Commit e9ee2373 authored by Jeremy BLEYER's avatar Jeremy BLEYER

Added contact penalty example and licenses

parent 53f479f5
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# .. # gedit: set fileencoding=utf8 :
# .. raw:: html
#
# <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
#
# .. _LinearElasticity2D:
#
# .. _LinearElasticity2D:
#
# =========================
# 2D linear elasticity
......
#
raw:: html
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
# .. _ModalAnalysis:
#
# ==========================================
......
#
# .. # gedit: set fileencoding=utf8 :
# .. raw:: html
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# <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
#
# .. _OrthotropicElasticity:
#
......
#
raw:: html
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
# .. _ReissnerMindlinDG:
#
# ==============================================================
......
#
raw:: html
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
# .. _ReissnerMindlinQuads:
#
# ==========================================
......
.. _vonMisesPlasticity:
.. raw:: html
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
==================================================
Elasto-plastic analysis of a 2D von Mises material
==================================================
......
.. # gedit: set fileencoding=utf8 :
.. raw:: html
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
.. _LinearElasticity2D:
.. _LinearElasticity2D:
=========================
2D linear elasticity
......
.. # gedit: set fileencoding=utf8 :
.. raw:: html
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
.. _OrthotropicElasticity:
......
.. raw:: html
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
.. _ModalAnalysis:
......
.. raw:: html
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
.. _ReissnerMindlinDG:
......
.. raw:: html
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
.. _ReissnerMindlinQuads:
......
......@@ -22,6 +22,10 @@ illustrating the versatility of FEniCS.
The full set of demos can be obtained from the *COmputational MEchanics Toolbox* (COMET) available at
https://gitlab.enpc.fr/jeremy.bleyer/comet-fenics.
--------------------
Citing and license
--------------------
If you find these demos useful for your research work, please consider citing them using the following
Zenodo DOI https://doi.org/10.5281/zenodo.1287832
......@@ -34,6 +38,9 @@ Zenodo DOI https://doi.org/10.5281/zenodo.1287832
author={Jeremy Bleyer},
year={2018}}
All this work is licensed under the `Creative Commons Attribution-ShareAlike 4.0 International License <http://creativecommons.org/licenses/by-sa/4.0/>`_ |license|.
.. |license| image:: https://i.creativecommons.org/l/by-sa/4.0/88x31.png
-----------------------
How do I get started ?
......
......@@ -51,8 +51,8 @@
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="elasto-plastic-analysis-of-a-2d-von-mises-material">
<span id="vonmisesplasticity"></span><h1>Elasto-plastic analysis of a 2D von Mises material<a class="headerlink" href="#elasto-plastic-analysis-of-a-2d-von-mises-material" title="Permalink to this headline"></a></h1>
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p><div class="section" id="elasto-plastic-analysis-of-a-2d-von-mises-material">
<h1>Elasto-plastic analysis of a 2D von Mises material<a class="headerlink" href="#elasto-plastic-analysis-of-a-2d-von-mises-material" title="Permalink to this headline"></a></h1>
<div class="section" id="introduction">
<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
<p>This example is concerned with the incremental analysis of an elasto-plastic
......@@ -410,6 +410,7 @@ when considering a zero hardening modulus.</p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -51,7 +51,7 @@
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="d-linear-elasticity">
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p><div class="section" id="d-linear-elasticity">
<span id="linearelasticity2d"></span><h1>2D linear elasticity<a class="headerlink" href="#d-linear-elasticity" title="Permalink to this headline"></a></h1>
<div class="section" id="introduction">
<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
......@@ -220,6 +220,7 @@ writing/reading. Prefered output format is now .xdmf:</p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -217,7 +217,7 @@ div.nboutput div.output_area.stderr {
.ansi-bold { font-weight: bold; }
.ansi-underline { text-decoration: underline; }
</style>
<div class="admonition note">
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p><div class="admonition note">
<p class="admonition-title">The corresponding files can be obtained from:</p>
<ul class="simple">
<li>Jupyter Notebook: <a class="reference download internal" href="../../_downloads/axisymmetric_elasticity.ipynb" download=""><code class="xref download docutils literal"><span class="pre">axisymmetric_elasticity.ipynb</span></code></a></li>
