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<!DOCTYPE html>
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<p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
<ul>
<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><ul>
<li class="toctree-l3"><a class="reference internal" href="installation.html#duplicate-openmp-runtimes-on-macos">Duplicate OpenMP runtimes on macOS</a></li>
</ul>
</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>
</ul>
</li>
</ul>
</li>
<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#the-loading-path-file">The loading path file</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#path-and-block-parameters">Path and 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>
<li class="toctree-l4"><a class="reference internal" href="simulation/solver.html#pre-2-0-text-inputs">Pre-2.0 text inputs</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#mean-field-composites">Mean-field composites</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#legacy-text-inputs">Legacy text inputs</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#constitutive-laws-written-in-python">Constitutive laws written in Python</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.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#stress-measure-and-tangent-rate">Stress measure and tangent rate</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/modular_python.html">Building materials in Python (<code class="docutils literal notranslate"><span class="pre">modular</span></code>)</a><ul>
<li class="toctree-l3"><a class="reference internal" href="simulation/modular_python.html#quick-start">Quick start</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/modular_python.html#elasticity">Elasticity</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/modular_python.html#yield-criteria">Yield criteria</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/modular_python.html#isotropic-hardening">Isotropic hardening</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/modular_python.html#kinematic-hardening">Kinematic hardening</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/modular_python.html#mechanisms">Mechanisms</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/modular_python.html#tangent-operator-and-finite-strain">Tangent operator and finite strain</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/modular_python.html#see-also">See also</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="simulation/python_umat.html">Constitutive laws in Python (PYEXT)</a><ul>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_umat.html#quick-start">Quick start</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_umat.html#the-contract">The contract</a><ul>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_umat.html#step-cuts-and-errors">Step cuts and errors</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_umat.html#batch-entry-point-and-explicit-registration">Batch entry point and explicit registration</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_umat.html#performance">Performance</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_umat.html#examples">Examples</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/python_umat.html#api-reference">API reference</a><ul>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_umat.html#simcoon.PythonUMAT"><code class="docutils literal notranslate"><span class="pre">PythonUMAT</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_umat.html#simcoon.StepCut"><code class="docutils literal notranslate"><span class="pre">StepCut</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_umat.html#simcoon.registered"><code class="docutils literal notranslate"><span class="pre">registered()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_umat.html#simcoon.pyumat.register"><code class="docutils literal notranslate"><span class="pre">register()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_umat.html#simcoon.pyumat.unregister"><code class="docutils literal notranslate"><span class="pre">unregister()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="simulation/python_umat.html#simcoon.pyumat.current"><code class="docutils literal notranslate"><span class="pre">current()</span></code></a></li>
</ul>
</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">Read the results</a><ul>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#layout">Layout</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#increment-bookkeeping">Increment bookkeeping</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#strain-and-stress-measures">Strain and stress measures</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#energies-state-variables-tangent">Energies, state variables, tangent</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#thermomechanical-runs">Thermomechanical runs</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#completion-status">Completion status</a></li>
<li class="toctree-l3"><a class="reference internal" href="simulation/output.html#saving-and-tabulating">Saving and tabulating</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>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor.html#the-basis-of-the-components">21. The basis of the components</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html">The basis of a tensor: frames, convected bases and the metric</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#the-lab-basis-is-the-default">1. The lab basis is the default</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#an-orthonormal-basis-and-its-description">2. An orthonormal basis and its description</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#to-basis-the-same-tensor-in-another-basis">3. <code class="docutils literal notranslate"><span class="pre">to_basis</span></code>: the same tensor in another basis</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#tensors-in-different-bases-cannot-be-mixed">4. Tensors in different bases cannot be mixed</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#a-passive-rotation-ships-its-frame">5. A passive rotation ships its frame</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#an-active-rotation-is-a-transport">6. An active rotation is a transport</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#a-constitutive-law-written-in-its-material-frame">7. A constitutive law written in its material frame</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#batches-one-basis-for-all-or-one-per-tensor">8. Batches: one basis for all, or one per tensor</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#a-natural-basis-and-its-metric">9. A natural basis and its metric</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#with-basis-transport-by-keeping-the-components">10. <code class="docutils literal notranslate"><span class="pre">with_basis</span></code>: transport by keeping the components</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#invariants-with-the-metric">11. Invariants with the metric</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#contractions-dual-variances-need-no-metric">12. Contractions: dual variances need no metric</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#the-identity-tensor-is-the-metric">13. The identity tensor is the metric</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#fourth-order-tensors-in-a-natural-basis">14. Fourth-order tensors in a natural basis</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#push-forward-and-pull-back-carry-the-basis-along">15. Push-forward and pull-back carry the basis along</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#objectivity">16. Objectivity</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#a-convected-basis-per-gauss-point">17. A convected basis per Gauss point</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#housekeeping">18. Housekeeping</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#bases-that-come-from-elsewhere-ply-frames-shells-successive-transports">19. Bases that come from elsewhere: ply frames, shells, successive transports</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/continuum_mechanics/tensor_basis.html#the-variance-tag-raising-and-lowering-indices">20. The variance tag: raising and lowering indices</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>
