Interpretable Composition-to-Curve Prediction of Payne-like Softening in an Unvulcanized BR/BR–VMQ Benchmark: Critical-Strain Scaling and Qualitative Molecular-Dynamics Context

Predicting a filled elastomer’s strain-amplitude softening curve from formulation descriptors is difficult because the response combines matrix softening, filler-network breakdown, and interfacial effects. We reanalyze a public benchmark of 47 unvulcanized butadiene-rubber (BR) and butadiene-rubber/silicone-blend (BR–VMQ) compounds (carbon black, precipitated silica, and nano-CaCO3; 5–30 phr) to test an interpretable composition-to-curve model. A per-compound Kraus-type critical strain γc first overlaps the normalized total-softening curves onto a shared shape (R2=0.98; a necessary but not sufficient precondition for universality). A structural-kinetics model—a machine-learned parameterization of a Kraus-type form, not a new constitutive law—then predicts the full curve from the rubber family and loading (root-mean-square error (RMSE) of 0.031), with a held-out Payne-like-drop mean absolute error (MAE) of 0.040, tied with a random forest (p=0.87) and matched by a full-curve black-box baseline; the Kraus form thus buys interpretability at no cost to accuracy. Because the compounds are unvulcanized, the target is the total softening—matrix-dominated for the blend—not an isolated Payne term. Explicit filler-chemistry labels and coarse-grained molecular-dynamics descriptors add no held-out value beyond family and loading, so the molecular dynamics is used as qualitative structural context rather than for quantitative mechanism validation; this bounds the claim to the present benchmark and does not imply that filler chemistry is unimportant in general.