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Documenter.jl committed Oct 15, 2024
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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.11.0","generation_timestamp":"2024-10-14T23:22:07","documenter_version":"1.7.0"}}
{"documenter":{"julia_version":"1.11.0","generation_timestamp":"2024-10-15T09:23:43","documenter_version":"1.7.0"}}
54 changes: 27 additions & 27 deletions dev/api_reference/index.html
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2 changes: 1 addition & 1 deletion dev/expl_continuumbased/index.html
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\frac{\boldsymbol{\Delta x}^{ik} \times \boldsymbol{a}^{ijk}}{a^{ijk}} \; \mathrm{d} V_2^i \; .\]</p><table><tr><th style="text-align: left">Size</th><th style="text-align: left">Symbol</th><th style="text-align: left">Unit</th></tr><tr><td style="text-align: left">Relative area measures</td><td style="text-align: left"><span>$A^{ijk}$</span>, <span>$a^{ijk}$</span>, <span>$\boldsymbol{a}^{ijk}$</span></td><td style="text-align: left"><span>$[\mathrm{m}^2]$</span></td></tr><tr><td style="text-align: left">Effective two-neighbor volume</td><td style="text-align: left"><span>$V_2^i$</span></td><td style="text-align: left"><span>$[\mathrm{m}^6]$</span></td></tr><tr><td style="text-align: left">Number of two-neighbor interactions</td><td style="text-align: left"><span>$N_2^i$</span></td><td style="text-align: left"><span>$[-]$</span></td></tr><tr><td style="text-align: left">Material constant</td><td style="text-align: left"><span>$C_2$</span></td><td style="text-align: left"><span>$[\frac{\mathrm{kg}}{\mathrm{m}^9\mathrm{s}^2}]$</span></td></tr></table><h2 id="Three-neighbor-interactions"><a class="docs-heading-anchor" href="#Three-neighbor-interactions">Three-neighbor interactions</a><a id="Three-neighbor-interactions-1"></a><a class="docs-heading-anchor-permalink" href="#Three-neighbor-interactions" title="Permalink"></a></h2><img src="https://github.com/kaipartmann/Peridynamics.jl/assets/68582683/e908c804-a6d4-4bf6-b75a-988f33989213" width="250"/><p>Three-neighbor interactions regard the volume defined by the bond vectors between point <span>$i$</span> and its three neighbors <span>$j$</span>, <span>$k$</span> and <span>$l$</span>:</p><p class="math-container">\[V^{ijkl} = \left(\boldsymbol{\Delta X}^{ij} \times \boldsymbol{\Delta X}^{ik}\right) \cdot \boldsymbol{\Delta X}^{il} \;,\qquad
v^{ijkl} = \left(\boldsymbol{\Delta x}^{ij} \times \boldsymbol{\Delta x}^{ik}\right) \cdot \boldsymbol{\Delta x}^{il} \;.\]</p><p>Additionally, the effective three-neighbor volume</p><p class="math-container">\[ V_3^i = \frac{ \left(V_\mathcal{H}^i\right)^3}{N_3^i} \; .\]</p><p>is defined. For the internal force density of three-neighbor interactions, the equation</p><p class="math-container">\[\boldsymbol{b}_{3}^{\mathrm{int}, \, i} =
3 \, C_3 \int_{\mathcal{H}_3^i} \left( \frac{\left|{v^{ijkl}}\right|}{\left|{V^{ijkl}}\right|} - 1 \right)
\frac{\left(\boldsymbol{\Delta x}^{ik} \times \boldsymbol{\Delta x}^{il}\right) v^{ijkl}}{\left|{v^{ijkl}}\right|} \; \mathrm{d} V_3^i\]</p><p>with the material constant <span>$C_3$</span> is used.</p><table><tr><th style="text-align: left">Size</th><th style="text-align: left">Symbol</th><th style="text-align: left">Unit</th></tr><tr><td style="text-align: left">Relative volume measures</td><td style="text-align: left"><span>$V^{ijkl}$</span>, <span>$v^{ijkl}$</span></td><td style="text-align: left"><span>$[\mathrm{m}^3]$</span></td></tr><tr><td style="text-align: left">Effective three-neighbor volume</td><td style="text-align: left"><span>$V_3^i$</span></td><td style="text-align: left"><span>$[\mathrm{m}^9]$</span></td></tr><tr><td style="text-align: left">Number of three-neighbor interactions</td><td style="text-align: left"><span>$N_3^i$</span></td><td style="text-align: left"><span>$[-]$</span></td></tr><tr><td style="text-align: left">Material constant</td><td style="text-align: left"><span>$C_3$</span></td><td style="text-align: left"><span>$[\frac{\mathrm{kg}}{\mathrm{m}^{13}\mathrm{s}^2}]$</span></td></tr></table></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../expl_nosbased/">« Non-ordinary state-based peridynamics</a><a class="docs-footer-nextpage" href="../expl_damage/">Damage in peridynamics formulations »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 14 October 2024 23:22">Monday 14 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\frac{\left(\boldsymbol{\Delta x}^{ik} \times \boldsymbol{\Delta x}^{il}\right) v^{ijkl}}{\left|{v^{ijkl}}\right|} \; \mathrm{d} V_3^i\]</p><p>with the material constant <span>$C_3$</span> is used.