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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"><a class="reference internal" href="about.html">About</a></li>
<li class="toctree-l1"><a class="reference internal" href="installation.html">Installation</a><ul>
<li class="toctree-l2"><a class="reference internal" href="installation.html#quick-install">Quick install</a></li>
<li class="toctree-l2"><a class="reference internal" href="installation.html#blas-lapack-and-openmp">BLAS/LAPACK and OpenMP</a></li>
<li class="toctree-l2"><a class="reference internal" href="installation.html#developer-installation">Developer installation</a><ul>
<li class="toctree-l3"><a class="reference internal" href="installation.html#prerequisites-conda">Prerequisites (conda)</a></li>
<li class="toctree-l3"><a class="reference internal" href="installation.html#prerequisites-system-packages">Prerequisites (system packages)</a></li>
<li class="toctree-l3"><a class="reference internal" href="installation.html#building-from-source">Building from source</a></li>
<li class="toctree-l3"><a class="reference internal" href="installation.html#running-tests">Running tests</a></li>
<li class="toctree-l3"><a class="reference internal" href="installation.html#using-simcoon-with-fedoo">Using simcoon with fedoo</a></li>
</ul>
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</ul>
</li>
<li class="toctree-l1 current"><a class="current reference internal" href="#">External</a><ul>
<li class="toctree-l2"><a class="reference internal" href="#umext-plugin-format">UMEXT Plugin Format</a></li>
<li class="toctree-l2"><a class="reference internal" href="#umaba-plugin-format-abaqus-compatibility">UMABA Plugin Format (Abaqus Compatibility)</a></li>
<li class="toctree-l2"><a class="reference internal" href="#umans-plugin-format-ansys-compatibility">UMANS Plugin Format (Ansys Compatibility)</a></li>
<li class="toctree-l2"><a class="reference internal" href="#compiling-external-plugins">Compiling External Plugins</a></li>
<li class="toctree-l2"><a class="reference internal" href="#setting-up-input-files">Setting Up Input Files</a></li>
<li class="toctree-l2"><a class="reference internal" href="#testing-external-plugins">Testing External Plugins</a></li>
<li class="toctree-l2"><a class="reference internal" href="#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>
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<section id="external">
<h1>External<a class="headerlink" href="#external" title="Link to this heading"></a></h1>
<p>Simcoon offers the possibility to develop your own user material plugin that can be loaded at runtime by the solver.
You can develop such an external plugin using the Simcoon API. Three plugin formats are available:</p>
<ul class="simple">
<li><p><strong>UMEXT</strong> (<code class="docutils literal notranslate"><span class="pre">umat_plugin_ext_api</span></code>): Native simcoon format using Armadillo vectors and matrices</p></li>
<li><p><strong>UMABA</strong> (<code class="docutils literal notranslate"><span class="pre">umat_plugin_aba_api</span></code>): Abaqus UMAT-compatible format for existing Fortran/C++ UMATs</p></li>
<li><p><strong>UMANS</strong> (<code class="docutils literal notranslate"><span class="pre">umat_plugin_ans_api</span></code>): ANSYS USERMAT-compatible format for existing Fortran/C++ USERMATs</p></li>
</ul>
<p>Examples are provided in the <code class="docutils literal notranslate"><span class="pre">external/</span></code> folder.</p>
<section id="umext-plugin-format">
<h2>UMEXT Plugin Format<a class="headerlink" href="#umext-plugin-format" title="Link to this heading"></a></h2>
<p>The UMEXT format is the native simcoon plugin format that uses Armadillo vectors and matrices directly.
