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<section id="modules">
<h1>Modules<a class="headerlink" href="#modules" title="Link to this heading">¶</a></h1>
<section id="module-pylabfea.basic">
<span id="module-basic"></span><h2>Module Basic<a class="headerlink" href="#module-pylabfea.basic" title="Link to this heading">¶</a></h2>
<p>Module pylabfea.basic introduces basic methods and attributes like calculation of
equivalent stresses and strain, conversions of
cylindrical to principal stresses and vice versa, and the classes <code class="docutils literal notranslate"><span class="pre">Stress</span></code> and <code class="docutils literal notranslate"><span class="pre">Strain</span></code>
for efficient operations with these quantities.</p>
<p>uses NumPy, pickle</p>
<p>Version: 4.0 (2021-11-27)
Author: Alexander Hartmaier, ICAMS/Ruhr University Bochum, Germany
Email: <a class="reference external" href="mailto:alexander.hartmaier%40rub.de">alexander<span>.</span>hartmaier<span>@</span>rub<span>.</span>de</a>
distributed under GNU General Public License (GPLv3)</p>
<dl class="py class">
<dt class="sig sig-object py" id="pylabfea.basic.Strain">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">Strain</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sv</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#Strain"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.Strain" title="Link to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.13)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
<p>Stores and converts Voigt strain tensors into different formats,
calculates principle strain and equivalent strain.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>sv</strong> (<em>list-like object</em><em>, </em><em>must be 1D with length 6</em>) – Voigt-strain components</p>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">voigt,</span> <span class="pre">v</span></span></dt>
<dd><p>Strain tensor in Voigt notation</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>1d-array (size 6)</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">tens,</span> <span class="pre">t</span></span></dt>
<dd><p>Strain tensor in matrix notation</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>3x3 array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">princ,</span> <span class="pre">p</span></span></dt>
<dd><p>Principal strains</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>1d-array (size 3)</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pylabfea.basic.Strain.eeq">
<span class="sig-name descname"><span class="pre">eeq</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#Strain.eeq"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.Strain.eeq" title="Link to this definition">¶</a></dt>
<dd><p>Calculate equivalent strain</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>equiv</strong> – Equivalent strain</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pylabfea.basic.Strain.inv">
<span class="sig-name descname"><span class="pre">inv</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#Strain.inv"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.Strain.inv" title="Link to this definition">¶</a></dt>
<dd><p>Calculate inverse of strain tensor ignoring zeros.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>inv</strong></p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>(6,) array</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="pylabfea.basic.Stress">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">Stress</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sv</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#Stress"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.Stress" title="Link to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.13)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
<p>Stores and converts Voigt stress tensors into different formats,
calculates principle stresses, equivalent stresses and transforms into cylindrical coordinates.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>sv</strong> (<em>list-like object</em><em>, </em><em>must be 1D with length 6</em>) – Voigt-stress components</p>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">voigt,</span> <span class="pre">v</span></span></dt>
<dd><p>Stress tensor in Voigt notation</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>1d-array (size 6)</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">tens,</span> <span class="pre">t</span></span></dt>
<dd><p>Stress tensor in matrix notation</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>3x3 array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">princ,</span> <span class="pre">p</span></span></dt>
<dd><p>Principal stresses</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>1d-array (size 3)</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">hydrostatic,</span> <span class="pre">h</span></span></dt>
<dd><p>Hydrostatic stress component</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pylabfea.basic.Stress.cyl">
<span class="sig-name descname"><span class="pre">cyl</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#Stress.cyl"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.Stress.cyl" title="Link to this definition">¶</a></dt>
<dd><p>Calculate cylindrical stress tensor</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>cyl</strong> – stress in cylindrical form: (J2 eqiv. stress, polar angle, hydrostatic)</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>(3,) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pylabfea.basic.Stress.lode_ang">
<span class="sig-name descname"><span class="pre">lode_ang</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#Stress.lode_ang"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.Stress.lode_ang" title="Link to this definition">¶</a></dt>
<dd><p>Calculate Lode angle:
Transforms principal stress space into hydrostatic stress, eqiv. stress, and Lode angle;