......@@ -2805,6 +2805,7 @@ if (IPython.notebook.kernel != null) {
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -51,7 +51,7 @@
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="orthotropic-linear-elasticity">
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p><div class="section" id="orthotropic-linear-elasticity">
<span id="orthotropicelasticity"></span><h1>Orthotropic linear elasticity<a class="headerlink" href="#orthotropic-linear-elasticity" title="Permalink to this headline"></a></h1>
<div class="section" id="introduction">
<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
......@@ -198,6 +198,7 @@ that:</p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -51,7 +51,7 @@
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="modal-analysis-of-an-elastic-structure">
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p><div class="section" id="modal-analysis-of-an-elastic-structure">
<span id="modalanalysis"></span><h1>Modal analysis of an elastic structure<a class="headerlink" href="#modal-analysis-of-an-elastic-structure" title="Permalink to this headline"></a></h1>
<div class="section" id="introduction">
<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
......@@ -261,6 +261,7 @@ and the beam theory eigenfrequencies :</p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -217,7 +217,7 @@ div.nboutput div.output_area.stderr {
.ansi-bold { font-weight: bold; }
.ansi-underline { text-decoration: underline; }
</style>
<div class="admonition note">
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p><div class="admonition note">
<p class="admonition-title">The corresponding files can be obtained from:</p>
<ul class="simple">
<li>Jupyter Notebook: <a class="reference download internal" href="../../_downloads/periodic_homog_elas.ipynb" download=""><code class="xref download docutils literal"><span class="pre">periodic_homog_elas.ipynb</span></code></a></li>
......@@ -2141,6 +2141,7 @@ if (IPython.notebook.kernel != null) {
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -51,7 +51,7 @@
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="reissner-mindlin-plate-with-a-discontinuous-galerkin-approach">
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p><div class="section" id="reissner-mindlin-plate-with-a-discontinuous-galerkin-approach">
<span id="reissnermindlindg"></span><h1>Reissner-Mindlin plate with a Discontinuous-Galerkin approach<a class="headerlink" href="#reissner-mindlin-plate-with-a-discontinuous-galerkin-approach" title="Permalink to this headline"></a></h1>
<div class="section" id="introduction">
<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
......@@ -195,6 +195,7 @@ so that no term arise in the linear functional):</p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -51,7 +51,7 @@
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="reissner-mindlin-plate-with-quadrilaterals">
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p><div class="section" id="reissner-mindlin-plate-with-quadrilaterals">
<span id="reissnermindlinquads"></span><h1>Reissner-Mindlin plate with Quadrilaterals<a class="headerlink" href="#reissner-mindlin-plate-with-quadrilaterals" title="Permalink to this headline"></a></h1>
<div class="section" id="introduction">
<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
......@@ -188,6 +188,7 @@ the thin plate solution.</p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -217,7 +217,7 @@ div.nboutput div.output_area.stderr {
.ansi-bold { font-weight: bold; }
.ansi-underline { text-decoration: underline; }
</style>
<div class="admonition note">
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p><div class="admonition note">
<p class="admonition-title">The corresponding files can be obtained from:</p>
<ul class="simple">
<li>Jupyter Notebook: <a class="reference download internal" href="../../_downloads/thermoelasticity.ipynb" download=""><code class="xref download docutils literal"><span class="pre">thermoelasticity.ipynb</span></code></a></li>
......@@ -4327,6 +4327,7 @@ if (IPython.notebook.kernel != null) {
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -217,7 +217,7 @@ div.nboutput div.output_area.stderr {
.ansi-bold { font-weight: bold; }
.ansi-underline { text-decoration: underline; }
</style>
<div class="admonition note">
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p><div class="admonition note">
<p class="admonition-title">The corresponding files can be obtained from:</p>
<ul class="simple">
<li>Jupyter Notebook: <a class="reference download internal" href="../../_downloads/thermoelasticity_transient.ipynb" download=""><code class="xref download docutils literal"><span class="pre">thermoelasticity_transient.ipynb</span></code></a></li>
......@@ -2891,6 +2891,7 @@ Mechanics and Engineering, 85(3), 349-365.
