Speaker
Description
In this contribution, we present formulations for hyperelastic physics-augmented neural network (PANN) constitutive models that fulfill the polyconvexity condition. Polyconvex constitutive models are based on energy potentials which are convex functions in certain deformation measures. From a material modelling perspective, polyconvexity is desirable as it ensures a materially stable behavior of the constitutive model and potentially enhances its generalization capabilities.
We present polyconvex PANN modelling approaches for purely mechanical [1,2], \linebreak parametrized [3], and multiphysical electro-elastic material behavior [4]. We apply the models to different material datasets, including synthetic data of homogenized microstructures and experimental data of 3D printing materials. For some material classes, polyconvex constitutive models show an excellent performance and improve the model’s generalization and material stability compared to unrestricted PANN approaches. In other cases, however, polyconvex PANNs fail to represent the material behavior and have bad prediction qualities. This is caused by the mathematical structure of polyconvex constitutive models.
Overall, we discuss how polyconvex PANN models can be formulated, what the opportunities and benefits of such models are, and what constitutes their limits of applicability.
REFERENCES
[1] D.K. Klein, M. Fernández, R.J. Martin, P. Neff, O. Weeger. “Polyconvex anisotropic hyperelasticity with neural networks”. Journal of the Mechanics and Physics of Solids 159:104703 (2022)
[2] L. Linden, D.K. Klein, K.A. Kalina, J. Brummund, O. Weeger, M. Kästner. “Neural networks meet hyperelasticity: A guide to enforcing physics”. Journal of the Mechanics and Physics of Solids 179:105363 (2023)
[3] D.K. Klein, F.J. Roth, I. Valizadeh, O. Weeger. “Parametrized polyconvex hyperelasticity with physics-augmented neural networks“, Data-Centric Engineering 4:e25 (2023)
[4] D.K. Klein, R. Ortigosa, J. Martínez-Frutos, O. Weeger. „Nonlinear electro-elastic finite element analysis with neural network constitutive models“. Computer Methods in Applied Mechanics and Engineering 425:116910 (2024
