The central result is a split between models. The self-consistent (SC) and finite-element (FEM) simulations reproduced the observed trend toward faster creep as applied stress increased in amorphous PEI. They also predicted that the material's load would become concentrated in an increasingly uneven set of regions as creep progressed. The two-state (2S) model, by contrast, overestimated stress localization.
The work is an arXiv preprint marked v1 and dated 28 Aug 2026. It asks how differences in local stress across the material relate to the overall acceleration of creep and to the structure that carries the load, while testing how the three models compare with experiment.
The comparison starts with local relaxation
Researchers compared previously reported creep measurements in injection-molded amorphous PEI with a two-state model, a self-consistent model and a finite-element model. The experiments covered temperatures from 198 °C to 213 °C and tensile stresses from 1 to 15 MPa; the polymer's glass transition temperature was 213 °C.
The SC and FEM calculations used experimentally determined log-normal distributions of unstressed relaxation times, a common elastic modulus and Maxwell viscoelasticity. Their relaxation times were also made local-stress-dependent, allowing the calculations to represent differences between regions. The local acceleration rule used the exponential of minus the squared ratio of local stress to a local effective yield stress, the model's stress scale for that region. The comparison then tested whether the overall, macroscopic acceleration had an analogous stress dependence.
To fit the relaxation-time distribution used by the SC model, the researchers applied a least-squares fit to experimental linear creep data. The main text reports a distribution-width parameter of 1.86 ± 0.03 and a characteristic relaxation time of 0.21 ± 0.03 seconds.
The 2S model used a different picture. It treated creep as a series of stress-relaxation events and assumed that once a domain relaxed, it instantly lost its stress and remained stress-free. The comparison found that 2S overestimated stress localization, while SC and FEM followed the experimental trend toward faster creep at higher applied stress.
A load-carrying structure emerges
The load-sharing result becomes more tangible in the model calculations. Compliance here is the model's measure of creep response. At the starting normalized value of 1, the most loaded 20% of the material carried 20% of the applied load. During creep, SC and FEM predicted rising stress heterogeneity, meaning that different modeled regions carried increasingly different amounts of stress, alongside an increasingly concentrated load-carrying substructure. The predicted heterogeneity eventually reached a plateau.
At matched normalized compliance, predictions at higher applied stress showed lower stress heterogeneity, and FEM predicted less heterogeneity than SC.
At the macroscopic level, the reported acceleration had the same exponential-of-squared-stress form as the local rule. The effective macroscopic parameter Y decreased as compliance increased.
A narrow window for the conclusions
The study keeps its claims within a narrow modeling window. The analysis considers strains smaller than 0.06, excluding rejuvenation, chain orientation and geometric non-linearity from the retained analysis. The experimental comparison concerns injection-molded amorphous PEI under the stated temperature and stress range, so the supplied results do not establish the same behavior for other polymers or conditions.
The evidence here is a qualitative model comparison. No formal uncertainty estimate for the model comparison is reported.
Disclosures
The authors report no funding sources or conflicts of interest or competing interests. Supporting data are available from the corresponding author upon reasonable request.
Paper data and sources
Original title: Weakly non-linear creep of amorphous polymers near their glass transition, comparisons between models and experiment
Authors: Martin Roman-Faure, Zhaocheng Zhang, Catalin Picu et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text