Automated Discovery of Material Models in Continuum Solid Mechanics

The mathematical description of the mechanical behavior of solid materials at the continuum scale is one of the oldest and most challenging tasks in solid mechanics and material science. The process of finding adequate mathematical formulae to describe the material characteristics is called material modeling and it is traditionally a time-consuming, intuition-driven and error-prone task. The new advances in data-driven and machine-learning-based methods promise an automation of the material model discovery process. In this work, the novel method EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) is discussed, which aims to mitigate the two main weak spots of the state-of-the-art machine-learning-based methods for material modeling; their data inefficiency and their physical uninterpretability. Instead of deploying a supervised training process informed by many labeled stress-strain data pairs, which are difficult to acquire experimentally, at the core of EUCLID stands an unsupervised and physics-driven training process that is informed by full-field displacement and reaction force data. In this way, all data needed for the material characterization can be acquired from a single experiment. Further, instead of describing the material behavior by uninterpretable black-box models, EUCLID discovers a suitable material model from a potentially large set of candidate models using sparse regression. A sparsity promoting regularization term ensures that the discovered model is parsimonious, i.e., it entails a small number of material parameters, function evaluations and internal variables, thus increasing the physical interpretability and efficiency of the model. By posing certain restrictions on the material model candidates, it is ensured that the discovered models fulfill physical requirements that are well-known in the field. In this thesis, EUCLID is studied in the context of hyperelastic materials, elastoplastic materials and generalized standard materials. The method is verified by numerical tests, proving that EUCLID infers from indirect data appropriate material models that are encoded by parsimonious mathematical expressions. Finally, the current challenges and future perspectives of EUCLID are critically discussed