Your plugin must inherit from <code class="docutils literal notranslate"><span class="pre">umat_plugin_ext_api</span></code> and implement the following interface:</p>
<div class="highlight-cpp notranslate"><div class="highlight"><pre><span></span><span class="cp">#include</span><span class="w"> </span><span class="cpf"><simcoon/Continuum_mechanics/Umat/umat_plugin_api.hpp></span>
<span class="k">class</span><span class="w"> </span><span class="nc">umat_plugin_ext</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">umat_plugin_ext_api</span><span class="w"> </span><span class="p">{</span>
<span class="k">public</span><span class="o">:</span>
<span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="w"> </span><span class="n">name</span><span class="p">()</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="k">override</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="s">"umext"</span><span class="p">;</span><span class="w"> </span><span class="c1">// Material name used in material.dat</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">umat_external_M</span><span class="p">(</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="w"> </span><span class="o">&</span><span class="n">umat_name</span><span class="p">,</span><span class="w"> </span><span class="c1">// Material model name</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">arma</span><span class="o">::</span><span class="n">vec</span><span class="w"> </span><span class="o">&</span><span class="n">Etot</span><span class="p">,</span><span class="w"> </span><span class="c1">// Total strain at beginning of increment</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">arma</span><span class="o">::</span><span class="n">vec</span><span class="w"> </span><span class="o">&</span><span class="n">DEtot</span><span class="p">,</span><span class="w"> </span><span class="c1">// Strain increment</span>
<span class="w"> </span><span class="n">arma</span><span class="o">::</span><span class="n">vec</span><span class="w"> </span><span class="o">&</span><span class="n">sigma</span><span class="p">,</span><span class="w"> </span><span class="c1">// Stress tensor (in/out)</span>
<span class="w"> </span><span class="n">arma</span><span class="o">::</span><span class="n">mat</span><span class="w"> </span><span class="o">&</span><span class="n">Lt</span><span class="p">,</span><span class="w"> </span><span class="c1">// Tangent modulus (output)</span>
<span class="w"> </span><span class="n">arma</span><span class="o">::</span><span class="n">mat</span><span class="w"> </span><span class="o">&</span><span class="n">L</span><span class="p">,</span><span class="w"> </span><span class="c1">// Elastic stiffness (output)</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">arma</span><span class="o">::</span><span class="n">mat</span><span class="w"> </span><span class="o">&</span><span class="n">DR</span><span class="p">,</span><span class="w"> </span><span class="c1">// Rotation increment matrix</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">&</span><span class="n">nprops</span><span class="p">,</span><span class="w"> </span><span class="c1">// Number of material properties</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">arma</span><span class="o">::</span><span class="n">vec</span><span class="w"> </span><span class="o">&</span><span class="n">props</span><span class="p">,</span><span class="w"> </span><span class="c1">// Material properties</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">&</span><span class="n">nstatev</span><span class="p">,</span><span class="w"> </span><span class="c1">// Number of state variables</span>
<span class="w"> </span><span class="n">arma</span><span class="o">::</span><span class="n">vec</span><span class="w"> </span><span class="o">&</span><span class="n">statev</span><span class="p">,</span><span class="w"> </span><span class="c1">// State variables (in/out)</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">T</span><span class="p">,</span><span class="w"> </span><span class="c1">// Temperature at start</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">DT</span><span class="p">,</span><span class="w"> </span><span class="c1">// Temperature increment</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">Time</span><span class="p">,</span><span class="w"> </span><span class="c1">// Current time</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">DTime</span><span class="p">,</span><span class="w"> </span><span class="c1">// Time increment</span>
