]). Note that the [[Cubic Traction Law]] has no elastic regime, which means is its cohesive damage length will include all cohesive zones after any finite deformation occurs. It is therefore better to avoid the [[Cubic Traction Law]] when modeling needs to determine the cohesive damage length.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* If the cohesive zone is modeling a visible process, such as fiber bridging in composites or wood crack growth, the experiment might be closer to sum of "Debonded Crack Length" and "Cohesive Damage Length" (''i.e.'', the crack length include a process zone defined as any cohesive zones beyond their elastic limit and the sum or two plotting options in [[NairnFEAMPM]] or [[NairnFEAMPMViz]]). Note that the [[Cubic Traction Law]] has no elastic regime, which means is its cohesive damage length will include all cohesive zones after any finite deformation occurs. It is therefore better to avoid the [[Cubic Traction Law]] when modeling needs to determine the cohesive damage length.</div></td></tr> </table>

Nairnj http://osupdocs.forestry.oregonstate.edu/index.php?title=Traction_Laws&diff=7572&oldid=prev Nairnj: /* Fracture Mechanics Energy Release Rate */ 2021-01-03T18:10:58Z

<p><span dir="auto"><span class="autocomment">Fracture Mechanics Energy Release Rate</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:10, 3 January 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l43">Line 43:</td> <td colspan="2" class="diff-lineno">Line 43:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Find total dissipated energy for all cohesive zones on one crack by summing [[MPM Archiving Options|czmdisp results]] for each zone times that zone's area. The net result is a force (in [[NairnFEAMPM]] or [[NairnFEAMPMViz]], this summation is done by plotting "CZM Mode I Force" and "CZM Mode II Force").</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Find total dissipated energy for all cohesive zones on one crack by summing [[MPM Archiving Options|czmdisp results]] for each zone times that zone's area. The net result is a force (in [[NairnFEAMPM]] or [[NairnFEAMPMViz]], this summation is done by plotting "CZM Mode I Force" and "CZM Mode II Force").</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Cross plot mode forces as a function of ''effective'' crack length</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Cross plot mode forces as a function of ''effective'' crack length</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 slopes of the cross plots are mode I and mode II energy release rates as <del style="font-weight: bold; text-decoration: none;">function </del>of crack length. Their sum is total energy release rate.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 slopes of the cross plots are mode I and mode II energy release rates as <ins style="font-weight: bold; text-decoration: none;">functions </ins>of crack length. Their sum is total energy release rate.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When using cohesive zones to model experiments, the key challenge is to determine ''effective'' crack length by methods that correspond to the experimentally-measured crack length. Some options are:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When using cohesive zones to model experiments, the key challenge is to determine ''effective'' crack length by methods that correspond to the experimentally-measured crack length. Some options are:</div></td></tr> </table>

Nairnj