Speaker
Description
Calibrating constitutive models based on experimental data is a common task to ensure the reliability of numerical models in solid mechanics. This calibration is usually accompanied by quantifying material parameter uncertainties, either through approximations considering asymptotic normality or stochastic approaches such as Bayesian methods. However, propagating these material parameter uncertainties to estimate the uncertainty of simulation results is essential for validating numerical models. In recent years, numerous methods have been developed for this purpose, each with its own advantages and disadvantages. Apart from many sampling-based methods, the first-order second-moment method provides reasonable uncertainty approximations in case the input parameter uncertainties are small. In this contribution, we demonstrate that the first-order second-moment method can be seamlessly integrated into the nonlinear finite element solution scheme for transient thermal problems. Although being intrusive in the sense that modifications to the finite element code are required, this approach rewards by enabling efficient uncertainty quantification without significant additional effort. In particular, the required first-order derivatives are computed using internal numerical differentiation, which is based on analytical derivatives and the additional solution of a linear system with multiple right-hand sides. This allows us to consider the uncertainties of material parameters and boundary conditions in our numerical model and propagate them to the simulation results. The efficacy of this approach is demonstrated for the calibration and uncertainty quantification of thermal material parameters in transient thermal finite element computations. Additionally, the uncertainty propagation is studied for a validation example. It is found that an additional computational effort of approximately 16% is required for integrated uncertainty quantification compared to a regular finite element simulation. The quantified uncertainties using the first-order second-moment method are compared to reference results obtained with the Monte Carlo method, revealing only minor deviations.
