Verification‐, Stability‐, and Validation‐Based Model Selection for Incompressible Rubber‐Like Materials

ABSTRACT A systematic framework for the selection and assessment of hyperelastic constitutive models for rubber‐like materials is presented. The approach integrates verification, stability, and validation within a unified methodology to ensure reliable material parameter identification. While least‐squares fitting enables accurate reproduction of experimental data, the resulting parameter sets may suffer from instability or limited predictive capability. To address this, parameter stability is quantified using information‐based optimality criteria, providing a measure of identifiability and robustness. The proposed framework is applied to Treloar's classical dataset, considering multiple hyperelastic models. The results demonstrate that model accuracy alone is not sufficient for reliable model selection and highlight the importance of stability and validation. Among the investigated models, the Carroll formulation provides the best compromise between fitting quality, parameter stability, and predictive performance across different deformation modes.