Speaker
Description
The formulation and calibration of constitutive models remain challenging for materials exhibiting complex nonlinear elastic or inelastic behavior. In recent years, data-based or data-driven approaches have gained significant attention within the computational mechanics community to address these challenges. However, these methods typically require extensive datasets, often consisting of stress-strain relationships, which are fundamental in solid mechanics.
This contribution introduces a robust two-step methodology for the automated calibration of hyperelastic constitutive models, relying solely on experimentally measurable data. In the first step, data-driven identification (DDI) is employed to extract pairs of stress and strain states [1]. This approach requires only the application of boundary conditions and the displacement field, which can be obtained through full-field measurement techniques such as digital image correlation (DIC). The second step involves calibrating a physics-augmented neural network (PANN) [2] using the identified plane stress data. The PANN framework inherently satisfies the common principles of hyperelasticity by construction while offering remarkable flexibility. Furthermore, its implementation into finite element (FE) codes is straightforward.
To illustrate the effectiveness of the proposed methodology, we present several descriptive examples. Synthetic two-dimensional data are generated using a reference constitutive model and subsequently used to train the PANN. The calibrated PANN is then validated through three-dimensional FE simulations, where its results are benchmarked against 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).
