Stochastic hyperelastic modeling considering dependency of material parameters

This paper investigates the uncertainty of a hyperelastic model by treating random material parameters as stochastic variables. For its stochastic discretization a polynomial chaos expansion (PCE) is used. An important aspect in our work is the consideration of stochastic dependencies in the stochastic modeling of Ogden’s material model. To this end, artificial experiments are generated using the auto-regressive moving average process based on real experiments. The parameter identification for all data provides statistics of Ogden’s material parameters, which are subsequently used for stochastic modeling. Stochastic dependencies are incorporated into the PCE using a Nataf transformation from dependent distributed random variables to independent standard normal distributed ones. The representative numerical example shows that our proposed method adequately takes into account the stochastic dependencies of Ogden’s material parameters.