definition of positive cosine for Lode angle is applied</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>arg</strong> (either float or object of class <code class="docutils literal notranslate"><span class="pre">Material</span></code>) – if type is float: interpreted as equivalent stress
if type is <code class="docutils literal notranslate"><span class="pre">Material</span></code>: method of that class is used
to calculate equivalent stress</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>la</strong> – Lode angle</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pylabfea.basic.Stress.seq">
<span class="sig-name descname"><span class="pre">seq</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mat</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#Stress.seq"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.Stress.seq" title="Link to this definition">¶</a></dt>
<dd><p>calculate Hill-type equivalent stress, invokes corresponding method of class <code class="docutils literal notranslate"><span class="pre">Material</span></code></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>mat</strong> (object of class <code class="docutils literal notranslate"><span class="pre">Material</span></code>) – contains Hill parameters and method needed for Hill-type equivalent stress
(optional, default=None)</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>seq</strong> – equivalent stress; material specific (J2, Hill, Tresca, Barlat) if mat is provided,
J2 equivalent stress otherwise</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pylabfea.basic.Stress.seq_j2">
<span class="sig-name descname"><span class="pre">seq_j2</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#Stress.seq_j2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.Stress.seq_j2" title="Link to this definition">¶</a></dt>
<dd><p>Calculate J2 principal stress</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>sj2</strong> – equivalent stress</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pylabfea.basic.Stress.theta">
<span class="sig-name descname"><span class="pre">theta</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#Stress.theta"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.Stress.theta" title="Link to this definition">¶</a></dt>
<dd><p>Calculate polar angle in deviatoric plane</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>ang</strong> – polar angle of stress in deviatoric plane</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a></p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="py data">
<dt class="sig sig-object py" id="pylabfea.basic.a_vec">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">a_vec</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">array([</span> <span class="pre">0.81649658,</span> <span class="pre">-0.40824829,</span> <span class="pre">-0.40824829])</span></em><a class="headerlink" href="#pylabfea.basic.a_vec" title="Link to this definition">¶</a></dt>
<dd><p>First unit vector spanning deviatoric stress plane (real axis)</p>
</dd></dl>
<dl class="py data">
<dt class="sig sig-object py" id="pylabfea.basic.b_vec">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">b_vec</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">array([</span> <span class="pre">0.</span>        <span class="pre">,</span>  <span class="pre">0.70710678,</span> <span class="pre">-0.70710678])</span></em><a class="headerlink" href="#pylabfea.basic.b_vec" title="Link to this definition">¶</a></dt>
<dd><p>Second unit vector spanning deviatoric stress plane (imaginary axis)</p>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.eps_eq">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">eps_eq</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ndarray</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#eps_eq"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.eps_eq" title="Link to this definition">¶</a></dt>
<dd><p>Calculate equivalent strain</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>eps</strong> (<em>(</em><em>3</em><em>,</em><em>)</em><em>, </em><em>(</em><em>6</em><em>,</em><em>)</em><em>, </em><em>(</em><em>nsc</em><em>,</em><em>3</em><em>) or </em><em>(</em><em>nsc</em><em>,</em><em>6</em><em>) </em><em>array</em>) – (3,) or (nsc,3): Principal strains;
(6,) or (nsc,6): Voigt strains</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>eeq</strong> – equivalent strains</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a> or (nsc,) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.pickle2mat">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">pickle2mat</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">path</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'./'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#pickle2mat"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.pickle2mat" title="Link to this definition">¶</a></dt>
<dd><p>Read pickled material file.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>name</strong> (<em>string</em>) – File name of pickled material to be read.</p></li>
<li><p><strong>path</strong> (<em>string</em>) – Path under which pickle-files are stored (optional, default: ‘./’)</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>pcl</strong> – unpickled material</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>Material object</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.polar_ang">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">polar_ang</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sig</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#polar_ang"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.polar_ang" title="Link to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.s_cyl">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">s_cyl</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sig</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mat</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#s_cyl"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.s_cyl" title="Link