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.

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)