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:

\[E^*(\omega) = 2(1 + \nu)\,G^*(\omega)\]

This means every OSCILLATION-capable model in RheoJAX works with DMTA data after a simple modulus conversion at the fit() / predict() boundary.

What’s in This Section

DMTA Theory & Conversion

E* ↔ G* conversion, Poisson’s ratio, Kramers–Kronig, relaxation spectra

DMTA Model Selection & Applicability

Complete inventory: 45 compatible models, 11 transforms, decision tables, recommended starting points

Numerical Implementation

JIT strategy, parameter bounds, convergence, FAST_MODE, memory management

DMTA Workflows

8 end-to-end workflows (direct fit, TTS, Bayesian, CSV loading, HVM, cross-domain)

DMTA Measurement Protocols

ISO/ASTM protocol mapping, instrument geometries, heating rates

Knowledge Extraction from DMTA Data

T_g extraction, relaxation spectrum, tan(delta), plateau modulus, cooperativity

Future Extensions

Planned: frequency-dependent nu, nonlinear DMA, FEM export

Example Notebooks

01_dmta_basics

E* ↔ G* conversion fundamentals

02_dmta_master_curve

Multi-temperature TTS + GMM/FZSS fitting on real data

03_dmta_fractional_models

Fractional viscoelasticity + Bayesian UQ

04_dmta_relaxation

Time-domain E(t) Prony series + cross-domain

05_dmta_vitrimer

HVM/HVNM with tensile deformation

06_dmta_model_selection

Multi-model comparison (synthetic + real data)

07_dmta_tts_pipeline

Raw multi-T → TTS → fit → WLF extraction

08_dmta_cross_domain

Frequency ↔ relaxation domain consistency