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<!DOCTYPE html>
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<title>Simcoon — Constitutive Modeling and Material Library — Simcoon 1.11.1 documentation</title>
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<p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
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<li class="toctree-l1"><a class="reference internal" href="about.html">About</a></li>
<li class="toctree-l1"><a class="reference internal" href="installation.html">Installation</a><ul>
<li class="toctree-l2"><a class="reference internal" href="installation.html#quick-install">Quick install</a></li>
<li class="toctree-l2"><a class="reference internal" href="installation.html#blas-lapack-and-openmp">BLAS/LAPACK and OpenMP</a></li>
<li class="toctree-l2"><a class="reference internal" href="installation.html#developer-installation">Developer installation</a><ul>
<li class="toctree-l3"><a class="reference internal" href="installation.html#prerequisites-conda">Prerequisites (conda)</a></li>
<li class="toctree-l3"><a class="reference internal" href="installation.html#prerequisites-system-packages">Prerequisites (system packages)</a></li>
<li class="toctree-l3"><a class="reference internal" href="installation.html#building-from-source">Building from source</a></li>
<li class="toctree-l3"><a class="reference internal" href="installation.html#running-tests">Running tests</a></li>
<li class="toctree-l3"><a class="reference internal" href="installation.html#using-simcoon-with-fedoo">Using simcoon with fedoo</a></li>
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<li class="toctree-l1"><a class="reference internal" href="external.html">External</a><ul>
<li class="toctree-l2"><a class="reference internal" href="external.html#umext-plugin-format">UMEXT Plugin Format</a></li>
<li class="toctree-l2"><a class="reference internal" href="external.html#umaba-plugin-format-abaqus-compatibility">UMABA Plugin Format (Abaqus Compatibility)</a></li>
<li class="toctree-l2"><a class="reference internal" href="external.html#umans-plugin-format-ansys-compatibility">UMANS Plugin Format (Ansys Compatibility)</a></li>
<li class="toctree-l2"><a class="reference internal" href="external.html#compiling-external-plugins">Compiling External Plugins</a></li>
<li class="toctree-l2"><a class="reference internal" href="external.html#setting-up-input-files">Setting Up Input Files</a></li>
<li class="toctree-l2"><a class="reference internal" href="external.html#testing-external-plugins">Testing External Plugins</a></li>
<li class="toctree-l2"><a class="reference internal" href="external.html#running-the-tests">Running the Tests</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="simulation/index.html">Simulation</a><ul>
<li class="toctree-l2"><a class="reference internal" href="simulation/solver.html">Use the solver</a><ul>
<li class="toctree-l3"><a class="reference internal" href="simulation/solver.html#elastic-tensile-test">Elastic tensile test</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/solver.html#solver-parameters">Solver parameters</a><ul>
<li class="toctree-l4"><a class="reference internal" href="simulation/solver.html#corotational-spin-rate-types">Corotational spin rate types</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="simulation/solver.html#define-the-loading-path">Define the loading path</a><ul>
<li class="toctree-l4"><a class="reference internal" href="simulation/solver.html#general-structure">General structure</a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/solver.html#block-parameters">Block parameters</a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/solver.html#step-definitions">Step definitions</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="simulation/solver.html#examples">Examples</a><ul>
<li class="toctree-l4"><a class="reference internal" href="simulation/solver.html#cyclic-loading-plasticity">Cyclic loading (plasticity)</a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/solver.html#hyperelasticity-with-deformation-gradient-control">Hyperelasticity with deformation gradient control</a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/solver.html#finite-deformation-with-spin-logarithmic-strain">Finite deformation with spin (logarithmic strain)</a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/solver.html#thermomechanical-loading">Thermomechanical loading</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="simulation/output.html">Configure the output</a><ul>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#file-structure">File structure</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#basic-example">Basic example</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#strain-output-options">Strain output options</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#stress-output-options">Stress output options</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#rotation-output-options">Rotation output options</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#tangent-modulus-output">Tangent modulus output</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#temperature-output">Temperature output</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#internal-state-variables">Internal state variables</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#block-output-control">Block output control</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#hyperelasticity-example">Hyperelasticity example</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#default-values">Default values</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#result-file-format">Result file format</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="simulation/fea_integration.html">FEA Integration</a><ul>