<span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">Wm</span><span class="p">,</span><span class="w"> </span><span class="c1">// Mechanical work (in/out)</span>
<span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">Wm_r</span><span class="p">,</span><span class="w"> </span><span class="c1">// Reversible work (in/out)</span>
<span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">Wm_ir</span><span class="p">,</span><span class="w"> </span><span class="c1">// Irreversible work (in/out)</span>
<span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">Wm_d</span><span class="p">,</span><span class="w"> </span><span class="c1">// Dissipated work (in/out)</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">&</span><span class="n">ndi</span><span class="p">,</span><span class="w"> </span><span class="c1">// Number of direct stress components</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">&</span><span class="n">nshr</span><span class="p">,</span><span class="w"> </span><span class="c1">// Number of shear stress components</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="o">&</span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="c1">// True if first increment</span>
<span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">tnew_dt</span><span class="w"> </span><span class="c1">// Suggested time step ratio</span>
<span class="w"> </span><span class="p">)</span><span class="w"> </span><span class="k">override</span><span class="p">;</span>
<span class="p">};</span>
<span class="c1">// Required factory functions</span>
<span class="k">extern</span><span class="w"> </span><span class="s">"C"</span><span class="w"> </span><span class="n">umat_plugin_ext_api</span><span class="o">*</span><span class="w"> </span><span class="n">create_api</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">umat_plugin_ext</span><span class="p">();</span>
<span class="p">}</span>
<span class="k">extern</span><span class="w"> </span><span class="s">"C"</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">destroy_api</span><span class="p">(</span><span class="n">umat_plugin_ext_api</span><span class="o">*</span><span class="w"> </span><span class="n">p</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">delete</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
<span class="p">}</span>
</pre></div>
</div>
<p>The file <code class="docutils literal notranslate"><span class="pre">external/umat_plugin_ext.cpp</span></code> provides a complete example implementing a thermoelastic material.</p>
</section>
<section id="umaba-plugin-format-abaqus-compatibility">
<h2>UMABA Plugin Format (Abaqus Compatibility)<a class="headerlink" href="#umaba-plugin-format-abaqus-compatibility" title="Link to this heading"></a></h2>
<p>The UMABA format provides a compatibility layer for existing Abaqus UMAT subroutines.
Your plugin wraps an external <code class="docutils literal notranslate"><span class="pre">umat_</span></code> function with the standard Abaqus signature.</p>
<div class="highlight-cpp notranslate"><div class="highlight"><pre><span></span><span class="cp">#include</span><span class="w"> </span><span class="cpf"><simcoon/Continuum_mechanics/Umat/umat_plugin_api.hpp></span>
<span class="c1">// Declare the external UMAT subroutine (Fortran or C++)</span>
<span class="k">extern</span><span class="w"> </span><span class="s">"C"</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">umat_</span><span class="p">(</span><span class="kt">double</span><span class="w"> </span><span class="o">*</span><span class="n">stress</span><span class="p">,</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">*</span><span class="n">statev</span><span class="p">,</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">*</span><span class="n">ddsdde</span><span class="p">,</span><span class="w"> </span><span class="p">...);</span>
<span class="p">}</span>
<span class="k">class</span><span class="w"> </span><span class="nc">umat_plugin_aba</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">umat_plugin_aba_api</span><span class="w"> </span><span class="p">{</span>