</p><table><tr><th style="text-align: left">Size</th><th style="text-align: left">Symbol</th><th style="text-align: left">Unit</th></tr><tr><td style="text-align: left">Relative volume measures</td><td style="text-align: left"><span>$V^{ijkl}$</span>, <span>$v^{ijkl}$</span></td><td style="text-align: left"><span>$[\mathrm{m}^3]$</span></td></tr><tr><td style="text-align: left">Effective three-neighbor volume</td><td style="text-align: left"><span>$V_3^i$</span></td><td style="text-align: left"><span>$[\mathrm{m}^9]$</span></td></tr><tr><td style="text-align: left">Number of three-neighbor interactions</td><td style="text-align: left"><span>$N_3^i$</span></td><td style="text-align: left"><span>$[-]$</span></td></tr><tr><td style="text-align: left">Material constant</td><td style="text-align: left"><span>$C_3$</span></td><td style="text-align: left"><span>$[\frac{\mathrm{kg}}{\mathrm{m}^{13}\mathrm{s}^2}]$</span></td></tr></table></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../expl_nosbased/">« Non-ordinary state-based peridynamics</a><a class="docs-footer-nextpage" href="../expl_damage/">Damage in peridynamics formulations »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Tuesday 15 October 2024 09:23">Tuesday 15 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2 changes: 1 addition & 1 deletion dev/expl_damage/index.html
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2 \, C_2 \int_{\mathcal{H}_2^i} d^{ijk} \left( \frac{a^{ijk}}{A^{ijk}} - 1 \right)
\frac{\boldsymbol{\Delta x}^{ik} \times \boldsymbol{a}^{ijk}}{a^{ijk}} \; \mathrm{d} V_2^i \]</p><p>with the two-neighbor interaction failure quantity <span>$d^{ijk} \in \{0;1\}$</span>.</p><p>For three-neighbor interactions the internal force density eventually reads</p><p class="math-container">\[\boldsymbol{b}_{3}^{\mathrm{int}, \, i} =
3 \, C_3 \int_{\mathcal{H}_3^i} d^{ijkl} \left( \frac{\left|{v^{ijkl}}\right|}{\left|{V^{ijkl}}\right|} - 1 \right)
\frac{\left(\boldsymbol{\Delta x}^{ik} \times \boldsymbol{\Delta x}^{il}\right) v^{ijkl}}{\left|{v^{ijkl}}\right|} \; \mathrm{d} V_3^i\]</p><p>with the three-neighbor interaction failure quantity <span>$d^{ijkl} \in \{0;1\}$</span>.</p><table><tr><th style="text-align: left">Size</th><th style="text-align: left">Symbol</th><th style="text-align: left">Unit</th></tr><tr><td style="text-align: left">Bond failure quantity</td><td style="text-align: left"><span>$d^{ij} \in \{0;1\}$</span></td><td style="text-align: left"><span>$[-]$</span></td></tr><tr><td style="text-align: left">Two-neighbor interaction failure quantity</td><td style="text-align: left"><span>$d^{ijk} \in \{0;1\}$</span></td><td style="text-align: left"><span>$[-]$</span></td></tr><tr><td style="text-align: left">Three-neighbor interaction failure quantity</td><td style="text-align: left"><span>$d^{ijkl} \in \{0;1\}$</span></td><td style="text-align: left"><span>$[-]$</span></td></tr></table></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../expl_continuumbased/">« Continuum-kinematics-inspired peridynamics</a><a class="docs-footer-nextpage" href="../expl_references/">References »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 14 October 2024 23:22">Monday 14 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\frac{\left(\boldsymbol{\Delta x}^{ik} \times \boldsymbol{\Delta x}^{il}\right) v^{ijkl}}{\left|{v^{ijkl}}\right|} \; \mathrm{d} V_3^i\]</p><p>with the three-neighbor interaction failure quantity <span>$d^{ijkl} \in \{0;1\}$</span>.</p><table><tr><th style="text-align: left">Size</th><th style="text-align: left">Symbol</th><th style="text-align: left">Unit</th></tr><tr><td style="text-align: left">Bond failure quantity</td><td style="text-align: left"><span>$d^{ij} \in \{0;1\}$</span></td><td style="text-align: left"><span>$[-]$</span></td></tr><tr><td style="text-align: left">Two-neighbor interaction failure quantity</td><td style="text-align: left"><span>$d^{ijk} \in \{0;1\}$</span></td><td style="text-align: left"><span>$[-]$</span></td></tr><tr><td style="text-align: left">Three-neighbor interaction failure quantity</td><td style="text-align: left"><span>$d^{ijkl} \in \{0;1\}$</span></td><td style="text-align: left"><span>$[-]$</span></td></tr></table></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../expl_continuumbased/">« Continuum-kinematics-inspired peridynamics</a><a class="docs-footer-nextpage" href="../expl_references/">References »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Tuesday 15 October 2024 09:23">Tuesday 15 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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