<li class="toctree-l3"><a class="reference internal" href="simulation/fea_integration.html#overview">Overview</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/fea_integration.html#supported-fea-software">Supported FEA Software</a><ul>
<li class="toctree-l4"><a class="reference internal" href="simulation/abaqus.html">Abaqus Integration</a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/ansys.html">Ansys Integration</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="simulation/fea_integration.html#key-differences">Key Differences</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/fea_integration.html#available-models">Available Models</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="examples/index.html">Examples</a><ul>
<li class="toctree-l2"><a class="reference internal" href="examples/index.html#analysis-and-processing-examples">Analysis and processing examples</a><ul>
<li class="toctree-l3"><a class="reference internal" href="examples/analysis/directional_stiffness.html">Effective properties of a cubic material</a></li>
<li class="toctree-l3"><a class="reference internal" href="examples/analysis/eshelby_numerical_vs_analytical.html">Numerical vs Analytical Eshelby Tensor Comparison</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/eshelby_numerical_vs_analytical.html#aspect-ratio-sweep">Aspect Ratio Sweep</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/eshelby_numerical_vs_analytical.html#numerical-integration-convergence">Numerical Integration Convergence</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/eshelby_numerical_vs_analytical.html#plot-analytical-vs-numerical-eshelby-tensor-components">Plot: Analytical vs Numerical Eshelby Tensor Components</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/eshelby_numerical_vs_analytical.html#relative-error-analysis">Relative Error Analysis</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/eshelby_numerical_vs_analytical.html#plot-error-comparison-with-limiting-cases">Plot: Error Comparison with Limiting Cases</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/eshelby_numerical_vs_analytical.html#convergence-to-limiting-cases">Convergence to Limiting Cases</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/analysis/hyperelastic_parameter_identification.html">Parameter Identification for Mooney-Rivlin Hyperelastic Material</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/hyperelastic_parameter_identification.html#methodology-overview">Methodology Overview</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/hyperelastic_parameter_identification.html#mooney-rivlin-constitutive-model">Mooney-Rivlin Constitutive Model</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/hyperelastic_parameter_identification.html#experimental-data-treloar-s-rubber-experiments">Experimental Data: Treloar’s Rubber Experiments</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/hyperelastic_parameter_identification.html#forward-model-stress-prediction-using-simcoon">Forward Model: Stress Prediction using simcoon</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/hyperelastic_parameter_identification.html#cost-function-stress-based-mean-squared-error">Cost Function: Stress-Based Mean Squared Error</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/hyperelastic_parameter_identification.html#parameter-identification-using-differential-evolution">Parameter Identification using Differential Evolution</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/hyperelastic_parameter_identification.html#visualization-functions">Visualization Functions</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/analysis/hyperelastic_parameter_identification.html#main-execution">Main Execution</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/analysis/objective_rates.html">Comparison of objective rates</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="examples/index.html#continuum-mechanics-examples">Continuum Mechanics Examples</a><ul>
<li class="toctree-l3"><a class="reference internal" href="examples/continuum_mechanics/constitutive_relations.html">Constitutive Library Examples</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/constitutive_relations.html#l-iso">L_iso</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/constitutive_relations.html#m-iso">M_iso</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/constitutive_relations.html#l-cubic">L_cubic</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/constitutive_relations.html#m-cubic">M_cubic</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/constitutive_relations.html#l-isotrans">L_isotrans</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/constitutive_relations.html#m-isotrans">M_isotrans</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/constitutive_relations.html#l-ortho">L_ortho</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/constitutive_relations.html#m-ortho">M_ortho</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/continuum_mechanics/rotation.html">Rotation library Examples</a></li>
<li class="toctree-l3"><a class="reference internal" href="examples/continuum_mechanics/stress_measures.html">Stress transfer: Cauchy → PKI/PKII/Kirchhoff</a></li>
<li class="toctree-l3"><a class="reference internal" href="examples/continuum_mechanics/stress_transfer_helpers.html">Stress transfer library examples</a></li>
