Capture broadband, history-dependent material response with a compact fractional-hybrid model.
Propellant and other viscoelastic materials respond across broad time scales, and their constitutive behavior can evolve with operating conditions. A compact standard Prony model may not reproduce that changing response with sufficient fidelity.
Phractals combines fractional and classical model elements to represent long material memory without requiring a large expansion of discrete relaxation branches. The comparison keeps the numerical reference, hybrid prediction, and integer-order baseline visible together.
The animation compares ground-truth displacement with a fractional-hybrid model and a standard integer-order Prony model using the same parameter count, while the lower panels expose normalized error across the motor section.
Ground truth, fractional-hybrid, and integer-order Prony displacement fields are paired with their normalized errors.
The hybrid formulation preserves the material-fit reference while requiring far fewer model parameters and reducing the RMS error compared with the equivalent Prony baseline.
Represent broadband creep, relaxation, and damping with compact models.
Expose where a conventional constitutive baseline diverges from the numerical reference.
Improve confidence in simulations that depend on long loading and operating histories.
Retain thermal-memory effects and microscale behavior without resolving every feature in the production model.
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Study transient deformation in compliant, heterogeneous materials where damping and history shape the response.
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Couple temperature and deformation in a two-way workflow without building a custom coupling chain.
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