to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.sdev">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">sdev</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sig</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#sdev"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.sdev" title="Link to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.seq_J2">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">seq_J2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sig</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#seq_J2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.seq_J2" title="Link to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.sig_cyl2princ">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">sig_cyl2princ</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s_cyl</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">ndarray</span></span></span><a class="reference internal" href="_modules/pylabfea/basic.html#sig_cyl2princ"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.sig_cyl2princ" title="Link to this definition">¶</a></dt>
<dd><p>Convert cylindrical stress into 3D Cartesian principle stress</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>s_cyl</strong> (<em>(</em><em>2</em><em>,</em><em>)</em><em>, </em><em>(</em><em>3</em><em>,</em><em>)</em><em>, </em><em>(</em><em>N</em><em>,</em><em>2</em><em>) or </em><em>(</em><em>N</em><em>,</em><em>3</em><em>) </em><em>array</em>) – Cylindrical stress in form (seq, theta, (optional: p))</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>s_princ</strong> – principle deviatoric stresses</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>(3,) or (N,3) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.sig_cyl2voigt">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">sig_cyl2voigt</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sig_cyl</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eigen_vector</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ndarray</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">ndarray</span></span></span><a class="reference internal" href="_modules/pylabfea/basic.html#sig_cyl2voigt"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.sig_cyl2voigt" title="Link to this definition">¶</a></dt>
<dd><p>Convert cylindrical stress and eigenvectors into Voigt stress tensor</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>sig_cyl</strong> (<em>(</em><em>3</em><em>,</em><em>) or </em><em>(</em><em>N</em><em>,</em><em>3</em><em>) </em><em>array</em>) – Cylindrical stress in form (seq, theta, p)</p></li>
<li><p><strong>eigen_vector</strong> (<em>(</em><em>3</em><em>,</em><em>3</em><em>) or </em><em>(</em><em>N</em><em>,</em><em>3</em><em>,</em><em>3</em><em>) </em><em>array</em>) – Eigenvectors of stress tensor</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>sig_voigt</strong> – Voigt stress tensor</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>(6,) or (N,6) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.sig_dev">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">sig_dev</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sig</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ndarray</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">ndarray</span></span></span><a class="reference internal" href="_modules/pylabfea/basic.html#sig_dev"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.sig_dev" title="Link to this definition">¶</a></dt>
<dd><p>Calculate deviatoric stress component from given stress tensor</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>sig</strong> (<em>(</em><em>3</em><em>,</em><em>)</em><em>, </em><em>(</em><em>6</em><em>,</em><em>) </em><em>(</em><em>N</em><em>,</em><em>3</em><em>) or </em><em>(</em><em>N</em><em>,</em><em>6</em><em>) </em><em>array</em>)</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>sd</strong> – deviatoric stresses</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a> or (N,) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.sig_eq_j2">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">sig_eq_j2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sig</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ndarray</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#sig_eq_j2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.sig_eq_j2" title="Link to this definition">¶</a></dt>
<dd><p>Calculate sj2 equivalent stress from any stress tensor</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>sig</strong> (<em>(</em><em>3</em><em>,</em><em>)</em><em>, </em><em>(</em><em>6</em><em>,</em><em>) </em><em>(</em><em>N</em><em>,</em><em>3</em><em>) or </em><em>(</em><em>N</em><em>,</em><em>6</em><em>) </em><em>array</em>) – (3,), (N,3): Principal stress or list of principal stresses;
(6,), (N,6): Voigt stress</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>seq</strong> – sj2 equivalent stresses</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a> or (N,) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.sig_polar_ang">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">sig_polar_ang</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sig</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ndarray</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#sig_polar_ang"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.sig_polar_ang" title="Link to this definition">¶</a></dt>
<dd><p>Transform stresses into polar angle on deviatoric plane spanned by a_vec and b_vec</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>sig</strong> (<em>(</em><em>3</em><em>,</em><em>)</em><em>, </em><em>(</em><em>6</em><em>,</em><em>) </em><em>(</em><em>N</em><em>,</em><em>3</em><em>) or </em><em>(</em><em>N</em><em>,</em><em>6</em><em>) </em><em>array</em>) – (3,), (N,3): Principal stresses;