<span class="k">public</span><span class="o">:</span>
<span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="w"> </span><span class="n">name</span><span class="p">()</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="k">override</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="s">"umaba"</span><span class="p">;</span><span class="w"> </span><span class="c1">// Material name used in material.dat</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">umat_abaqus</span><span class="p">(</span>
<span class="w"> </span><span class="n">simcoon</span><span class="o">::</span><span class="n">phase_characteristics</span><span class="w"> </span><span class="o">&</span><span class="n">rve</span><span class="p">,</span><span class="w"> </span><span class="c1">// RVE state (contains material props, state vars)</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">arma</span><span class="o">::</span><span class="n">mat</span><span class="w"> </span><span class="o">&</span><span class="n">DR</span><span class="p">,</span><span class="w"> </span><span class="c1">// Rotation increment</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">Time</span><span class="p">,</span><span class="w"> </span><span class="c1">// Current time</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">DTime</span><span class="p">,</span><span class="w"> </span><span class="c1">// Time increment</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">&</span><span class="n">ndi</span><span class="p">,</span><span class="w"> </span><span class="c1">// Number of direct stress components</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">&</span><span class="n">nshr</span><span class="p">,</span><span class="w"> </span><span class="c1">// Number of shear stress components</span>
<span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="o">&</span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="c1">// True if first increment</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">&</span><span class="n">solver_type</span><span class="p">,</span><span class="w"> </span><span class="c1">// Solver type</span>
<span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">tnew_dt</span><span class="w"> </span><span class="c1">// Suggested time step ratio</span>
<span class="w"> </span><span class="p">)</span><span class="w"> </span><span class="k">override</span><span class="p">;</span>
<span class="p">};</span>
</pre></div>
</div>
<p>The Abaqus UMAT function signature:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>void umat_(double *stress, double *statev, double *ddsdde, double &sse, double &spd, double &scd, double &rpl, double *ddsddt, double *drplde, double &drpldt, const double *stran, const double *dstran, const double *time, const double &dtime, const double &temperature, const double &Dtemperature, const double &predef, const double &dpred, char *cmname, const int &ndi, const int &nshr, const int &ntens, const int &nstatev, const double *props, const int &nprops, const double &coords, const double *drot, double &pnewdt, const double &celent, const double *dfgrd0, const double *dfgrd1, const int &noel, const int &npt, const double &layer, const int &kspt, const int &kstep, const int &kinc)
</pre></div>
</div>
<table class="docutils align-default">
<thead>
<tr class="row-odd"><th class="head"><p>parameter</p></th>
<th class="head"><p>definition</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>stress</p></td>
<td><p>array containing the components of the stress tensor (dimension ntens)</p></td>
</tr>
<tr class="row-odd"><td><p>statev</p></td>
<td><p>array containing the evolution variables (dimension nstatev)</p></td>
</tr>
<tr class="row-even"><td><p>ddsdde</p></td>
<td><p>array containing the mechanical tangent operator (dimension ntens*ntens)</p></td>
</tr>
<tr class="row-odd"><td><p>sse</p></td>
<td><p>specific elastic strain energy</p></td>
</tr>
<tr class="row-even"><td><p>spd</p></td>
<td><p>plastic dissipation</p></td>
</tr>
<tr class="row-odd"><td><p>scd</p></td>
<td><p>creep dissipation</p></td>
</tr>
<tr class="row-even"><td><p>rpl</p></td>
<td><p>volumetric heat generation (coupled analysis only)</p></td>
</tr>
<tr class="row-odd"><td><p>ddsddt</p></td>
<td><p>array containing the thermal tangent operator</p></td>
</tr>
<tr class="row-even"><td><p>drplde</p></td>