<li class="toctree-l3"><a class="reference internal" href="examples/continuum_mechanics/yield_criteria.html">Yield Criteria Examples</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/yield_criteria.html#von-mises-equivalent-stress">Von Mises equivalent stress</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/yield_criteria.html#tresca-equivalent-stress">Tresca equivalent stress</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/yield_criteria.html#drucker-equivalent-stress">Drucker equivalent stress</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/yield_criteria.html#hill-anisotropic-yield-criterion">Hill anisotropic yield criterion</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/yield_criteria.html#hill-configurational-tensor">Hill configurational tensor</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/yield_criteria.html#yield-surface-visualization">Yield surface visualization</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/yield_criteria.html#d-yield-surfaces">3D Yield Surfaces</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/yield_criteria.html#plane-stress-11-22">Plane Stress (σ₁₁, σ₂₂)</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/yield_criteria.html#tension-shear-11-12">Tension-Shear (σ₁₁, σ₁₂)</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/yield_criteria.html#hill-anisotropy-parameters">Hill Anisotropy Parameters</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/yield_criteria.html#drucker-parameter-b">Drucker Parameter b</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="examples/index.html#heterogeneous-materials-simulation">Heterogeneous materials simulation</a><ul>
<li class="toctree-l3"><a class="reference internal" href="examples/heterogeneous/effective_props.html">Micromechanics Examples</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/effective_props.html#plotting-the-results">Plotting the results</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/effective_props.html#effect-of-aspect-ratio-on-effective-stiffness">Effect of Aspect Ratio on Effective Stiffness</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/heterogeneous/eshelby_tensors.html">Eshelby Tensor Examples</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/eshelby_tensors.html#eshelby-tensor-for-a-sphere">Eshelby tensor for a sphere</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/eshelby_tensors.html#eshelby-tensor-for-an-infinite-cylinder">Eshelby tensor for an infinite cylinder</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/eshelby_tensors.html#eshelby-tensor-for-prolate-ellipsoid">Eshelby tensor for prolate ellipsoid</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/eshelby_tensors.html#eshelby-tensor-for-oblate-ellipsoid">Eshelby tensor for oblate ellipsoid</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/eshelby_tensors.html#eshelby-tensor-for-penny-shaped-crack">Eshelby tensor for penny-shaped crack</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/eshelby_tensors.html#numerical-eshelby-tensor-for-general-ellipsoid">Numerical Eshelby tensor for general ellipsoid</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/eshelby_tensors.html#hill-s-interaction-tensor">Hill’s interaction tensor</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/heterogeneous/homogenization.html">2 phase composite homogenization example</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/homogenization.html#effect-of-aspect-ratio-on-eshelby-tensor-components">Effect of aspect ratio on Eshelby tensor components</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="examples/index.html#hyperelasticity">Hyperelasticity</a><ul>
<li class="toctree-l3"><a class="reference internal" href="examples/hyperelasticity/HYPER_numerical.html">Hyperelastic models - use the API</a></li>
<li class="toctree-l3"><a class="reference internal" href="examples/hyperelasticity/HYPER_umat.html">Hyperelastic models - use the umat</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="examples/index.html#constitutive-laws-examples">Constitutive Laws Examples</a><ul>
<li class="toctree-l3"><a class="reference internal" href="examples/umats/ELISO.html">Isotropic elasticity examples</a></li>
<li class="toctree-l3"><a class="reference internal" href="examples/umats/ELIST.html">Transversely Isotropic Elasticity Example</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/umats/ELIST.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/umats/ELORT.html">Orthotropic Elasticity Example</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/umats/ELORT.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/umats/EPCHA.html">Plasticity with Chaboche Hardening Example</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/umats/EPCHA.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/umats/EPICP.html">Plasticity with isotropic hardening example</a></li>
<li class="toctree-l3"><a class="reference internal" href="examples/umats/EPKCP.html">Plasticity with Isotropic and Kinematic Hardening Example</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/umats/EPKCP.