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<!DOCTYPE html>
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<p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
<ul class="current">
<li class="toctree-l1 current"><a class="current reference internal" href="#">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#tangent-operator-modes">Tangent-operator modes</a></li>
<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/python_solver.html">In-memory Python solver</a><ul>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_solver.html#quick-start">Quick start</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_solver.html#loading-control">Loading control</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_solver.html#thermomechanical-loading">Thermomechanical loading</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_solver.html#legacy-file-formats">Legacy file formats</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_solver.html#json-configuration">JSON configuration</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_solver.html#solver-parameters">Solver parameters</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_solver.html#api-reference">API reference</a><ul>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_solver.html#simcoon.solver.StepMeca"><code class="docutils literal notranslate"><span class="pre">StepMeca</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_solver.html#simcoon.solver.StepThermomeca"><code class="docutils literal notranslate"><span class="pre">StepThermomeca</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_solver.html#simcoon.solver.Block"><code class="docutils literal notranslate"><span class="pre">Block</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_solver.html#simcoon.solver.solve"><code class="docutils literal notranslate"><span class="pre">solve()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_solver.html#simcoon.solver.from_file"><code class="docutils literal notranslate"><span class="pre">from_file()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_solver.html#simcoon.solver.material_from_file"><code class="docutils literal notranslate"><span class="pre">material_from_file()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_solver.html#simcoon.solver.SolverResults"><code class="docutils literal notranslate"><span class="pre">SolverResults</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="simulation/umat_catalog.html">Constitutive model (UMAT) catalog</a><ul>
<li class="toctree-l3"><a class="reference internal" href="simulation/umat_catalog.html#small-strain-mechanical-models">Small-strain mechanical models</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/umat_catalog.html#shape-memory-alloys-finite-strain-multiscale-plugins">Shape memory alloys, finite strain, multiscale, plugins</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/umat_catalog.html#state-variable-statev-layout-for-adapter-served-names">State variable (statev) layout for adapter-served names</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/umat_catalog.html#tangent-operator-mode">Tangent-operator mode</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/umat_catalog.html#validation-and-performance">Validation and performance</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="simulation/umat_tutorial.html">Hands-on: writing a UMAT with simcoon</a><ul>
<li class="toctree-l3"><a class="reference internal" href="simulation/umat_tutorial.html#the-model">The model</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/umat_tutorial.html#step-1-anatomy-of-a-umat">Step 1 — anatomy of a UMAT</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/umat_tutorial.html#step-2-trial-state-typed">Step 2 — trial state, typed</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/umat_tutorial.html#step-3-radial-return-closed-form">Step 3 — radial return, closed form</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/umat_tutorial.html#step-4-the-continuum-tangent-derived-and-built">Step 4 — the continuum tangent, derived and built</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/umat_tutorial.html#step-5-validation">Step 5 — validation</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/umat_tutorial.html#where-to-go-next">Where to go next</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="simulation/identification.html">Parameter Identification</a><ul>
<li class="toctree-l3"><a class="reference internal" href="simulation/identification.html#overview">Overview</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/identification.html#key-system">Key System</a><ul>
<li class="toctree-l4"><a class="reference internal" href="simulation/identification.html#parameter-class">Parameter class</a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/identification.html#constant-class">Constant class</a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/identification.html#file-operations">File operations</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="simulation/identification.html#identification-global-optimization"><code class="docutils literal notranslate"><span class="pre">identification()</span></code> — Global Optimization</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/identification.html#calc-cost-multi-level-weighted-cost"><code class="docutils literal notranslate"><span class="pre">calc_cost()</span></code> — Multi-Level Weighted Cost</a><ul>
<li class="toctree-l4"><a class="reference internal" href="simulation/identification.html#weight-levels">Weight levels</a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/identification.html#metrics">Metrics</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="simulation/identification.html#using-with-external-solvers">Using with External Solvers</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/identification.html#gallery-examples">Gallery Examples</a></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/convergence_study.html">Increment size convergence study</a></li>
