Models Handbook

The RheoJAX model handbook gathers narrative deep dives for every rheological model implemented in rheojax.models. Use it alongside the API reference for parameter signatures and the Model Selection Guide tree for high-level guidance.

Note

Each page follows a consistent template (overview, governing equations, parameter table, regimes/assumptions, usage snippets, troubleshooting, and references) so you can quickly compare models across families.

Overview

• Models Summary & Selection Guide

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Linear Viscoelastic Models

Classical spring-dashpot elements, fractional generalizations, and multi-mode models for fitting small-amplitude oscillatory and relaxation data.

Classical & Fractional

• Classical Viscoelastic Models
  • Quick Reference
  • Overview
  • Model Hierarchy
  • When to Use Which Model
  • Key Parameters
  • Quick Start
  • Model Documentation
  • See Also
  • References
• Fractional Viscoelastic Models
  • Quick Reference
  • Overview
  • Model Hierarchy
  • When to Use Which Model
  • Key Parameters
  • Quick Start
  • Model Documentation
  • See Also
  • References
• Generalized Maxwell Model (Multi-Mode)
  • Quick Reference
  • Notation Guide
  • Overview
  • Physical Foundations
  • Governing Equations
  • Parameters
  • Validity and Assumptions
  • What You Can Learn
  • Transparent Element Minimization
  • Two-Step NLSQ Fitting
  • Bayesian Inference Support
  • Usage
  • Experimental Design
  • Fitting Guidance
  • Model Comparison
  • API References
  • Usage Examples
  • See Also
  • References

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Nonlinear & Flow Models

Models for large deformations, steady-state flow curves, and constitutive ODE systems including Giesekus, flow viscoplastic, and kinematic hardening.

Nonlinear Viscoelastic

• Giesekus Nonlinear Viscoelastic Models
  • Overview
  • Model Variants
  • Key Features
  • Supported Protocols
  • Quick Start
  • When to Use Giesekus
  • References

Flow & Viscoplastic

• Flow Curve Models
  • Quick Reference
  • Overview
  • Model Hierarchy
  • When to Use Which Model
  • Material Examples
  • Key Parameters
  • Quick Start
  • Model Documentation
  • See Also
  • References

Elasto-Viscoplastic (IKH/FIKH)

• Isotropic-Kinematic Hardening (IKH) Models
  • Overview
  • Model Hierarchy
  • When to Use Which Model
  • Key Features
  • Quick Start
  • Model Documentation
  • References
• Fractional IKH (FIKH) Models
  • Overview
  • Model Hierarchy
  • When to Use FIKH
  • Model Comparison
  • Key Features
  • Quick Start
  • Model Documentation
  • References

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Thixotropy, Yielding & Soft Glassy Models

Structural-kinetics models (DMT, Fluidity), mean-field emulsion models (HL), shear transformation zones (STZ), elasto-plastic lattice models (EPM), soft glassy rheology (SGR), and mode-coupling theory (ITT-MCT).

Thixotropic & Yield Stress

• DMT Thixotropic Models
  • Overview
  • Model Hierarchy
  • When to Use Which Model
  • Key Features
  • Quick Start
  • Model Documentation
  • References
• Fluidity Models
  • Overview
  • Model Hierarchy
  • When to Use Which Model
  • Quick Comparison
  • Key Equations
  • Quick Start
  • Protocol-Specific Recommendations
  • Model Documentation
  • References
  • See Also
• Hébraud-Lequeux (HL) Models
  • Quick Reference
  • Overview
  • Physical Framework
  • Key Parameters
  • Model Predictions
  • Quick Start
  • Model Documentation
  • See Also
  • References
• Shear Transformation Zone (STZ) Models
  • Quick Reference
  • Overview
  • Physical Framework
  • Key Parameters
  • Model Predictions
  • Quick Start
  • Model Documentation
  • See Also
  • References
• Elasto-Plastic Models (EPM)
  • Quick Reference
  • Overview
  • Model Hierarchy
  • When to Use Which Model
  • Supported Protocols
  • Physical Context
  • Key Parameters
  • Quick Start
  • Model Documentation
  • References
  • See Also

Soft Glassy & Mode-Coupling

• Soft Glassy Rheology (SGR) Models
  • Quick Reference
  • Overview
  • Model Hierarchy
  • When to Use Which Model
  • SGR Phase Diagram
  • Key Parameters
  • Quick Start
  • Model Documentation
  • See Also
  • References
• ITT-MCT Models
  • Overview
  • Available Models
  • Model Selection Guide
  • Supported Protocols
  • Theoretical Framework
  • Physical Context
  • Key Parameters
  • References

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Transient Networks & Vitrimer Models

Distribution-tensor polymer network models (TNT, VLB), hybrid vitrimer models with BER kinetics (HVM), and nanoparticle-filled nanocomposite extensions (HVNM).

Transient Networks

• Transient Network Theory (TNT)
  • Overview
  • Model Hierarchy
  • When to Use Which Model
  • Failure Modes
  • Feature Comparison Matrix
  • Decision Framework
  • Key Parameters
  • Quick Start
  • Bayesian Inference
  • Supported Protocols
  • Model Documentation
  • See Also
  • References
• VLB Transient Network Models
  • Overview
  • Model Variants
  • Model Hierarchy
  • When to Use Which Model
  • Supported Protocols
  • Quick Start
  • Relation to TNT Models
  • Model Documentation
  • References

Vitrimer & Nanocomposite

• HVM (Hybrid Vitrimer Model)
  • Overview
  • Model Hierarchy
  • Quick Reference
  • When to Use This Model
  • Supported Protocols
  • Quick Start
  • Key Physics: Factor-of-2
  • Model Documentation
  • References
• HVNM (Hybrid Vitrimer Nanocomposite Model)
  • Overview
  • Model Hierarchy
  • Quick Reference
  • When to Use This Model
  • Supported Protocols
  • Quick Start
  • Key Physics
  • Model Documentation
  • References

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DMTA / DMA Analysis

Support for Dynamic Mechanical (Thermal) Analysis data via automatic E* ↔ G* modulus conversion.

DMTA

• DMTA / DMA Analysis
  • Quick Start
  • The Key Insight
  • Recommended Starting Points
  • What’s in This Section
  • Example Notebooks

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LAOS Analysis

Specialized tools for large-amplitude oscillatory shear analysis.

LAOS

• Sequence of Physical Processes (SPP) Models
  • Quick Reference
  • Overview
  • SPP Framework
  • When to Use SPP Analysis
  • Key Concepts
  • Quick Start
  • Model Documentation
  • SPP vs. Ewoldt (FTC) Frameworks
  • See Also
  • References