<td><p>variation of RPL with strain increments</p></td>
</tr>
<tr class="row-odd"><td><p>drpldt</p></td>
<td><p>variation of RPL with temperature</p></td>
</tr>
<tr class="row-even"><td><p>stran</p></td>
<td><p>array containing total strain component (dimension ntens) at the beginning of increment</p></td>
</tr>
<tr class="row-odd"><td><p>dstran</p></td>
<td><p>array containing the component of total strain increment (dimension ntens)</p></td>
</tr>
<tr class="row-even"><td><p>time</p></td>
<td><p>two component array: step time and total time at beginning of increment</p></td>
</tr>
<tr class="row-odd"><td><p>dtime</p></td>
<td><p>time increment</p></td>
</tr>
<tr class="row-even"><td><p>temperature</p></td>
<td><p>temperature value at the beginning of increment</p></td>
</tr>
<tr class="row-odd"><td><p>Dtemperature</p></td>
<td><p>temperature increment</p></td>
</tr>
<tr class="row-even"><td><p>predef</p></td>
<td><p>predefined field variables</p></td>
</tr>
<tr class="row-odd"><td><p>dpred</p></td>
<td><p>predefined field increments</p></td>
</tr>
<tr class="row-even"><td><p>cmname</p></td>
<td><p>user-defined material name</p></td>
</tr>
<tr class="row-odd"><td><p>ndi</p></td>
<td><p>number of direct stress components</p></td>
</tr>
<tr class="row-even"><td><p>nshr</p></td>
<td><p>number of shear stress components</p></td>
</tr>
<tr class="row-odd"><td><p>ntens</p></td>
<td><p>number stress and strain components</p></td>
</tr>
<tr class="row-even"><td><p>nstatev</p></td>
<td><p>number of evolution variables</p></td>
</tr>
<tr class="row-odd"><td><p>props</p></td>
<td><p>array containing material properties</p></td>
</tr>
<tr class="row-even"><td><p>nprops</p></td>
<td><p>number of material properties</p></td>
</tr>
<tr class="row-odd"><td><p>coords</p></td>
<td><p>coordinates of the considered point</p></td>
</tr>
<tr class="row-even"><td><p>drot</p></td>
<td><p>rotation increment matrix (dimension 3*3)</p></td>
</tr>
<tr class="row-odd"><td><p>pnewdt</p></td>
<td><p>ratio of suggested new time increment</p></td>
</tr>
<tr class="row-even"><td><p>celent</p></td>
<td><p>characteristic element length</p></td>
</tr>
<tr class="row-odd"><td><p>dfgrd0</p></td>
<td><p>array containing the deformation gradient at the beginning of increment (dimension 3*3)</p></td>
</tr>
<tr class="row-even"><td><p>dfgrd1</p></td>
<td><p>array containing the deformation gradient at the end of increment (dimension 3*3)</p></td>
</tr>
<tr class="row-odd"><td><p>noel</p></td>
<td><p>element number</p></td>
</tr>
<tr class="row-even"><td><p>npt</p></td>
<td><p>integration point number</p></td>
</tr>
<tr class="row-odd"><td><p>layer</p></td>
<td><p>layer number - not used</p></td>
</tr>
<tr class="row-even"><td><p>kspt</p></td>
<td><p>section point number within the current layer - not used</p></td>
</tr>
<tr class="row-odd"><td><p>kstep</p></td>
<td><p>step number</p></td>
</tr>
<tr class="row-even"><td><p>kinc</p></td>
<td><p>increment number</p></td>
</tr>
</tbody>
</table>
<p>The file <code class="docutils literal notranslate"><span class="pre">external/umat_plugin_aba.cpp</span></code> provides a complete example, and <code class="docutils literal notranslate"><span class="pre">external/UMAT_ABAQUS_ELASTIC.f</span></code> is a sample Fortran UMAT.</p>
</section>
<section id="umans-plugin-format-ansys-compatibility">
<h2>UMANS Plugin Format (Ansys Compatibility)<a class="headerlink" href="#umans-plugin-format-ansys-compatibility" title="Link to this heading"></a></h2>
<p>The UMANS format provides a compatibility layer for existing Ansys USERMAT subroutines.
Your plugin wraps an external <code class="docutils literal notranslate"><span class="pre">usermat_</span></code> function with the standard Ansys signature.</p>
<div class="highlight-cpp notranslate"><div class="highlight"><pre><span></span><span class="cp">#include</span><span class="w"> </span><span class="cpf"><simcoon/Continuum_mechanics/Umat/umat_plugin_api.hpp></span>
<span class="c1">// Declare the external USERMAT subroutine (Fortran)</span>
<span class="k">extern</span><span class="w"> </span><span class="s">"C"</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">usermat_</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">matId</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">elemId</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">kDomIntPt</span><span class="p">,</span><span class="w"> </span><span class="p">...);</span>
