Uncertainty quantification in constitutive model calibration and discovery in computational solid mechanics

Constitutive modeling is fundamental to computational solid mechanics. In contrast to model calibration, model discovery aims to find not only the material parameters but also a suitable model structure and thus offers more flexibility if necessary. For both approaches, experimental data are used that are noisy and may be sparse and thus introduce uncertainty. By quantifying the uncertainty, it can be propagated through subsequent steps, ultimately enabling uncertainty-aware decision-making. However, the computational costs of most available methods for statistical model calibration using full-field displacement data are too high for applications with strict time constraints, such as structural health monitoring. Previously proposed methods for uncertainty quantification in model discovery are either not flexible enough or are based on Bayesian principles. The definition of well-informed priors for the individual material parameters is complicated both by their large number and by the fact that their relevance is not known in advance. In this thesis, the current state of uncertainty quantification in the calibration and discovery of constitutive models is improved significantly. A parametric physics-informed neural network is developed that enables statistical model calibration in near real-time. Furthermore, an automated framework for uncertainty quantification in model discovery is developed that does not require prior knowledge about the material parameters and can also infer complex probability densities through the use of normalizing flows. In addition, this thesis also leads to advancements in further aspects of constitutive model calibration and discovery that are related to the developments of the statistical methods. A robust and fully automated framework for deterministic model discovery is presented, which employs statistical model selection criteria to avoid manual intervention in the selection process. Moreover, a unifying perspective on both traditional and novel approaches to model calibration and discovery, as well as their classification, is presented. The advancements in this thesis, particularly with respect to uncertainty quantification, are mainly achieved through the careful integration of state-of-the-art machine learning methods into the theoretical framework of solid mechanics, ensuring physical consistency and interpretability. The capabilities of the developed methods are demonstrated for linear elastic and hyperelastic materials by several numerical tests, including experimental data. All methods are critically discussed with respect to their current limitations and potential for further developments.