(6,), (N,6): Voigt stress</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>theta</strong> – polar angles in deviatoric plane as positive angle between sig and a_vec in range [-pi,+p]</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a> or (N,) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.sig_princ">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">sig_princ</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sig</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ndarray</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#sig_princ"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.sig_princ" title="Link to this definition">¶</a></dt>
<dd><p>Convert Voigt stress tensors into principal stresses and eigenvectors.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>sig</strong> (<em>(</em><em>6</em><em>,</em><em>)</em><em>, </em><em>(</em><em>nsc</em><em>,</em><em>6</em><em>)</em><em>, </em><em>(</em><em>3</em><em>,</em><em>3</em><em>)</em><em>, or </em><em>(</em><em>nsc</em><em>,</em><em>3</em><em>,</em><em>3</em><em>) </em><em>array</em>) – Voigt stress tensor (dim=6) or Cartesian stress tensor (dim=3x3)</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><strong>spa</strong> (<em>(3,) or (nsc,3) array</em>) – Principal stresses</p></li>
<li><p><strong>eva</strong> (<em>(3,3) or (nsc,3,3) array</em>) – Eigenvectors/rotation matrices of stress tensor</p></li>
</ul>
</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.sig_princ2cyl">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">sig_princ2cyl</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sig</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mat</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">ndarray</span></span></span><a class="reference internal" href="_modules/pylabfea/basic.html#sig_princ2cyl"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.sig_princ2cyl" title="Link to this definition">¶</a></dt>
<dd><p>Convert principal stress into cylindrical stress vector</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>sig</strong> (<em>(</em><em>3</em><em>,</em><em>)</em><em>, </em><em>(</em><em>6</em><em>,</em><em>)</em><em>, </em><em>(</em><em>N</em><em>,</em><em>3</em><em>) or </em><em>(</em><em>N</em><em>,</em><em>6</em><em>) </em><em>array</em>) – stress to be converted, if (3,) or (N,3) principal stress is assumed</p></li>
<li><p><strong>mat</strong> (object of class <code class="docutils literal notranslate"><span class="pre">Material</span></code>) – Material for Hill-type principal stress (optional)</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>sc</strong> – stress in cylindrical coordinates (seq, theta, p)</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>(3,) or (N,3) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.sp_cart">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">sp_cart</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">scyl</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#sp_cart"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.sp_cart" title="Link to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.sprinc">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">sprinc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sig</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#sprinc"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.sprinc" title="Link to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pylabfea.basic.svoigt">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">svoigt</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">scyl</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">evec</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/basic.html#svoigt"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.basic.svoigt" title="Link to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py data">
<dt class="sig sig-object py" id="pylabfea.basic.yf_tolerance">
<span class="sig-prename descclassname"><span class="pre">pylabfea.basic.</span></span><span class="sig-name descname"><span class="pre">yf_tolerance</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">0.005</span></em><a class="headerlink" href="#pylabfea.basic.yf_tolerance" title="Link to this definition">¶</a></dt>
<dd><p>Plastic yielding if yield function > yf_tolerance</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>Tolerance</p>
</dd>
</dl>
</dd></dl>
</section>
<section id="module-pylabfea.model">
<span id="module-model"></span><h2>Module Model<a class="headerlink" href="#module-pylabfea.model" title="Link to this heading">¶</a></h2>
<p>Module pylabefea.model introduces global functions for mechanical quantities
and class <code class="docutils literal notranslate"><span class="pre">Model</span></code> that contains that attributes and methods needed in FEA.
Materials are defined in module pylabfea.material</p>
<p>uses NumPy, SciPy, MatPlotLib</p>
<p>Version: 4.1 (2022-02-22)
Author: Alexander Hartmaier, ICAMS/Ruhr University Bochum, Germany
Email: <a class="reference external" href="mailto:alexander.hartmaier%40rub.de">alexander<span>.</span>hartmaier<span>@</span>rub<span>.</span>de</a>
distributed under GNU General Public License (GPLv3)</p>
<dl class="py class">
<dt class="sig sig-object py" id="pylabfea.model.Model">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pylabfea.model.</span></span><span class="sig-name descname"><span class="pre">Model</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">planestress</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/model.html#Model"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.model.Model" title="Link to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.13)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
<p>Class for finite element model. Defines necessary attributes and methods
for pre-processing (defining geometry, material assignments, mesh and
boundary conditions);
solution (invokes numerical solver for non-linear problems);
and post-processing (visualization of results on meshed geometry,
homogenization of results into global quantities).</p>
<p><em>Geometry and sections</em> can be defined with the methods <code class="docutils literal notranslate"><span class="pre">geom</span></code> and <code class="docutils literal notranslate"><span class="pre">assign</span></code>.
