Validation of the variable-order springpot model beyond creep

Validate the variable-order springpot rheological model with time-dependent fractional order β(t) and parameters (E, η, β0, β∞, γ, δ) under non-creep loading histories, specifically stress relaxation, cyclic loading, and thermo-viscoelastic conditions, by assessing its predictive accuracy and consistency against experimental data and determining its applicability outside sustained constant-stress creep.

Background

The paper introduces a variable-order springpot rheological model to capture the creep behavior of polymers, where the fractional order β varies over time to represent transitions between glassy, transition, and rubbery phases. The model parameters are calibrated via a cross-entropy optimization approach and validated using creep data for polypropylene (PP) and polyvinyl chloride (PVC).

Although the governing equations are claimed to be extendable to other loading histories, the study presents validation only for creep. The authors explicitly state that validation under relaxation, cyclic, and thermo-viscoelastic histories remains to be done, identifying a concrete gap: determining whether the same variable-order framework accurately describes polymer responses across different loading programmes beyond constant-stress creep.

References

While the present study focuses on creep loading, the governing equations are readily extendable to other histories (relaxation, cyclic, thermo-viscoelasticity) by exploiting the variable-order kernel. Validation under such conditions is left for future work.

— Advanced creep modelling for polymers: A variable-order fractional calculus approach  (2510.11765 - Ribeiro et al., 13 Oct 2025) in Section 4 (Results and Discussion), end of section

Whether an $\alpha$ extracted from an impedance sweep predicts the time-domain kernel under spiking excitation is untested for every entry in that table.

— Fractional-order hardware for neuromorphic computing: Is the order really the problem?  (2609.10882 - Teuscher, 9 Sep 2026) in Section 7.3, “Gaps, stated as questions”

Despite these recent efforts, several questions remain open in LCE viscoelasticity. First, it remains largely unclear how the individual contributions of different rate-dependent processes govern the LCE behaviors under different loading paths and temperatures.

— Elastic theory of ideal liquid crystal elastomers  (2610.26688 - Usmanova et al., 19 Oct 2026) in Section 5.4, final paragraph