From Cavitation–Strain Correlation to Admissible Model Discovery: Towards Extrapolation-Credible Creep Constitutive Modelling

Long-term creep prediction requires extrapolation from accelerated tests to service conditions with different stress, stress state, temperature, and exposure time. This paper proposes an admissible-discovery framework for extrapolation-credible creep constitutive modelling. The central argument is that creep modelling is not ordinary parameter calibration, but discovery of admissible model architectures from sparse, noisy, and regime-biased observations, guided by inverse-problem logic, observable–mechanism mapping, identifiability analysis, and regime-transfer validation. The framework is motivated by the limitations of correlation-based creep modelling, especially treating cavitation damage as a fixed linear function of creep strain. Reanalysis of Dyson’s cavitation data shows that the strain-controlled interpretation is locally useful, whereas the same observations in the time frame support a more mechanism-traceable damage evolution law. Bayesian inference, uncertainty quantification, machine learning, Gaussian-process modelling, active learning, and sensitivity analysis should therefore be used not for flexible curve fitting, but to expose non-identifiability, residual structure, missing mechanisms, and data gaps, thereby supporting admissible constitutive-equation discovery. Extrapolation credibility depends on architectures that are physically admissible, structurally identifiable, observable, transferable, and meaningful beyond calibration.