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -63,6 +63,7 @@
<ul>
<li class="toctree-l1"><a class="reference internal" href="intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -71,6 +71,7 @@
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -55,6 +55,7 @@
<ul>
<li class="toctree-l1"><a class="reference internal" href="intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#about-the-author">About the author</a></li>
</ul>
......@@ -103,6 +104,7 @@
<ul>
<li class="toctree-l1"><a class="reference internal" href="intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -64,6 +64,9 @@ getting started with FEniCS using solid mechanics examples.</p>
illustrating the versatility of FEniCS.</p>
<p>The full set of demos can be obtained from the <em>COmputational MEchanics Toolbox</em> (COMET) available at
<a class="reference external" href="https://gitlab.enpc.fr/jeremy.bleyer/comet-fenics">https://gitlab.enpc.fr/jeremy.bleyer/comet-fenics</a>.</p>
</div>
<div class="section" id="citing-and-license">
<h2>Citing and license<a class="headerlink" href="#citing-and-license" title="Permalink to this headline"></a></h2>
<p>If you find these demos useful for your research work, please consider citing them using the following
Zenodo DOI <a class="reference external" href="https://doi.org/10.5281/zenodo.1287832">https://doi.org/10.5281/zenodo.1287832</a></p>
<div class="highlight-none"><div class="highlight"><pre><span></span>@article{bleyer2018numericaltours,
......@@ -74,6 +77,7 @@ author={Jeremy Bleyer},
year={2018}}
</pre></div>
</div>
<p>All this work is licensed under the <a class="reference external" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a> <img alt="license" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png" />.</p>
</div>
<div class="section" id="how-do-i-get-started">
<h2>How do I get started ?<a class="headerlink" href="#how-do-i-get-started" title="Permalink to this headline"></a></h2>
......@@ -110,6 +114,7 @@ a joint research unit of <a class="reference external" href="http://www.enpc.fr"
<ul class="current">
<li class="toctree-l1 current"><a class="current reference internal" href="#">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="#about-the-author">About the author</a></li>
</ul>
......@@ -121,6 +126,7 @@ a joint research unit of <a class="reference external" href="http://www.enpc.fr"
<li class="toctree-l2"><a class="reference internal" href="demo/thermoelasticity/thermoelasticity.html">Linear thermoelasticity (weak coupling)</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/thermoelasticity/thermoelasticity_transient.html">Thermo-elastic evolution problem (full coupling)</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/modal_analysis_dynamics/cantilever_modal.py.html">Modal analysis of an elastic structure</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/elastodynamics/demo_elastodynamics.py.html">Time-integration of elastodynamics equation</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="homogenization.html">Homogenization of heterogeneous materials</a><ul>
......@@ -128,10 +134,13 @@ a joint research unit of <a class="reference external" href="http://www.enpc.fr"
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="demo/viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/contact/penalty.html">Hertzian contact with a rigid indenter using a penalty approach</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
<li class="toctree-l1"><a class="reference internal" href="beams_and_plates.html">Beams and plates</a><ul>
<li class="toctree-l2"><a class="reference internal" href="demo/timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
</ul>
......
......@@ -77,6 +77,7 @@
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -73,6 +73,7 @@
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#about-the-author">About the author</a></li>
</ul>
......
