The legitimacy of decoupled forms in dynamic constitutive modeling has long lacked rigorous mathematical criteria. To address this, we propose a unified legitimacy-assessment framework based on Weighted Singular Value Decomposition (SVD) and CANDECOMP/PARAFAC (CP) tensor decomposition. This framework introduces an inverse-variance weighting strategy that quantifies experimental reliability from data dispersion, thereby enhancing the physical consistency of model diagnosis. Applied to annealed copper, our analysis reveals that the flow stress exhibits pronounced low-rank characteristics in both two-dimensional (strain–stress state) and quasi-static three-dimensional spaces, validating the use of decoupled models. However, under dynamic conditions and in the full four-dimensional space (incorporating temperature), the Rank-1 approximation error increases markedly, uncovering strong coupling among strain rate, temperature, and stress state. Furthermore, we demonstrate that a coupled constitutive model, informed by the CP decomposition results, significantly improves predictive accuracy. The proposed framework provides a theoretical foundation for simplifying and constructing high-fidelity, data-driven constitutive models.
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