There are pre-defined options that make the generation of laminate structures
particularly easy. But also more general section can be defined and each section
can be associated with a different material.</p>
<p><em>Boundary conditions</em> on left-hand-side and bottom nodes are always assumed
to be static (typically with values of zero);
Boundary conditions on right-hand-side and top nodes are considered as load
steps starting from zero.
Default boundary conditions are:</p>
<blockquote>
<div><ul class="simple">
<li><p>lhs: fixed in x-direction (ux=0), free in y-direction (fy=0)</p></li>
<li><p>bot: fixed in y-direction (uy=0), free in x-direction (fx=0)</p></li>
<li><p>rhs: free (fx=fy=0)</p></li>
<li><p>top: free (fx=fy=0)</p></li>
</ul>
</div></blockquote>
<p>There are pre-defined sets of nodes to top, bottom, left and right boundaries to
which either force or displacement controlled loads can be applied in x or y-direction
with the methods <code class="docutils literal notranslate"><span class="pre">bctop</span></code>, <code class="docutils literal notranslate"><span class="pre">bcbot</span></code>, <code class="docutils literal notranslate"><span class="pre">bcleft</span></code>, <code class="docutils literal notranslate"><span class="pre">bcright</span></code>. Furthermore, it is
possible to define boundary conditions for a freely defined set of nodes with the
method <code class="docutils literal notranslate"><span class="pre">bcnode</span></code>. The latter option if useful, to fix only one corner node when
laterally free boundaries shall be implemented. It can also be used to simulate
loads on parts of boundaries, as it occurs for indentations, etc.</p>
<p><em>Visualization</em> is performed with the method <code class="docutils literal notranslate"><span class="pre">plot</span></code>, which can display various
mechanical quantities on the deformed mesh. Homogenization of boundary loads is
simply performed with the method <code class="docutils literal notranslate"><span class="pre">calc_glob</span></code> by which all global stresses and
strains are obtained by averaging over the element values and by summing up the
boundary loads for comparison. This is particularly useful when calculating the
stress-strain behavior of a structure.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.13)"><em>int</em></a>) – Dimensionality of model (optional, default: 1)</p></li>
<li><p><strong>planestress</strong> (<em>Boolean</em>) – Sets plane-stress condition (optional, default: False)</p></li>
</ul>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.dim">
<span class="sig-name descname"><span class="pre">dim</span></span><a class="headerlink" href="#pylabfea.model.Model.dim" title="Link to this definition">¶</a></dt>
<dd><p>Dimensionality of model (1 and 2 are supported in this version)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>integer</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.planestress">
<span class="sig-name descname"><span class="pre">planestress</span></span><a class="headerlink" href="#pylabfea.model.Model.planestress" title="Link to this definition">¶</a></dt>
<dd><p>Sets plane-stress condition</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>Boolean</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.Nsec">
<span class="sig-name descname"><span class="pre">Nsec</span></span><a class="headerlink" href="#pylabfea.model.Model.Nsec" title="Link to this definition">¶</a></dt>
<dd><p>Number of sections (defined in <code class="docutils literal notranslate"><span class="pre">geom</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.13)">int</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.LS">
<span class="sig-name descname"><span class="pre">LS</span></span><a class="headerlink" href="#pylabfea.model.Model.LS" title="Link to this definition">¶</a></dt>
<dd><p>Absolute lengths of sections (defined in <code class="docutils literal notranslate"><span class="pre">geom</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>1-d array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.lenx">
<span class="sig-name descname"><span class="pre">lenx</span></span><a class="headerlink" href="#pylabfea.model.Model.lenx" title="Link to this definition">¶</a></dt>
<dd><p>Size of model in x-direction (defined in <code class="docutils literal notranslate"><span class="pre">geom</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.leny">
<span class="sig-name descname"><span class="pre">leny</span></span><a class="headerlink" href="#pylabfea.model.Model.leny" title="Link to this definition">¶</a></dt>
<dd><p>Size of model in y-direction (defined in <code class="docutils literal notranslate"><span class="pre">geom</span></code>, default leny=1)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.thick">
<span class="sig-name descname"><span class="pre">thick</span></span><a class="headerlink" href="#pylabfea.model.Model.thick" title="Link to this definition">¶</a></dt>
