Natural rubber-based elastomers are relevant for many technical applications, of which vehicle tyres are the most famous. What makes these materials attractive are their very high deformability and outstanding resistance against failure. The response of these elastomers is highly nonlinear, and at higher stretch levels, crystallites can form in the polymer network. The description of these complex phenomena by means of classical constitutive models is very challenging and, if possible, comes along with a very high computational effort. In this contribution, we introduce a novel Physics-augmented neural network (PANN) approach, extending our recent model of the isochoric response of incompressible elastomers [1]. The newly-developed approach enables to highly precisely and computationally efficiently model deformation and strain-induced crystallisation of rubber. The training of the PANN is carried out considering sparse experimental data. For validation, the response to unseen load paths is investigated, and excellent agreement with the experiments is obtained. Moreover, it is demonstrated that the model can capture the stress response and make sound predictions on the crystallisation, even if only stress-stretch data is available from experiments. Finally, it is demonstrated that the proposed PANN approach can also be employed for the prediction of crack phenomena. To this end, it is combined with the classical phase-field approach to fracture, establishing a hybrid model [1]. REFERENCES: [1] F. Dammaß, K. A. Kalina and M. Kästner, Neural Networks Meet Phase-Field: A Hybrid Fracture Model. Preprint, 2024. DOI: 10.2139/ssrn.5070356.