A Precise, Efficient and Flexible Physics-Augmented Neural Network Model for Strain-Induced Crystallization
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Strain-induced crystallization acts as a self-reinforcing mechanism in certain elastomers, strongly affecting their mechanical behavior. To develop a suitable continuum-scale model describing this inelastic phenomenon, we propose a two-potential framework based on the concept of generalized standard materials (GSMs) [1]. In particular, we follow the idea of physics-augmented neural networks (PANNs) to define the required energy and dissipation potentials in a precise, yet flexible manner. Accordingly, any discovered behavior is ensured to adhere to essential physical principles, including objectivity, isotropy and thermodynamic consistency. The evolution of the degree of crystallinity is defined by means of derivatives of the potentials as a classical GSM-type equation with two additional Lagrange multipliers and associated Karush-Kuhn-Tucker conditions. We thereby ensure boundedness of the crystallinity, allowing its interpretation as a concentration of crystalline phase. Following an incremental variational framework, the governing model and field equations are equivalently derived in time-discrete form, providing a basis for a finite element implementation. The PANN-based model is evaluated for several sets of stress and crystallinity data of unfilled natural rubber. Very good agreement is achieved for the training data, as well as satisfactory generalization behavior for unseen deformation sequences. The model’s applicability for deformation states of arbitrary complexity is demonstrated by means of a notched specimen, in which reasonable field distributions of both the stress and the crystallinity are predicted. Moreover, we demonstrate the PANN’s ability to flexibly generalize across different materials by employing it for carbon black-filled natural rubber, achieving comparable results. References: [1] Friedrichs K., Dammaß F., Kalina K.A., K¨astner M., Precise, efficient and flexible modeling of crystallizing elastomers based on physics-augmented neural networks arXiv-Preprint, arXiv:2511.14553, 2025
