Bayesian constitutive model selection for inertial microcavitation rheometry

The Inertial Microcavitation Rheometry (IMR) technique can determine the constitutive material model that describes soft matter response in the ultra-high-strain-rate regime (>10³ 1/s). The technique least-squares fits between the inertial Rayleigh-Plesset-type numerical simulations and experimental observations [Estrada et al. J. Mech. Phys. Solids (2017)]. Model hyperparameter calibration are used to find the material properties that result in the best fit. Alternatively, we use a Bayesian constitutive model selection approach without hyperparameters and span a wide range of material parameter values for the IMR simulations. We consider laser-induced cavitation (LIC) experiments in three different materials: gelatin, agarose, and polymethyl methacrylate. We generate probability distribution functions (PDFs) in phase space involving the bubble radius and wall velocity. A database of IMR simulations for a library of material constitutive models is compared to the PDFs to assess agreement between the experiments and numerical simulations. The best fitting parameters are extracted from the PDFs for each of the models. This approach is compared to the original IMR method. Model plausibilities are presented for varying levels of experimental error.