DMTA / DMA Analysis¶
RheoJAX supports data from Dynamic Mechanical (Thermal) Analysis instruments through automatic E* ↔ G* modulus conversion. All 45 oscillation-capable models can fit DMTA data without any model-level changes.
Quick Start¶
from rheojax.models import FractionalZenerSolidSolid
model = FractionalZenerSolidSolid()
model.fit(
omega, E_star,
test_mode='oscillation',
deformation_mode='tension',
poisson_ratio=0.5, # rubber (0.35 for glassy, 0.40 for semicrystalline)
)
E_pred = model.predict(omega, test_mode='oscillation') # returns E*
The Key Insight¶
The relaxation spectrum \(H(\tau)\) is a material property independent of deformation mode. Shear, tension, and bending all share the same spectrum — only the amplitude scale changes:
This means every OSCILLATION-capable model in RheoJAX works with DMTA
data after a simple modulus conversion at the fit() / predict()
boundary.
Recommended Starting Points¶
FractionalZenerSolidSolid— broad glass transitions (3–5 params)GeneralizedMaxwell— any spectrum shape + FEM exportHVMLocal— vitrimers with \(T_v\)Mastercurve→FractionalZenerSolidSolid— multi-temperature TTS workflow
See DMTA Model Selection & Applicability for the complete model and transform applicability guide.
What’s in This Section¶
E* ↔ G* conversion, Poisson’s ratio, Kramers–Kronig, relaxation spectra |
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Complete inventory: 45 compatible models, 11 transforms, decision tables, recommended starting points |
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JIT strategy, parameter bounds, convergence, FAST_MODE, memory management |
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8 end-to-end workflows (direct fit, TTS, Bayesian, CSV loading, HVM, cross-domain) |
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ISO/ASTM protocol mapping, instrument geometries, heating rates |
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T_g extraction, relaxation spectrum, tan(delta), plateau modulus, cooperativity |
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Planned: frequency-dependent nu, nonlinear DMA, FEM export |
Example Notebooks¶
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E* ↔ G* conversion fundamentals |
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Multi-temperature TTS + GMM/FZSS fitting on real data |
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Fractional viscoelasticity + Bayesian UQ |
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Time-domain E(t) Prony series + cross-domain |
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HVM/HVNM with tensile deformation |
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Multi-model comparison (synthetic + real data) |
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Raw multi-T → TTS → fit → WLF extraction |
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Frequency ↔ relaxation domain consistency |
- DMTA Theory & Conversion
- DMTA Model Selection & Applicability
- Numerical Implementation
- DMTA Workflows
- Workflow 1: Direct Fit with Modulus Conversion
- Workflow 2: Master Curve from Multi-T DMTA
- Workflow 3: NLSQ -> NUTS for Uncertainty
- Workflow 4: Loading DMTA CSV Files
- Workflow 5: Vitrimer DMTA with HVM
- Workflow 6: Model Selection Query
- Workflow 7: Bounds Handling for Real DMTA Data
- Workflow 8: Cross-Domain Validation
- DMTA Measurement Protocols
- Knowledge Extraction from DMTA Data
- Glass Transition Temperature \(T_g\)
- Relaxation Spectrum \(H(\tau)\)
- Loss Tangent \(\tan\delta\) Analysis
- Storage Modulus Crossover and Modulus Drop
- Molecular Weight from Plateau Modulus
- Plateau Modulus \(E_\infty\) / \(G_N^0\)
- Fractional Order \(\alpha\) and Cooperativity
- WLF / Arrhenius Activation Energy
- Network Topology (Vitrimer Models)
- Future Extensions