Efficient Modelling of Rubber Fracture Combining Phase-Field and Neural Networks
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Natural rubber-based elastomers are relevant for many technical applications, of which vehicle tyres are the most prominent. Their attractiveness primarily lies in their exceptional deformability and outstanding resistance to failure. The mechanical 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 challenging and, if possible, comes along with a very high computational effort. In this contribution, we introduce a novel Physics-Augmented Neural Network (PANN) constitutive model [1], extending our recent model of the isochoric response of incompressible elastomers [2]. The newly developed approach enables the modelling of deformation and crystallisation of rubber with high precision and computational efficiency. Parameterisation is carried out considering sparse experimental data. We then combine the PANN model of bulk deformation with the classical phase-field approach to fracture. In doing so, we establish a hybrid fracture model that serves to efficiently predict crack phenomena in rubber [3]. REFERENCES [1] K. Friedrichs, F. Dammaß, K.A. Kalina, M. Kästner. Precise, efficient and flexible modeling of crystallizing elastomers based on physics-augmented neural networks. arXiv:2511.14553 [2] F. Dammaß, K.A. Kalina, M. Kästner. When invariants matter: The role of I1 and I2 in neural network models of incompressible hyperelasticity. Mechanics of Materials. 2025;210:105443. [3] F. Dammaß, K.A. Kalina, M. Kästner. Neural Networks Meet Phase-Field: A Hybrid Fracture Model. Computer Methods in Applied Mechanics and Engineering. 2025;440:117937.
