Traditional physical experiments have only allowed for the observation of specific stress states (uniaxial, biaxial, hydrostatic) which offer only low and limited data for the description of material responses in mechanics. It is therefore crucial for constitutive models to be able to generalize well to unseen stress states. Hence, phenomenological constitutive laws have been designed to generalize in a thermodynamically consistent manner which allows them to be trained on limited experimental data and then be used to predict material responses ingeneral stress states. However, they are not automatable, i.e. their development is time-consuming and dependent on user knowledge since they are in general limited by specific user-chosen model forms, and hence oftentimes experience a type of model-form error, which means that the model often is not descriptive enough to fully fit the data which results from incomplete knowledge about the material response. Data-driven (or machine-learning-based) constitutive modeling on the other hand is an emerging field in computational solid mechanics with many potential advantages compared to traditional phenomenological modeling such as increased accuracy and the no functional form selection which enables automatization of the constitutive calibration process. However, these approaches typically require a significant amount of data, are not designed to fulfill thermodynamic principles, and need to be trained on data that explores the full stress space with a variety of complex loading paths. In a series of papers, this thesis extends the state-of-the-art by proposing and analyzing multiple physics-augmented data-driven constitutive modeling concepts that allow for the automatic fulfillment of crucial physical concepts and work on limited data to bridge the gap between phenomenological and data-driven approaches. Firstly, we describe physics-augmented data-driven constitutive modeling approaches for hyperelastic materials that automatically fulfill constitutive constraints. This idea is then extended to elastoplastic material behavior where a data-driven modular elastoplasticity hybrid framework is discussed that can be trained on a variable amount of data by relying on the modularity of the elasto-plasticity formulation where each component of the model can be chosen to be either a classical phenomenological or a data-driven model depending on the amount of available information. Lastly, we show that interpretable functional forms for all components of the modular framework can be obtained by relying on extreme sparsification of physics-augmented neural networks.