<dd><p>Thickness of 2d-model (defined in <code class="docutils literal notranslate"><span class="pre">geom</span></code>, default thick=1)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.nonlin">
<span class="sig-name descname"><span class="pre">nonlin</span></span><a class="headerlink" href="#pylabfea.model.Model.nonlin" title="Link to this definition">¶</a></dt>
<dd><p>Indicates non-linearity of model (defined in <code class="docutils literal notranslate"><span class="pre">assign</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>Boolean</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.mat">
<span class="sig-name descname"><span class="pre">mat</span></span><a class="headerlink" href="#pylabfea.model.Model.mat" title="Link to this definition">¶</a></dt>
<dd><p>List of materials assigned to sections of model, same dimensions as LS
(defined in <code class="docutils literal notranslate"><span class="pre">assign</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.13)">list</a> of objects to class Material</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.ubcbot">
<span class="sig-name descname"><span class="pre">ubcbot</span></span><a class="headerlink" href="#pylabfea.model.Model.ubcbot" title="Link to this definition">¶</a></dt>
<dd><p>True: displacement BC on rhs nodes; False: force BC on rhs nodes
(defined in <code class="docutils literal notranslate"><span class="pre">bcright</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>dim-array of Boolean</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.bcb">
<span class="sig-name descname"><span class="pre">bcb</span></span><a class="headerlink" href="#pylabfea.model.Model.bcb" title="Link to this definition">¶</a></dt>
<dd><p>Nodal displacements in x or y-direction for lhs nodes
(defined in <code class="docutils literal notranslate"><span class="pre">bcbot</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>dim-array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.ubcleft">
<span class="sig-name descname"><span class="pre">ubcleft</span></span><a class="headerlink" href="#pylabfea.model.Model.ubcleft" title="Link to this definition">¶</a></dt>
<dd><p>True: displacement BC on rhs nodes; False: force BC on rhs nodes
(defined in <code class="docutils literal notranslate"><span class="pre">bcright</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>dim-array of Boolean</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.bcl">
<span class="sig-name descname"><span class="pre">bcl</span></span><a class="headerlink" href="#pylabfea.model.Model.bcl" title="Link to this definition">¶</a></dt>
<dd><p>Nodal displacement in x or y-direction for lhs nodes
(defined in <code class="docutils literal notranslate"><span class="pre">bcleft</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>dim-array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.ubcright">
<span class="sig-name descname"><span class="pre">ubcright</span></span><a class="headerlink" href="#pylabfea.model.Model.ubcright" title="Link to this definition">¶</a></dt>
<dd><p>True: displacement BC on rhs nodes; False: force BC on rhs nodes
(defined in <code class="docutils literal notranslate"><span class="pre">bcright</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>dim-array of Boolean</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.bcr">
<span class="sig-name descname"><span class="pre">bcr</span></span><a class="headerlink" href="#pylabfea.model.Model.bcr" title="Link to this definition">¶</a></dt>
<dd><p>Nodal displacements/forces in x or y-direction for rhs nodes
(defined in <code class="docutils literal notranslate"><span class="pre">bcright</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>dim-array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.ubctop">
<span class="sig-name descname"><span class="pre">ubctop</span></span><a class="headerlink" href="#pylabfea.model.Model.ubctop" title="Link to this definition">¶</a></dt>
<dd><p>True: displacement BC on top nodes; False: force BC on top nodes
(defined in <code class="docutils literal notranslate"><span class="pre">bctop</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>Boolean</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.bct">
<span class="sig-name descname"><span class="pre">bct</span></span><a class="headerlink" href="#pylabfea.model.Model.bct" title="Link to this definition">¶</a></dt>
<dd><p>Nodal displacements/forces in x or y-direction for top nodes
(defined in <code class="docutils literal notranslate"><span class="pre">bctop</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>dim-array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.Nnode">
<span class="sig-name descname"><span class="pre">Nnode</span></span><a class="headerlink" href="#pylabfea.model.Model.Nnode" title="Link to this definition">¶</a></dt>