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="continuum_mechanics/index.html">Continuum Mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="continuum_mechanics/functions/index.html">Continuum Mechanics generic functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html">The Constitutive Library</a><ul>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.Ireal"><code class="docutils literal notranslate"><span class="pre">Ireal()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.Ivol"><code class="docutils literal notranslate"><span class="pre">Ivol()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.Idev"><code class="docutils literal notranslate"><span class="pre">Idev()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.Ireal2"><code class="docutils literal notranslate"><span class="pre">Ireal2()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.Idev2"><code class="docutils literal notranslate"><span class="pre">Idev2()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.Ith"><code class="docutils literal notranslate"><span class="pre">Ith()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.Ir2"><code class="docutils literal notranslate"><span class="pre">Ir2()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.Ir05"><code class="docutils literal notranslate"><span class="pre">Ir05()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.L_iso"><code class="docutils literal notranslate"><span class="pre">L_iso()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.M_iso"><code class="docutils literal notranslate"><span class="pre">M_iso()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.L_cubic"><code class="docutils literal notranslate"><span class="pre">L_cubic()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.M_cubic"><code class="docutils literal notranslate"><span class="pre">M_cubic()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.L_ortho"><code class="docutils literal notranslate"><span class="pre">L_ortho()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.M_ortho"><code class="docutils literal notranslate"><span class="pre">M_ortho()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.L_isotrans"><code class="docutils literal notranslate"><span class="pre">L_isotrans()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.M_isotrans"><code class="docutils literal notranslate"><span class="pre">M_isotrans()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_constitutive.html#simcoon.H_iso"><code class="docutils literal notranslate"><span class="pre">H_iso()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="continuum_mechanics/functions/doc_rotation.html">The Rotation Library</a><ul>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_rotation.html#architecture">Architecture</a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_rotation.html#the-rotation-class">The Rotation Class</a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_rotation.html#euler-angle-conventions">Euler Angle Conventions</a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_rotation.html#practical-examples">Practical Examples</a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_rotation.html#see-also">See Also</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html">The Contimech Library</a><ul>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.dev"><code class="docutils literal notranslate"><span class="pre">dev()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.sph"><code class="docutils literal notranslate"><span class="pre">sph()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.tr"><code class="docutils literal notranslate"><span class="pre">tr()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.Mises_stress"><code class="docutils literal notranslate"><span class="pre">Mises_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.eta_stress"><code class="docutils literal notranslate"><span class="pre">eta_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.Mises_strain"><code class="docutils literal notranslate"><span class="pre">Mises_strain()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.eta_strain"><code class="docutils literal notranslate"><span class="pre">eta_strain()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.J2_stress"><code class="docutils literal notranslate"><span class="pre">J2_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.J2_strain"><code class="docutils literal notranslate"><span class="pre">J2_strain()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.J3_stress"><code class="docutils literal notranslate"><span class="pre">J3_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.J3_strain"><code class="docutils literal notranslate"><span class="pre">J3_strain()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.Macaulay_p"><code class="docutils literal notranslate"><span class="pre">Macaulay_p()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.Macaulay_n"><code class="docutils literal notranslate"><span class="pre">Macaulay_n()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.sign"><code class="docutils literal notranslate"><span class="pre">sign()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.normal_ellipsoid"><code class="docutils literal notranslate"><span class="pre">normal_ellipsoid()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.curvature_ellipsoid"><code class="docutils literal notranslate"><span class="pre">curvature_ellipsoid()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.sigma_int"><code class="docutils literal notranslate"><span class="pre">sigma_int()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.p_ikjl"><code class="docutils literal notranslate"><span class="pre">p_ikjl()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.auto_sym_dyadic"><code class="docutils literal notranslate"><span class="pre">auto_sym_dyadic()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.sym_dyadic"><code class="docutils literal notranslate"><span class="pre">sym_dyadic()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.auto_dyadic"><code class="docutils literal notranslate"><span class="pre">auto_dyadic()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.dyadic_4vectors_sym"><code class="docutils literal notranslate"><span