<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/neo_hookean_tensor.html">A Neo-Hookean material with the Tensor API</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/neo_hookean_tensor.html#material-and-deformation">0. Material and deformation</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/neo_hookean_tensor.html#strain-measures-and-their-transport">1. Strain measures and their transport</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/neo_hookean_tensor.html#the-law-in-the-reference-configuration-pkii-stress">2. The law in the reference configuration: PKII stress</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/neo_hookean_tensor.html#the-same-law-in-the-current-configuration-kirchhoff-stress">3. The same law in the current configuration: Kirchhoff stress</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/neo_hookean_tensor.html#stress-transport-one-object-three-measures">4. Stress transport: one object, three measures</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/neo_hookean_tensor.html#the-material-tangent-ds-de">5. The material tangent dS/dE</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/neo_hookean_tensor.html#tangent-transport-from-ds-de-to-the-spatial-moduli">6. Tangent transport: from dS/dE to the spatial moduli</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/neo_hookean_tensor.html#batch-a-full-uniaxial-stretch-curve-in-three-stress-measures">7. Batch: a full uniaxial-stretch curve in three stress measures</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/tensor.html">Tensor2 and Tensor4 Examples</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#building-typed-tensors">1. Building typed tensors</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#stiffness-and-compliance">2. Stiffness and compliance</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#contraction-sigma-l-epsilon">3. Contraction: sigma = L : epsilon</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#scalar-invariants">4. Scalar invariants</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#rotation-via-simcoon-rotation">5. Rotation via simcoon.Rotation</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#push-forward-and-pull-back">6. Push-forward and pull-back</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#material-frame-equivalence">7. Material-frame equivalence</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#arithmetic-and-dyadic-product">8. Arithmetic and dyadic product</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#building-isotropic-stiffness-from-projectors">9. Building isotropic stiffness from projectors</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#creating-a-batch-from-an-n-6-array">10. Creating a batch from an (N, 6) array</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#indexing-and-iteration">11. Indexing and iteration</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#batch-contraction-sigma-l-eps-for-100-gauss-points">12. Batch contraction: sigma = L : eps for 100 Gauss points</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#batch-von-mises-and-trace">13. Batch von Mises and trace</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#batch-rotation-with-scipy">14. Batch rotation with scipy</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#batch-push-forward-pull-back">15. Batch push-forward / pull-back</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#batch-tensor4-inverse-and-rotation">16. Batch Tensor4 inverse and rotation</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#concatenation-and-construction-from-lists">17. Concatenation and construction from lists</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#numpy-interop">18. numpy interop</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#arithmetic-on-batches">19. Arithmetic on batches</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#material-frame-equivalence-batch-version">20. Material-frame equivalence — batch version</a></li>
</ul>
</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/composite_parameter_identification.html">Composite Parameter Identification using Mori-Tanaka and Self-Consistent</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/composite_parameter_identification.html#problem-setup">Problem Setup</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/composite_parameter_identification.html#forward-model">Forward Model</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/heterogeneous/composite_parameter_identification.html#main-execution">Main Execution</a></li>
</ul>
</li>
<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>
<li class="toctree-l3"><a class="reference internal" href="examples/hyperelasticity/hyperelastic_umat_identification.html">Mooney-Rivlin identification with the MOORI UMAT and the simcoon API</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/hyperelasticity/hyperelastic_umat_identification.html#configuration">Configuration</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/hyperelasticity/hyperelastic_umat_identification.html#forward-model-the-moori-umat-through-sim-solver">Forward model: the MOORI UMAT through <code class="docutils literal notranslate"><span class="pre">sim.solver</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/hyperelasticity/hyperelastic_umat_identification.html#cost-function-sim-calc-cost-with-nmse-per-response">Cost function: <code class="docutils literal notranslate"><span class="pre">sim.calc_cost</span></code> with NMSE-per-response</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/hyperelasticity/hyperelastic_umat_identification.html#driver">Driver</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="examples/index.html#parameter-identification-examples">Parameter identification examples</a><ul>