<dd><p>Total number of nodes in Model (defined in <code class="docutils literal notranslate"><span class="pre">mesh</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.13)">int</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">NnodeX,</span> <span class="pre">NnodeY</span></span></dt>
<dd><p>Numbers of nodes in x and y-direction (defined in <code class="docutils literal notranslate"><span class="pre">mesh</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.13)">int</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.Nel">
<span class="sig-name descname"><span class="pre">Nel</span></span><a class="headerlink" href="#pylabfea.model.Model.Nel" title="Link to this definition">¶</a></dt>
<dd><p>Number of elements (defined in <code class="docutils literal notranslate"><span class="pre">mesh</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.13)">int</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.Ndof">
<span class="sig-name descname"><span class="pre">Ndof</span></span><a class="headerlink" href="#pylabfea.model.Model.Ndof" title="Link to this definition">¶</a></dt>
<dd><p>Number of degrees of freedom (defined in <code class="docutils literal notranslate"><span class="pre">mesh</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.13)">int</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.npos">
<span class="sig-name descname"><span class="pre">npos</span></span><a class="headerlink" href="#pylabfea.model.Model.npos" title="Link to this definition">¶</a></dt>
<dd><dl class="simple">
<dt>Nodal positions, dimension Ndof, same structure as u,f-arrays:</dt><dd><p>(x1, y1, x2, y1, …) (defined in <code class="docutils literal notranslate"><span class="pre">mesh</span></code>)</p>
</dd>
</dl>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>1d-array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">noleft,</span> <span class="pre">noright,</span> <span class="pre">nobot,</span> <span class="pre">notop</span></span></dt>
<dd><p>Lists of nodes on boundaries (defined in <code class="docutils literal notranslate"><span class="pre">mesh</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.13)">list</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.noinner">
<span class="sig-name descname"><span class="pre">noinner</span></span><a class="headerlink" href="#pylabfea.model.Model.noinner" title="Link to this definition">¶</a></dt>
<dd><p>List of inner nodes (defined in <code class="docutils literal notranslate"><span class="pre">mesh</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.13)">list</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.element">
<span class="sig-name descname"><span class="pre">element</span></span><a class="headerlink" href="#pylabfea.model.Model.element" title="Link to this definition">¶</a></dt>
<dd><p>List of objects of class <code class="docutils literal notranslate"><span class="pre">Element</span></code>, dimension Nel
(defined in <code class="docutils literal notranslate"><span class="pre">mesh</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.13)">list</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.u">
<span class="sig-name descname"><span class="pre">u</span></span><a class="headerlink" href="#pylabfea.model.Model.u" title="Link to this definition">¶</a></dt>
<dd><p>List of nodal displacements (defined in <code class="docutils literal notranslate"><span class="pre">solve</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>(Ndof,) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.f">
<span class="sig-name descname"><span class="pre">f</span></span><a class="headerlink" href="#pylabfea.model.Model.f" title="Link to this definition">¶</a></dt>
<dd><p>List of nodal forces (defined in <code class="docutils literal notranslate"><span class="pre">solve</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>(Ndof,) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.sgl">
<span class="sig-name descname"><span class="pre">sgl</span></span><a class="headerlink" href="#pylabfea.model.Model.sgl" title="Link to this definition">¶</a></dt>
<dd><p>Time evolution of global stress tensor with incremental load steps
(defined in <code class="docutils literal notranslate"><span class="pre">solve</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>(N,6) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.egl">
<span class="sig-name descname"><span class="pre">egl</span></span><a class="headerlink" href="#pylabfea.model.Model.egl" title="Link to this definition">¶</a></dt>
<dd><p>Time evolution of global total strain tensor with incremental load
steps (defined in <code class="docutils literal notranslate"><span class="pre">solve</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>(N,6) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.epgl">
<span class="sig-name descname"><span class="pre">epgl</span></span><a class="headerlink" href="#pylabfea.model.Model.epgl" title="Link to this definition">¶</a></dt>
<dd><p>Time evolution of global plastic strain tensor with incremental load