class="pre">dyadic_4vectors_sym()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.auto_sym_dyadic_operator"><code class="docutils literal notranslate"><span class="pre">auto_sym_dyadic_operator()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_contimech.html#simcoon.sym_dyadic_operator"><code class="docutils literal notranslate"><span class="pre">sym_dyadic_operator()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html">The Criteria Library</a><ul>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.Drucker_stress"><code class="docutils literal notranslate"><span class="pre">Drucker_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.dDrucker_stress"><code class="docutils literal notranslate"><span class="pre">dDrucker_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.Tresca_stress"><code class="docutils literal notranslate"><span class="pre">Tresca_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.dTresca_stress"><code class="docutils literal notranslate"><span class="pre">dTresca_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.P_Ani"><code class="docutils literal notranslate"><span class="pre">P_Ani()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.P_Hill"><code class="docutils literal notranslate"><span class="pre">P_Hill()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.P_DFA"><code class="docutils literal notranslate"><span class="pre">P_DFA()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.Hill_stress"><code class="docutils literal notranslate"><span class="pre">Hill_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.dHill_stress"><code class="docutils literal notranslate"><span class="pre">dHill_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.Ani_stress"><code class="docutils literal notranslate"><span class="pre">Ani_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.dAni_stress"><code class="docutils literal notranslate"><span class="pre">dAni_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.DFA_stress"><code class="docutils literal notranslate"><span class="pre">DFA_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.dDFA_stress"><code class="docutils literal notranslate"><span class="pre">dDFA_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.Eq_stress"><code class="docutils literal notranslate"><span class="pre">Eq_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_criteria.html#simcoon.dEq_stress"><code class="docutils literal notranslate"><span class="pre">dEq_stress()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="continuum_mechanics/functions/doc_transfer.html">Transfer helpers (Voigt <-> matrix)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_transfer.html#simcoon.v2t_strain"><code class="docutils literal notranslate"><span class="pre">v2t_strain()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_transfer.html#simcoon.t2v_strain"><code class="docutils literal notranslate"><span class="pre">t2v_strain()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_transfer.html#simcoon.v2t_stress"><code class="docutils literal notranslate"><span class="pre">v2t_stress()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_transfer.html#simcoon.t2v_stress"><code class="docutils literal notranslate"><span class="pre">t2v_stress()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="continuum_mechanics/functions/doc_stress.html">Stress conversions</a><ul>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_stress.html#simcoon.stress_convert"><code class="docutils literal notranslate"><span class="pre">stress_convert()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="continuum_mechanics/functions/doc_damage.html">The Damage Library</a><ul>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_damage.html#simcoon.damage_weibull"><code class="docutils literal notranslate"><span class="pre">damage_weibull()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_damage.html#simcoon.damage_kachanov"><code class="docutils literal notranslate"><span class="pre">damage_kachanov()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_damage.html#simcoon.damage_miner"><code class="docutils literal notranslate"><span class="pre">damage_miner()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_damage.html#simcoon.damage_manson"><code class="docutils literal notranslate"><span class="pre">damage_manson()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html">The Kinematics Library</a><ul>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.ER_to_F"><code class="docutils literal notranslate"><span class="pre">ER_to_F()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.eR_to_F"><code class="docutils literal notranslate"><span class="pre">eR_to_F()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.G_UdX"><code class="docutils literal notranslate"><span class="pre">G_UdX()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.G_Udx"><code class="docutils literal notranslate"><span class="pre">G_Udx()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.R_Cauchy_Green"><code class="docutils literal notranslate"><span class="pre">R_Cauchy_Green()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.L_Cauchy_Green"><code class="docutils literal notranslate"><span class="pre">L_Cauchy_Green()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.RU_decomposition"><code class="docutils literal notranslate"><span class="pre">RU_decomposition()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.VR_decomposition"><code class="docutils literal notranslate"><span class="pre">VR_decomposition()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.Inv_X"><code class="docutils literal notranslate"><span