DTE AICCOMAS 2025

Student

Dual-stage framework for constitutive modeling of hyperelastic materials based on data-driven identification and neural networks

  • Linden, Lennart (TU Dresden)
  • Kalina, Karl Alexander (TU Dresden)
  • Brummund, Jörg (TU Dresden)
  • Kästner, Markus (TU Dresden)

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For materials exhibiting complex nonlinear elastic or inelastic behavior, constitutive model formulation and calibration remain challenging tasks. Thus, in the field of computational mechanics, novel techniques – often referred to as data-driven or data-based methods – have become increasingly popular in the recent years. These methods, however, require a large amount of data, usually strains and stresses for problems in solid mechanics. In this contribution, we present a consistent dual-stage approach for the automated calibration of hyperelastic constitutive models which only requires experimentally measurable data. In the first step of our approach, data-driven identification (DDI) is used to generate tuples of stress and strain states [1]. This method identifies these data by only specifying the applied boundary conditions and displacement field, which can be determined using full-field measurement methods such as digital image correlation (DIC). In the proposed framework's second step, the data are used to calibrate a physics-augmented neural network (PANN) [2]. By construction, this model satisfies all common conditions of hyperelasticity although remaining extremely flexible. Furthermore, the PANN model can be easily implemented into a finite element (FE) code. We provide several descriptive examples to demonstrate the applicability of our approach. Therefore, two-dimensional synthetic data are exemplarily generated by using a reference constitutive model. The calibrated PANN is then applied in three-dimensional FE simulations, where the solution is compared to the reference model. [1] Leygue, A., Coret, M., Réthoré, J., Stainier, L. and Verron, E., Data-based derivation of material response, Computer Methods in Applied Mechanics and Engineering 331 (2018). [2] Linden, L., Klein, D. K., Kalina, K. A., Brummund, J., Weeger, O. and Kästner, M., Neural networks meet hyperelasticity: A guide to enforcing physics, Journal of the Mechanics and Physics of Solids 179 (2023).