<li class="toctree-l3"><a class="reference internal" href="examples/identification/chaboche_cyclic_identification.html">Chaboche Cyclic Plasticity Identification</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="examples/index.html#mechanical-constitutive-laws">Mechanical Constitutive Laws</a><ul>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/ELISO.html">Isotropic elasticity examples</a></li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/ELIST.html">Transversely Isotropic Elasticity Example</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/ELIST.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/ELORT.html">Orthotropic Elasticity Example</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/ELORT.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/EPCHA.html">Plasticity with Chaboche Hardening Example</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/EPCHA.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/EPICP.html">Plasticity with isotropic hardening example</a></li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/EPKCP.html">Plasticity with Isotropic and Kinematic Hardening Example</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/EPKCP.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/MODUL.html">Modular UMAT Example — Composable Elasto-Plasticity</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL.html#compose-the-constitutive-model">1. Compose the constitutive model</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL.html#run-the-solver">2. Run the solver</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL.html#plot-the-stress-strain-curve">3. Plot the stress-strain curve</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/MODUL_finite.html">Modular UMAT under Finite Strain — Hencky Hyperelasto-Plasticity</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_finite.html#compose-the-constitutive-model">1. Compose the constitutive model</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_finite.html#run-the-solver-under-nlgeom">2. Run the solver under NLGEOM</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_finite.html#plot-the-response">3. Plot the response</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/PRONY_N.html">Prony Series Viscoelastic Model (Generalized Maxwell)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/PRONY_N.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/SMA_TR.html">Shape Memory Alloy - Superelastic Model</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/SMA_TR.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/ZENER.html">Zener viscoelastic model</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/ZENER.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/ZENER_N.html">Generalized Zener model (N Kelvin branches)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/ZENER_N.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="examples/index.html#thermomechanical-constitutive-laws">Thermomechanical Constitutive Laws</a><ul>
<li class="toctree-l3"><a class="reference internal" href="examples/thermomechanical/ELISO.html">Isotropic elasticity (thermomechanical)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/ELISO.html#plotting-the-results">Plotting the results</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/thermomechanical/ELIST.html">Transversely isotropic elasticity (thermomechanical)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/ELIST.html#loading-in-direction-1">Loading in direction 1</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/ELIST.html#loading-in-direction-2">Loading in direction 2</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/thermomechanical/ELORT.html">Orthotropic elasticity (thermomechanical)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/ELORT.html#loading-in-direction-1">Loading in direction 1</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/ELORT.html#loading-in-direction-2">Loading in direction 2</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/ELORT.html#loading-in-direction-3">Loading in direction 3</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/thermomechanical/EPICP.html">Plasticity with isotropic hardening (thermomechanical)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/EPICP.html#plotting-the-results">Plotting the results</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/EPICP.html#increment-size-effect">Increment size effect</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/EPICP.html#plotting-the-increment-size-comparison">Plotting the increment size comparison</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/thermomechanical/EPKCP.html">Plasticity with kinematic hardening (thermomechanical)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/EPKCP.html#plotting-the-results">Plotting the results</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/EPKCP.html#increment-size-effect">Increment size effect</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/EPKCP.html#plotting-the-increment-size-comparison">Plotting the increment size comparison</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/thermomechanical/SMA_T.html">Shape Memory Alloy - Thermomechanical coupling</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/SMA_T.html#plotting-the-results">Plotting the results</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/SMA_T.html#increment-size-effect">Increment size effect</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/SMA_T.html#plotting-the-increment-size-comparison">Plotting the increment size comparison</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/thermomechanical/ZENER.html">Zener viscoelastic model (thermomechanical)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/ZENER.html#plotting-the-results">Plotting the results</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/ZENER.html#increment-size-effect">Increment size effect</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/ZENER.html#plotting-the-increment-size-comparison">Plotting the increment size comparison</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_tensor.html">Typed Tensors (Tensor2 / Tensor4)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_tensor.html#batch-operations">Batch operations</a></li>
<li class="toctree-l4"><a class="reference internal" href="continuum_mechanics/functions/doc_tensor.html#api-reference">API reference</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>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="continuum_mechanics/functions/doc_hyperelastic.html">Hyperelasticity</a></li>
<li class="toctree-l3"><a class="reference internal" href="continuum_mechanics/functions/doc_recovery_props.html">Recovery of Elastic Properties</a><ul>
<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>
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<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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<li class="toctree-l4"><a class="reference internal" href="cpp_api/homogenization/index.html#eshelby-tensor">Eshelby Tensor</a></li>
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<h1>About<a class="headerlink" href="#about" title="Link to this heading"></a></h1>
<p>Simcoon is a free, open-source library for the simulation of constitutive response of materials.