......@@ -86,6 +86,7 @@
<ul>
<li class="toctree-l1"><a class="reference internal" href="intro.html">Introduction</a><ul>
<li class="toctree-l2"><a class="reference internal" href="intro.html#what-is-it-about">What is it about ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#citing-and-license">Citing and license</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#how-do-i-get-started">How do I get started ?</a></li>
<li class="toctree-l2"><a class="reference internal" href="intro.html#about-the-author">About the author</a></li>
</ul>
......
This diff is collapsed.
......@@ -88,9 +88,11 @@
<li class="toctree-l1"><a class="reference internal" href="linear_problems.html">Linear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="demo/elasticity/2D_elasticity.py.html">2D linear elasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/elasticity/orthotropic_elasticity.py.html">Orthotropic linear elasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/elasticity/axisymmetric_elasticity.html">Axisymmetric formulation for elastic structures of revolution</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/thermoelasticity/thermoelasticity.html">Linear thermoelasticity (weak coupling)</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/thermoelasticity/thermoelasticity_transient.html">Thermo-elastic evolution problem (full coupling)</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/modal_analysis_dynamics/cantilever_modal.py.html">Modal analysis of an elastic structure</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/elastodynamics/demo_elastodynamics.py.html">Time-integration of elastodynamics equation</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="homogenization.html">Homogenization of heterogeneous materials</a><ul>
......@@ -98,10 +100,13 @@
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="demo/viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/contact/penalty.html">Hertzian contact with a rigid indenter using a penalty approach</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
<li class="toctree-l1"><a class="reference internal" href="beams_and_plates.html">Beams and plates</a><ul>
<li class="toctree-l2"><a class="reference internal" href="demo/timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
</ul>
......
......@@ -280,6 +280,10 @@ texinfo_documents = [
#{% set docname = env.doc2path(env.docname, base='doc') %}
nbsphinx_prolog = r"""
{% set docname = env.docname.split("/")[-1] %}
.. raw:: html
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
.. role:: raw-html(raw)
:format: html
.. nbinfo::
......
......@@ -22,6 +22,10 @@ illustrating the versatility of FEniCS.
The full set of demos can be obtained from the *COmputational MEchanics Toolbox* (COMET) available at
https://gitlab.enpc.fr/jeremy.bleyer/comet-fenics.
--------------------
Citing and license
--------------------
If you find these demos useful for your research work, please consider citing them using the following
Zenodo DOI https://doi.org/10.5281/zenodo.1287832
......@@ -34,6 +38,9 @@ Zenodo DOI https://doi.org/10.5281/zenodo.1287832
author={Jeremy Bleyer},
year={2018}}
All this work is licensed under the `Creative Commons Attribution-ShareAlike 4.0 International License <http://creativecommons.org/licenses/by-sa/4.0/>`_ |license|.
.. |license| image:: https://i.creativecommons.org/l/by-sa/4.0/88x31.png
-----------------------
How do I get started ?
......
.. _vonMisesPlasticity:
.. raw:: html
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><p align="center"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png"/></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a></p>
==================================================
Elasto-plastic analysis of a 2D von Mises material
==================================================
......
......@@ -6,7 +6,10 @@
"source": [
"# Hertzian contact with a rigid indenter using a penalty approach\n",
"\n",
"In this numerical tour, we explore the formulation of frictionless contact between a rigid surface (the indenter) and an elastic domain, representing an infinite half-space for the present case. Contact will be solved using a penalty formulation, that is small interpenetration between the solid and the identer will be authorized. Prerequisites for this tour are the formulation of an linear elasticity problem and the resolution of a general nonlinear variational problem."
