Physics-augmented neural networks for hyperelastic shell constitutive modeling
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Multiscale finite element schemes enable the simulation of arbitrary microstructures within the Mindlin–Reissner shell theory [1]. However, the FE2 approach drastically increases computational cost in the finite-strain case, undermining a main benefit of using shell formulations. Neural network (NN)-based surrogate constitutive model for shells can help to overcome this drawback by moving from a concurrent to a more efficient, sequential multiscale approach [2, 3]. In the present work, we formulate a thermodynamically consistent NN-based shell constitutive model, focusing on hyperelasticity. A feed-forward NN is used to model the strain energy per unit area as a function of the shell strain measures. The NN potential is complemented by two terms that ensure stress and energy normalization, respectively. Finally, we enforce the constitutive scaling law for hyperelastic shells in the NN model formulation, enabling the representation of different shell thicknesses without additional training data. The model is trained and validated using data from homogeneous and inhomogeneous shell representative volume elements.
