Bayesian optimal design accelerates discovery of material properties from bubble dynamics

An optimal sequential experimental design approach is developed to accurately and efficiently characterize soft material properties at high strain rates induced by bubble cavitation. This approach comprises two main components: optimal design and model inference. The former focuses on maximizing the expected information gain in a Bayesian statistical setting to design experiments that provide the most informative cavitation data about unknown material properties. The latter involves characterizing constitutive models and associated viscoelastic properties from measurements using a hybrid ensemble-based 4D-Var method (En4D-Var). These two parts employ the inertial microcavitation-based high strain-rate rheometry (IMR) method by Estrada et al. (J. Mech. Phys. Solids, 2018) to simulate the bubble dynamics under laser-induced cavitation. For demonstration, two sets of constitutive models are used to generate synthetic data and represent the viscoelastic behavior of stiff and soft polyacrylamide hydrogels. Accurate and efficient characterizations of the underlying models are presented.