Extracting the stress–strain properties of non-linear viscoelastic materials using the bubble inflation test

In this study, an inverse method based on the Levenberg–Marquardt algorithm was evaluated in a numerical experiment to determine the large strain viscoelastic properties from the bubble inflation test. The properties were determined by iteratively matching the calculated bubble pressure–piston displacement data from finite element simulations to a single set of bubble pressure–piston displacement data. The strain-dependent behaviour was characterised by a two-parameter Mooney–Rivlin hyperelastic model, while the time-dependent behaviour was characterised by a three-parameter power law equation. Different initial guesses were used to evaluate the inverse method, and transformation functions were applied to constrain the intermediate guesses to be within bounds. It was found that estimates of the viscoelastic properties could be obtained reasonably using only one set of bubble pressure–piston displacement data. Estimates of the properties were likely affected by the limited time duration of the test, as the behaviour at shorter and particularly larger time scales was less accurately predicted.