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 paper 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.