A Bayesian surrogate constitutive model to estimate failure probability of elastomers

Abstract

To calculate the uncertainty in the failure probability of elastomeric materials, a parametric and a non-parametric Bayesian-based stochastic constitutive model were evaluated. (i) A Bayesian linear regression calibration technique is created based on the Carroll model to construct a probabilistic hyper-elastic model in the parametric approach. The model was then calibrated using two methods: Maximum Likelihood Estimation (MLE) and Maximum a Posteriori (MAP) estimation, with the results compared. (ii) The Gaussian process (GP) is used in non-parametric hyper-parameters of the radial basis kernel computed using the limited-memory Broyden–Fletcher–Goldfarb–Shanno technique. Both models were trained and verified with regard to two sets of our experiments on silicon- and polyurethane-based elastomers to demonstrate their capabilities in modeling uncertainty propagation. Finally, failure probability analysis was carried out for these data sets using First Order Reliability Method (FORM) analysis and Crude Monte Carlo (CMC) simulation, with a limit state function based on the stochastic constitutive model at the failure point. Sensitivity analysis is also used to demonstrate the importance of Carroll model parameters in predicting failure likelihood. The results show that the parametric approach has great agreement with experimental data, not only for uncertainty quantification and model calibration, but also for calculating the failure probability of hyperelastic materials.