Uncertainty quantification of hyperelastic models for polystyrene and polypropylene foams via conformal prediction

Abstract This study addresses the limitations of deterministic constitutive models for polymer foams, which often fail to capture intrinsic material variability. It introduces a framework to quantify the predictive uncertainty of the Ogden hyperfoam model using the distribution-free method of conformal prediction (CP). A two-term Ogden model was calibrated using experimental uniaxial compression data from expanded polystyrene and expanded polypropylene (EPP). Different CP strategies were systematically evaluated based on their empirical coverage and average interval width on held-out test data. To prevent bias toward the high-stress densification regime, a logarithmic transformation was applied to generate proportional uncertainty bounds, and a rigorous 5-fold grouped cross-validation was implemented to evaluate the quantitative metrics without data leakage. The results identify Jackknife MinMax and standard cross-validation strategies as the optimal methods for EPP and expanded polystyrene, respectively, providing valid 95% coverage with the narrowest prediction intervals. This research offers a practical and statistically rigorous methodology for engineers to move beyond single-value predictions, enabling the incorporation of trustworthy uncertainty bounds into the design and analysis of foam-based components.