<span class="p">}</span>
<span class="k">class</span><span class="w"> </span><span class="nc">umat_plugin_ans</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">umat_plugin_ans_api</span><span class="w"> </span><span class="p">{</span>
<span class="k">public</span><span class="o">:</span>
<span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="w"> </span><span class="n">name</span><span class="p">()</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="k">override</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="s">"umans"</span><span class="p">;</span><span class="w"> </span><span class="c1">// Material name used in material.dat</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">umat_ansys</span><span class="p">(</span>
<span class="w"> </span><span class="n">simcoon</span><span class="o">::</span><span class="n">phase_characteristics</span><span class="w"> </span><span class="o">&</span><span class="n">rve</span><span class="p">,</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">arma</span><span class="o">::</span><span class="n">mat</span><span class="w"> </span><span class="o">&</span><span class="n">DR</span><span class="p">,</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">Time</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">DTime</span><span class="p">,</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">&</span><span class="n">ndi</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">&</span><span class="n">nshr</span><span class="p">,</span>
<span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="o">&</span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">&</span><span class="n">solver_type</span><span class="p">,</span>
<span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="o">&</span><span class="n">tnew_dt</span>
<span class="w"> </span><span class="p">)</span><span class="w"> </span><span class="k">override</span><span class="p">;</span>
<span class="p">};</span>
</pre></div>
</div>
<p>The Ansys USERMAT function signature:</p>
<div class="highlight-fortran notranslate"><div class="highlight"><pre><span></span><span class="k">subroutine </span><span class="n">usermat</span><span class="p">(</span>
<span class="w"> </span><span class="n">matId</span><span class="p">,</span><span class="w"> </span><span class="n">elemId</span><span class="p">,</span><span class="w"> </span><span class="n">kDomIntPt</span><span class="p">,</span><span class="w"> </span><span class="n">kLayer</span><span class="p">,</span><span class="w"> </span><span class="n">kSectPt</span><span class="p">,</span>
<span class="w"> </span><span class="n">ldstep</span><span class="p">,</span><span class="w"> </span><span class="n">isubst</span><span class="p">,</span><span class="w"> </span><span class="n">keycut</span><span class="p">,</span>
<span class="w"> </span><span class="n">nDirect</span><span class="p">,</span><span class="w"> </span><span class="n">nShear</span><span class="p">,</span><span class="w"> </span><span class="n">ncomp</span><span class="p">,</span><span class="w"> </span><span class="n">nStatev</span><span class="p">,</span><span class="w"> </span><span class="n">nProp</span><span class="p">,</span>
<span class="w"> </span><span class="nb">Time</span><span class="p">,</span><span class="w"> </span><span class="nb">dTime</span><span class="p">,</span><span class="w"> </span><span class="n">Temp</span><span class="p">,</span><span class="w"> </span><span class="n">dTemp</span><span class="p">,</span>
<span class="w"> </span><span class="n">stress</span><span class="p">,</span><span class="w"> </span><span class="n">ustatev</span><span class="p">,</span><span class="w"> </span><span class="n">dsdde</span><span class="p">,</span>
<span class="w"> </span><span class="n">sedEl</span><span class="p">,</span><span class="w"> </span><span class="n">sedPl</span><span class="p">,</span><span class="w"> </span><span class="n">epseq</span><span class="p">,</span>
<span class="w"> </span><span class="n">Strain</span><span class="p">,</span><span class="w"> </span><span class="n">dStrain</span><span class="p">,</span><span class="w"> </span><span class="n">epsPl</span><span class="p">,</span>