<li class="toctree-l3"><a class="reference internal" href="examples/identification/json_keys_identification.html">Identification through keys in a JSON material file</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/EPJCK.html">Johnson-Cook plasticity: strain-rate sensitivity</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#build-the-loading-path">2. Build the loading path</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL.html#run-the-solver">3. Run the solver</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL.html#plot-the-stress-strain-curve">4. Plot the stress-strain curve</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/MODUL_closest_point.html">Closest-Point Projection — Non-Proportional Loading</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_closest_point.html#the-ladder-of-models">1. The ladder of models</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_closest_point.html#the-figure-eight-in-strain-space">2. The figure-eight in strain space</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_closest_point.html#accuracy-at-coarse-increments">3. Accuracy at coarse increments</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_closest_point.html#global-newton-convergence-under-stress-control">4. Global Newton convergence under stress control</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_closest_point.html#plots">5. Plots</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#build-the-loading-path">2. Build the loading path</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_finite.html#run-the-solver-under-nlgeom">3. Run the solver under NLGEOM</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_finite.html#plot-the-response">4. Plot the response</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="examples/mechanical/MODUL_hyper_visco.html">Modular UMAT: Hyperelastic Block with Prony Branches (Finite-Strain Viscoelasticity)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_hyper_visco.html#compose-the-constitutive-model">1. Compose the constitutive model</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_hyper_visco.html#loading-paths">2. Loading paths</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_hyper_visco.html#rate-sweep">3. Rate sweep</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_hyper_visco.html#ramp-and-hold">4. Ramp and hold</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/MODUL_hyper_visco.html#plot">5. Plot</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_T.html">Shape Memory Alloy - Superelastic Model</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/SMA_T.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 - Transformation and Reorientation</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/SMA_TR.html#loading-protocol">Loading protocol</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/SMA_TR.html#from-shape-memory-to-superelasticity">From shape memory to superelasticity</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/mechanical/SMA_TR.html#shape-memory-effect-in-the-stress-temperature-strain-space">Shape memory effect in the stress-temperature-strain space</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#python-and-machine-learning-constitutive-laws">Python and machine-learning constitutive laws</a><ul>
<li class="toctree-l3"><a class="reference internal" href="examples/ml/pyumat_numpy_j2.html">J2 plasticity written in Python (PYEXT)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/ml/pyumat_numpy_j2.html#the-law">The law</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/ml/pyumat_numpy_j2.html#cyclic-uniaxial-loading-under-mixed-control">Cyclic uniaxial loading under mixed control</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/EPJCK.html">Johnson-Cook plasticity with adiabatic self-heating (thermomechanical)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/EPJCK.html#adiabatic-tension-at-two-strain-rates">Adiabatic tension at two strain rates</a></li>
<li class="toctree-l4"><a class="reference internal" href="examples/thermomechanical/EPJCK.html#plotting-the-results">Plotting the results</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#basis-the-reference-system-of-the-components">Basis: the reference system of the components</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>
</ul>
</li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="homogenization/index.html">Homogenization</a><ul>
<li class="toctree-l2"><a class="reference internal" href="homogenization/doc_eshelby.html">The Eshelby Library</a><ul>
<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>
</ul>
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</ul>
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<li class="toctree-l1"><a class="reference internal" href="cpp_api/index.html">C++ API Reference</a><ul>
<li class="toctree-l2"><a class="reference internal" href="cpp_api/index.html#namespace-overview">Namespace Overview</a><ul>
<li class="toctree-l3"><a class="reference internal" href="cpp_api/continuum_mechanics/index.html">Continuum Mechanics</a><ul>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/continuum_mechanics/functions/index.html">Mechanical Functions</a></li>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/continuum_mechanics/material.html">Material Properties</a></li>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/continuum_mechanics/micromechanics.html">Micromechanics</a></li>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/continuum_mechanics/index.html#overview">Overview</a></li>
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<li class="toctree-l3"><a class="reference internal" href="cpp_api/simulation/index.html">Simulation</a><ul>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/simulation/maths.html">Mathematical Functions</a></li>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/simulation/rotation.html">The Rotation Module</a></li>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/simulation/solver.html">Solver Functions</a></li>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/simulation/phase.html">Phase</a></li>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/simulation/index.html#overview">Overview</a></li>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/simulation/index.html#what-s-new-in-simcoon-2-0">What’s New in Simcoon 2.0</a></li>
</ul>
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<li class="toctree-l3"><a class="reference internal" href="cpp_api/homogenization/index.html">Homogenization</a><ul>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/homogenization/index.html#eshelby-tensor">Eshelby Tensor</a></li>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/homogenization/index.html#homogenization-schemes">Homogenization Schemes</a></li>
</ul>
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<li class="toctree-l3"><a class="reference internal" href="cpp_api/umat/index.html">User Material Subroutines</a><ul>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/umat/finite.html">Finite Strain Models</a></li>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/umat/mechanical.html">Mechanical Models</a></li>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/umat/thermomechanical.html">Thermomechanical Models</a></li>
<li class="toctree-l4"><a class="reference internal" href="cpp_api/umat/index.html#overview">Overview</a></li>
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