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Quantify the correlation between hardening parameters a1 and η in successful calibrations

Characterize the quantitative relationship between the hardening parameters a1 and η in the Perzyna-type viscoplastic hardening law α = a1 / ([ (a1/α0)^(1/η) + ξ ]^η) that underlies parameter combinations yielding relatively low calibration loss, in order to resolve identifiability and parameter interdependence observed during global sensitivity analyses.

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Background

During global sensitivity analysis, the authors observe many local minima and strong co-dependence among certain viscoplastic hardening parameters. In particular, combinations of a1 and η often yield similarly good fits, suggesting a structural correlation that affects identifiability and optimization.

They explicitly state that this correlation remains unknown, indicating a need to understand and formalize the dependence between a1 and η in the chosen hardening rule to improve calibration robustness and interpretability.

References

What the results of Figures \ref{fig:paper_loss_histogram} and \ref{fig:paper_corr_corr_2} reveal is that all sets of parameters that produce a relatively good solution present a certain (still unknown) correlation between $a_1$ and $\eta$.

— A multi-step calibration strategy for reliable parameter determination of salt rock mechanics constitutive models (2403.19426 - Honório et al., 28 Mar 2024) in Section 5.2, Global sensitivity analysis (GSA)