<span class="w"> </span><span class="n">prop</span><span class="p">,</span><span class="w"> </span><span class="n">coords</span><span class="p">,</span><span class="w"> </span><span class="n">rotateM</span><span class="p">,</span>
<span class="w"> </span><span class="n">defGrad_t</span><span class="p">,</span><span class="w"> </span><span class="n">defGrad</span><span class="p">,</span>
<span class="w"> </span><span class="n">tsstif</span><span class="p">,</span><span class="w"> </span><span class="n">epsZZ</span><span class="p">,</span>
<span class="w"> </span><span class="n">var1</span><span class="p">,</span><span class="w"> </span><span class="n">var2</span><span class="p">,</span><span class="w"> </span><span class="n">var3</span><span class="p">,</span><span class="w"> </span><span class="n">var4</span><span class="p">,</span><span class="w"> </span><span class="n">var5</span><span class="p">)</span>
</pre></div>
</div>
<table class="docutils align-default">
<thead>
<tr class="row-odd"><th class="head"><p>parameter</p></th>
<th class="head"><p>definition</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>matId</p></td>
<td><p>Material ID number</p></td>
</tr>
<tr class="row-odd"><td><p>elemId</p></td>
<td><p>Element number</p></td>
</tr>
<tr class="row-even"><td><p>kDomIntPt</p></td>
<td><p>Current integration point in element</p></td>
</tr>
<tr class="row-odd"><td><p>kLayer</p></td>
<td><p>Current layer number</p></td>
</tr>
<tr class="row-even"><td><p>kSectPt</p></td>
<td><p>Current section point within layer</p></td>
</tr>
<tr class="row-odd"><td><p>ldstep</p></td>
<td><p>Current load step</p></td>
</tr>
<tr class="row-even"><td><p>isubst</p></td>
<td><p>Current substep</p></td>
</tr>
<tr class="row-odd"><td><p>keycut</p></td>
<td><p>Cutback flag (output: set to 1 to request smaller time step)</p></td>
</tr>
<tr class="row-even"><td><p>nDirect</p></td>
<td><p>Number of direct stress components (typically 3)</p></td>
</tr>
<tr class="row-odd"><td><p>nShear</p></td>
<td><p>Number of shear stress components (typically 3)</p></td>
</tr>
<tr class="row-even"><td><p>ncomp</p></td>
<td><p>Number of stress/strain components (nDirect + nShear)</p></td>
</tr>
<tr class="row-odd"><td><p>nStatev</p></td>
<td><p>Number of state variables</p></td>
</tr>
<tr class="row-even"><td><p>nProp</p></td>
<td><p>Number of material properties</p></td>
</tr>
<tr class="row-odd"><td><p>Time</p></td>
<td><p>Current time</p></td>
</tr>
<tr class="row-even"><td><p>dTime</p></td>
<td><p>Time increment</p></td>
</tr>
<tr class="row-odd"><td><p>Temp</p></td>
<td><p>Current temperature</p></td>
</tr>
<tr class="row-even"><td><p>dTemp</p></td>
<td><p>Temperature increment</p></td>
</tr>
<tr class="row-odd"><td><p>stress</p></td>
<td><p>Stress tensor (in: at t, out: at t+dt), dimension ncomp</p></td>
</tr>
<tr class="row-even"><td><p>ustatev</p></td>
<td><p>State variables (in/out), dimension nStatev</p></td>
</tr>
<tr class="row-odd"><td><p>dsdde</p></td>
<td><p>Material tangent modulus (output), dimension ncomp×ncomp</p></td>
</tr>
<tr class="row-even"><td><p>sedEl</p></td>
<td><p>Elastic strain energy density (in/out)</p></td>
</tr>
<tr class="row-odd"><td><p>sedPl</p></td>
<td><p>Plastic strain energy density (in/out)</p></td>
</tr>
<tr class="row-even"><td><p>epseq</p></td>
<td><p>Equivalent plastic strain (in/out)</p></td>
</tr>
<tr class="row-odd"><td><p>Strain</p></td>
<td><p>Total strain at t, dimension ncomp</p></td>
</tr>
<tr class="row-even"><td><p>dStrain</p></td>
<td><p>Strain increment, dimension ncomp</p></td>
</tr>
<tr class="row-odd"><td><p>epsPl</p></td>
<td><p>Plastic strain components, dimension ncomp</p></td>
</tr>
<tr class="row-even"><td><p>prop</p></td>
<td><p>Material property array, dimension nProp</p></td>
</tr>
<tr class="row-odd"><td><p>coords</p></td>
<td><p>Integration point coordinates (x, y, z)</p></td>
</tr>
<tr class="row-even"><td><p>rotateM</p></td>
<td><p>Rotation matrix (3×3)</p></td>
</tr>
<tr class="row-odd"><td><p>defGrad_t</p></td>
<td><p>Deformation gradient at t (3×3)</p></td>
</tr>
<tr class="row-even"><td><p>defGrad</p></td>
<td><p>Deformation gradient at t+dt (3×3)</p></td>
</tr>
<tr class="row-odd"><td><p>tsstif</p></td>
<td><p>Transverse shear stiffness (for shells)</p></td>
</tr>
<tr class="row-even"><td><p>epsZZ</p></td>
<td><p>Out-of-plane strain (for plane stress)</p></td>
</tr>
<tr class="row-odd"><td><p>var1-var5</p></td>