https://www.scipedia.com/wd/index.php?action=history&feed=atom&title=Wick_et_al_2024aWick et al 2024a - Revision history2026-05-07T18:22:07ZRevision history for this page on the wikiMediaWiki 1.27.0-wmf.10https://www.scipedia.com/wd/index.php?title=Wick_et_al_2024a&diff=305157&oldid=prevJSanchez: JSanchez moved page Draft Sanchez Pinedo 116769186 to Wick et al 2024a2024-06-28T11:14:22Z<p>JSanchez moved page <a href="/public/Draft_Sanchez_Pinedo_116769186" class="mw-redirect" title="Draft Sanchez Pinedo 116769186">Draft Sanchez Pinedo 116769186</a> to <a href="/public/Wick_et_al_2024a" title="Wick et al 2024a">Wick et al 2024a</a></p>
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</td></tr></table>JSanchezhttps://www.scipedia.com/wd/index.php?title=Wick_et_al_2024a&diff=305156&oldid=prevJSanchez at 11:14, 28 June 20242024-06-28T11:14:13Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In this work, we consider one key component, namely the wave equation, of a recently proposed space-time variational material model. The overall model is derived from a thermodynamically consistent Hamilton functional in the space-time cylinder in which mechanics, temperature and internal variables couple. Through the derivation, rather unusual end time conditions for the second-order in time wave equation arise. In order to understand their behavior better, we solely focus on the wave equation (neglecting temperature and internal variables) and formulate a Galerkin finite element discretization in time and space. Based on this discretization and the corresponding implementation, some numerical simulations are conducted. Therein, both traditional initial conditions for the displacements and the velocities are considered, as well as our newly proposed conditions for initial time and final time acting on the velocity variable only</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In this work, we consider one key component, namely the wave equation, of a recently proposed space-time variational material model. The overall model is derived from a thermodynamically consistent Hamilton functional in the space-time cylinder in which mechanics, temperature and internal variables couple. Through the derivation, rather unusual end time conditions for the second-order in time wave equation arise. In order to understand their behavior better, we solely focus on the wave equation (neglecting temperature and internal variables) and formulate a Galerkin finite element discretization in time and space. Based on this discretization and the corresponding implementation, some numerical simulations are conducted. Therein, both traditional initial conditions for the displacements and the velocities are considered, as well as our newly proposed conditions for initial time and final time acting on the velocity variable only</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
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</table>JSanchezhttps://www.scipedia.com/wd/index.php?title=Wick_et_al_2024a&diff=305154&oldid=prevJSanchez at 11:14, 28 June 20242024-06-28T11:14:11Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 11:14, 28 June 2024</td>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">                                </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Abstract==</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In this work, we consider one key component, namely the wave equation, of a recently proposed space-time variational material model. The overall model is derived from a thermodynamically consistent Hamilton functional in the space-time cylinder in which mechanics, temperature and internal variables couple. Through the derivation, rather unusual end time conditions for the second-order in time wave equation arise. In order to understand their behavior better, we solely focus on the wave equation (neglecting temperature and internal variables) and formulate a Galerkin finite element discretization in time and space. Based on this discretization and the corresponding implementation, some numerical simulations are conducted. Therein, both traditional initial conditions for the displacements and the velocities are considered, as well as our newly proposed conditions for initial time and final time acting on the velocity variable only</ins></div></td></tr>
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</table>JSanchezhttps://www.scipedia.com/wd/index.php?title=Wick_et_al_2024a&diff=305153&oldid=prevJSanchez: Created blank page2024-06-28T11:14:09Z<p>Created blank page</p>
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