Its primarily objective was the developement of constitutive models for the simulation of heterogeneous materials, but now goes beyond with tools
to facilitate their full-field simulation. Together with <a class="reference external" href="https://microgen.readthedocs.io">microgen</a> for the CAD and meshing of heterogeneous materials and <a class="reference external" href="https://3mah.github.io/fedoo-docs">fedoo</a> our Finite Element solver,
we offer a comprehensive simulation set for the in-depth analysis of heterogeneous materials.</p>
<p>Simcoon is developed with the aim to be a high-quality scientific library to facilitate the analysis of the complex, non-linear behavior of systems.
It integrates tools to simulate the response of composite material response and thus integrates several algorithms for the analysis of heterogeneous materials.
Simcoon integrates an easy way to handle geometrical non-linearities : Use of Lagrangian measures, Eulerian measures and cumulative strains considering several spins : Jaumann, Green-Naghdi, Xi-Meyers-Bruhns logarithmic. With this last measure, cumulative strain correspond to a logarithmic strain measure and is the standard measure utilized for our constitutive laws.</p>
<p>Some of its main features are:</p>
<ul class="simple">
<li><p>Built on top of <strong>Armadillo</strong>, a high-quality C++ linear algebra library.</p></li>
<li><p>Uses <strong>Fastor</strong> for high-performance tensor operations.</p></li>
<li><p>Integrates several algorithms for heterogeneous materials analysis.</p></li>
<li><p>Provides both C++ and Python API to generate user material subroutines for Finite Element Analysis packages.</p></li>
</ul>
<p>simcoon is a C++ library with emphasis on speed and ease-of-use. Its principle focus is to provide tools to facilitate
the implementation of up-to-date constitutive model for materials in Finite Element Analysis Packages. This is done by
providing a C++ and a Python API to generate user material subroutine based on a library of functions. Also, simcoon
provides tools to analyse the behavior of material, considering loading at the material point level.</p>
<p>Simcoon is mainly developed by contributors from the staff and students of TIMC laboratory (Université Grenoble Alpes, France),
the I2M laboratory (Université de Bordeaux, France). It is released under the GNU General Public License: GPL, version 3.
Several institutions have contributed to the development of simcoon:</p>
<ul class="simple">
<li><p><strong>Université de Grenoble Alpes</strong>: University of Grenoble Alpes, France.</p></li>
<li><p><strong>Université de Bordeaux</strong>: University of Bordeaux, France.</p></li>
<li><p><strong>TIMC Laboratory</strong>: Recherche Translationnelle et Innovation en Médecine et Complexité, Grenoble, France.</p></li>
<li><p><strong>I2M Laboratory</strong>: Institut de Mécanique et d’Ingénierie, Bordeaux, France.</p></li>
<li><p><strong>LEM3 Laboratory</strong>: Laboratoire d’Étude des Microstructures et de Mécaniquedes Matériaux, Metz, Germany.</p></li>
<li><p><strong>TU Bergakademie Freiberg</strong>: School of Mines and Technical University in Freiberg, Germany.</p></li>
<li><p><strong>CNRS</strong>: National French Center for scientific research.</p></li>
</ul>
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