class="pre">Inv_X()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.Cauchy"><code class="docutils literal notranslate"><span class="pre">Cauchy()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.Green_Lagrange"><code class="docutils literal notranslate"><span class="pre">Green_Lagrange()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.Euler_Almansi"><code class="docutils literal notranslate"><span class="pre">Euler_Almansi()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.Log_strain"><code class="docutils literal notranslate"><span class="pre">Log_strain()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.finite_L"><code class="docutils literal notranslate"><span class="pre">finite_L()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.finite_D"><code class="docutils literal notranslate"><span class="pre">finite_D()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.finite_W"><code class="docutils literal notranslate"><span class="pre">finite_W()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.finite_Omega"><code class="docutils literal notranslate"><span class="pre">finite_Omega()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_kinematics.html#simcoon.finite_DQ"><code class="docutils literal notranslate"><span class="pre">finite_DQ()</span></code></a></li>
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<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_recovery_props.html#simcoon.check_symetries"><code class="docutils literal notranslate"><span class="pre">check_symetries()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_recovery_props.html#simcoon.L_iso_props"><code class="docutils literal notranslate"><span class="pre">L_iso_props()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_recovery_props.html#simcoon.M_iso_props"><code class="docutils literal notranslate"><span class="pre">M_iso_props()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_recovery_props.html#simcoon.L_isotrans_props"><code class="docutils literal notranslate"><span class="pre">L_isotrans_props()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_recovery_props.html#simcoon.M_isotrans_props"><code class="docutils literal notranslate"><span class="pre">M_isotrans_props()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_recovery_props.html#simcoon.L_cubic_props"><code class="docutils literal notranslate"><span class="pre">L_cubic_props()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_recovery_props.html#simcoon.M_cubic_props"><code class="docutils literal notranslate"><span class="pre">M_cubic_props()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_recovery_props.html#simcoon.L_ortho_props"><code class="docutils literal notranslate"><span class="pre">L_ortho_props()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_recovery_props.html#simcoon.M_ortho_props"><code class="docutils literal notranslate"><span class="pre">M_ortho_props()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_recovery_props.html#simcoon.M_aniso_props"><code class="docutils literal notranslate"><span class="pre">M_aniso_props()</span></code></a></li>
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<li class="toctree-l3"><a class="reference internal" href="homogenization/doc_eshelby.html#simcoon.Eshelby_sphere"><code class="docutils literal notranslate"><span class="pre">Eshelby_sphere()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="homogenization/doc_eshelby.html#simcoon.Eshelby_cylinder"><code class="docutils literal notranslate"><span class="pre">Eshelby_cylinder()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="homogenization/doc_eshelby.html#simcoon.Eshelby_prolate"><code class="docutils literal notranslate"><span class="pre">Eshelby_prolate()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="homogenization/doc_eshelby.html#simcoon.Eshelby_oblate"><code class="docutils literal notranslate"><span class="pre">Eshelby_oblate()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="homogenization/doc_eshelby.html#simcoon.Eshelby_penny"><code class="docutils literal notranslate"><span class="pre">Eshelby_penny()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="homogenization/doc_eshelby.html#simcoon.Eshelby"><code class="docutils literal notranslate"><span class="pre">Eshelby()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="homogenization/doc_eshelby.html#simcoon.T_II"><code class="docutils literal notranslate"><span class="pre">T_II()</span></code></a></li>
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<section id="simcoon-constitutive-modeling-and-material-library">
<h1>Simcoon — Constitutive Modeling and Material Library<a class="headerlink" href="#simcoon-constitutive-modeling-and-material-library" title="Link to this heading"></a></h1>
<a class="align-center reference internal image-reference" href="_images/simcoon_overview.pdf"><img alt="Simcoon overview" class="align-center" src="_images/simcoon_overview.pdf" style="width: 700px;" />
</a>
<section id="overview">
<h2>📌 Overview<a class="headerlink" href="#overview" title="Link to this heading"></a></h2>
<p>Simcoon is a free, open-source C++ library for simulating multiphysics systems. Its primary objective was the development of constitutive models for heterogeneous materials, and it now also provides tools for full-field simulation. Together with
[microgen](<a class="reference external" href="https://github.com/3MAH/microgen">https://github.com/3MAH/microgen</a>) for CAD and meshing of heterogeneous materials and
[fedoo](<a class="reference external" href="https://github.com/3MAH/fedoo">https://github.com/3MAH/fedoo</a>), our finite-element solver, the project provides a comprehensive toolset for analyzing heterogeneous materials.</p>