"In this numerical tour, we explore the formulation of frictionless contact between a rigid surface (the indenter) and an elastic domain, representing an infinite half-space for the present case. Contact will be solved using a penalty formulation, that is small interpenetration between the solid and the indenter will be authorized. Prerequisites for this tour are the formulation of an linear elasticity problem and the resolution of a general nonlinear variational problem. See for instance:\n",
"\n",
"* https://comet-fenics.readthedocs.io/en/latest/demo/elasticity/2D_elasticity.py.html\n",
"* https://fenicsproject.org/docs/dolfin/2018.1.0/python/demos/hyperelasticity/demo_hyperelasticity.py.html"
]
},
{
......@@ -28,13 +31,13 @@
"source": [
"The elastic (isotropic $E,\\nu$) solid will be represented by a 3D cubic domain of unit dimension and contact will take place on its top surface $z=0$, centered at $x=y=0$. Symmetry conditions will be applied on the $x=0$ and $y=0$ surfaces whereas the bottom surface $z=-1$ will be fully fixed. If contact appears on a small region of extent $a\\ll 1$, the problem can then be considered to be a good approximation of contact on a semi-infinite domain.\n",
"\n",
"The rigid indenter will not be explictly modeled (in terms of mesh in particular) but instead its distance with respect to the solid top surface will be given as an ``Expression``. We will also consider that the indenter radius $R$ is sufficiently large with respect to the contact region characteristic size $a$ so that the spherical surface can be approximated by a parabola. In this case, the distance between such an indenter and the top surface can be written as:\n",
"The rigid indenter will not be explictly modeled (in particular it will not be meshed) but instead its distance with respect to the solid top surface will be given as an ``Expression``. We will also consider that the indenter radius $R$ is sufficiently large with respect to the contact region characteristic size $a$ so that the spherical surface can be approximated by a parabola. In this case, the distance between such an indenter and the top surface can be written as:\n",
"\n",
"\\begin{equation}\n",
"h(x,y) = h_0 + \\dfrac{1}{2R}(x^2+y^2)\n",
"\\end{equation}\n",
"\n",
"where $h_0$ is the initial gap between both surfaces at $x=y=0$. Obviously, if $h_0>0$ there is no contact between both surfaces, contact appears only if $h_0=-d<0$ where $d$ will be the indenter depth inside the surface. This classical problem admits the following known analytical solution **[REF?]**:\n",
"where $h_0$ is the initial gap between both surfaces at $x=y=0$. Obviously, if $h_0>0$ there is no contact between both surfaces, contact appears only if $h_0=-d<0$ where $d$ will be the indenter depth inside the surface. This classical problem admits the following known analytical solution [[1,2]](#References):\n",
"\n",
"* the contact area is of circular shape and radius $a=\\sqrt{Rd}$\n",
"* the force exerted by the indenter onto the surface is $F=\\dfrac{4}{3}\\dfrac{E}{1-\\nu^2}ad$\n",
......@@ -66,40 +69,49 @@
"g \\geq 0, p\\geq 0, g\\cdot p =0 \\text{ on }\\Gamma\n",
"\\end{equation}\n",
"\n",
"where $g=h-u$ is the gap between the obstacle surface and the solid surface and $p$ is the pressure. One of the most simple way to solve approximately this contact condition consists in replacing the previous complementary conditions by the following penalized condition:\n",
"where $g=h-u$ is the gap between the obstacle surface and the solid surface and $p=-\\sigma_{zz}$ is the pressure. One of the most simple way to solve approximately this contact condition consists in replacing the previous complementary conditions by the following penalized condition:\n",
"\n",
"\\begin{equation}\n",
"p = k\\ppos(-g)\n",
"p = k\\langle -g\\rangle_+ = k\\langle u-h\\rangle_+\n",
"\\end{equation}\n",
"\n",
"where $k$ is a large penalizing stiffness coefficient. With the previous relation, the pressure will be positive but a small negative gap will be authorized. "
"where $\\langle x\\rangle_+ = (|x|+x)/2$ is the positive part (Mackauley bracket) and $k$ is a large penalizing stiffness coefficient. With the previous relation, the pressure will be positive but a small negative gap will be authorized.\n",
"\n",