steps (defined in <code class="docutils literal notranslate"><span class="pre">solve</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>(N,6) array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.glob">
<span class="sig-name descname"><span class="pre">glob</span></span><a class="headerlink" href="#pylabfea.model.Model.glob" title="Link to this definition">¶</a></dt>
<dd><p>Global values homogenized from BC or element solutions, contains the
elements:
‘ebc1’, ‘ebc2’, ‘sbc1’, ‘sbc2’ : global strain and stress from BC
(type: float)
‘eps’, ‘epl’, ‘sig’, : global strain, plastic strain, and stress
tensors homogenized
from element solutions (type: Voigt tensor)
(defined in <code class="docutils literal notranslate"><span class="pre">calc_global</span></code>)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>python dictionary</p>
</dd>
</dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="pylabfea.model.Model.Element">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Element</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">model</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nodes</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lx</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ly</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mat</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylabfea/model.html#Model.Element"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pylabfea.model.Model.Element" title="Link to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.13)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
<p>Class for isoparametric elements; supports
1-d elements with linear or quadratic shape function and full integration;
2-d quadrilateral elements with linear shape function and full integration</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>model</strong> (object of class <code class="docutils literal notranslate"><span class="pre">Model</span></code>) – Refers to parent class <code class="docutils literal notranslate"><span class="pre">Model</span></code> to inherit all attributes</p></li>
<li><p><strong>nodes</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.13)"><em>list</em></a>) – List of nodes belonging to element</p></li>
<li><p><strong>lx</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)"><em>float</em></a>) – Element size in x-direction</p></li>
<li><p><strong>ly</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)"><em>float</em></a>) – Element size in y-direction</p></li>
<li><p><strong>sect</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.13)"><em>int</em></a>) – Section in which element is located</p></li>
<li><p><strong>mat</strong> (object of class <code class="docutils literal notranslate"><span class="pre">Material</span></code>) – Material card with attributes and methods to be applied in element</p></li>
</ul>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.Element.Model">
<span class="sig-name descname"><span class="pre">Model</span></span><a class="headerlink" href="#pylabfea.model.Model.Element.Model" title="Link to this definition">¶</a></dt>
<dd><p>Refers to parent object (FE model)</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>object of class <code class="docutils literal notranslate"><span class="pre">Model</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.Element.nodes">
<span class="sig-name descname"><span class="pre">nodes</span></span><a class="headerlink" href="#pylabfea.model.Model.Element.nodes" title="Link to this definition">¶</a></dt>
<dd><p>List of nodes of this element</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.13)">list</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.Element.Lelx">
<span class="sig-name descname"><span class="pre">Lelx</span></span><a class="headerlink" href="#pylabfea.model.Model.Element.Lelx" title="Link to this definition">¶</a></dt>
<dd><p>Size of element in x-direction</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.Element.Lely">
<span class="sig-name descname"><span class="pre">Lely</span></span><a class="headerlink" href="#pylabfea.model.Model.Element.Lely" title="Link to this definition">¶</a></dt>
<dd><p>Size of element in y-direction</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)">float</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.Element.ngp">
<span class="sig-name descname"><span class="pre">ngp</span></span><a class="headerlink" href="#pylabfea.model.Model.Element.ngp" title="Link to this definition">¶</a></dt>
<dd><p>number of Gauss points</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.13)">int</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pylabfea.model.Model.Element.gpx">
<span class="sig-name descname"><span class="pre">gpx</span></span><a class="headerlink" href="#pylabfea.model.Model.Element.gpx" title="Link to this definition">¶</a></dt>
<dd><p>x-locations of Gauss points in element</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>1-d array</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">