<p>Simcoon aims to be a high-quality scientific library for analysing complex, nonlinear system behaviour. It emphasizes performance and ease of use and exposes a Python interface to simplify workflows. The principal focus is to provide a C++ API to generate user-material subroutines for finite-element packages. Simcoon also includes tools to analyse material-point behaviour under loading, such as a thermomechanical solver, a tool to predict effective properties of composites, and a built-in identification tool that combines genetic and gradient-based algorithms.</p>
<p>Simcoon supports geometric nonlinearity using Lagrangian and Eulerian measures, and cumulative strains with several objective rates (Jaumann, Green–Naghdi, and Xi–Meyers–Brühns logarithmic). The logarithmic cumulative-strain measure is the default used by the library’s constitutive laws.</p>
<p>Simcoon makes use of the FTensor library (<a class="reference external" href="http://www.wlandry.net/Projects/FTensor">http://www.wlandry.net/Projects/FTensor</a>) for tensor computations; FTensor is distributed under the GNU General Public License (GPL v2) and is included in this repository.</p>
<p>Simcoon is mainly developed by faculty and researchers from Université Grenoble Alpes (TIMC laboratory) and the University of Bordeaux (I2M Laboratory). Contributions also came from the LEM3 laboratory (Metz, France) and TU Bergakademie Freiberg (Germany). The project is released under the GNU General Public License (GPL v3).</p>
<p>[![GitHub license](<a class="reference external" href="https://img.shields.io/badge/license-GPL%203-blue.svg)](https://github.com/chemiskyy/simcoon/blob/master/LICENSE">https://img.shields.io/badge/license-GPL%203-blue.svg)](https://github.com/chemiskyy/simcoon/blob/master/LICENSE</a>)</p>
</section>
<section id="installation">
<h2>⚙️ Installation<a class="headerlink" href="#installation" title="Link to this heading"></a></h2>
<p>Install via conda:</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>conda<span class="w"> </span>install<span class="w"> </span>-c<span class="w"> </span>conda-forge<span class="w"> </span>simcoon
</pre></div>
</div>
<p>Complete installation instructions are available on the
<a class="reference internal" href="installation.html"><span class="doc">Installation</span></a> page.</p>
<p>The guide covers:
- Conda-based installation
- Building from source
- Optional dependencies</p>
<section id="key-features">
<h3>Key features<a class="headerlink" href="#key-features" title="Link to this heading"></a></h3>
<ul class="simple">
<li><p>📐 Finite strain mechanics</p></li>
<li><p>🧱 Modular constitutive models</p></li>
<li><p>🐍 Python bindings</p></li>
<li><p>⚡ High-performance C++ core</p></li>
</ul>
</section>
<section id="getting-started">
<h3>🚀 Getting started<a class="headerlink" href="#getting-started" title="Link to this heading"></a></h3>
<p>New users should begin with:</p>
<ul class="simple">
<li><p><a class="reference internal" href="simulation/solver.html"><span class="doc">Use the solver</span></a></p></li>
<li><p><a class="reference internal" href="examples/index.html"><span class="doc">Examples</span></a></p></li>
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<section id="documentation">
<h3>📚 Documentation<a class="headerlink" href="#documentation" title="Link to this heading"></a></h3>
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<li class="toctree-l2"><a class="reference internal" href="installation.html#developer-installation">Developer installation</a></li>
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<li class="toctree-l2"><a class="reference internal" href="external.html#umext-plugin-format">UMEXT Plugin Format</a></li>
<li class="toctree-l2"><a class="reference internal" href="external.html#umaba-plugin-format-abaqus-compatibility">UMABA Plugin Format (Abaqus Compatibility)</a></li>
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<li class="toctree-l2"><a class="reference internal" href="external.html#running-the-tests">Running the Tests</a></li>
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<li class="toctree-l1"><a class="reference internal" href="simulation/index.html">Simulation</a><ul>
<li class="toctree-l2"><a class="reference internal" href="simulation/solver.html">Use the solver</a></li>
<li class="toctree-l2"><a class="reference internal" href="simulation/output.html">Configure the output</a></li>
<li class="toctree-l2"><a class="reference internal" href="simulation/fea_integration.html">FEA Integration</a></li>
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<li class="toctree-l1"><a class="reference internal" href="examples/index.html">Examples</a><ul>
<li class="toctree-l2"><a class="reference internal" href="examples/index.html#analysis-and-processing-examples">Analysis and processing examples</a></li>
<li class="toctree-l2"><a class="reference internal" href="examples/index.html#continuum-mechanics-examples">Continuum Mechanics Examples</a></li>
<li class="toctree-l2"><a class="reference internal" href="examples/index.html#heterogeneous-materials-simulation">Heterogeneous materials simulation</a></li>
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<li class="toctree-l2"><a class="reference internal" href="examples/index.html#constitutive-laws-examples">Constitutive Laws Examples</a></li>
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<li class="toctree-l2"><a class="reference internal" href="homogenization/doc_eshelby.html">The Eshelby Library</a></li>
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