Speaker
Description
Slender, beam-like structures with hyperelastic base materials and complex cross-sectional shapes exhibit highly nonlinear constitutive responses in terms of their effective strain measures and stress resultants. This behavior is determined by the base material as well as geometric nonlinearities on the cross-sectional scale. While classical constitutive models for beams are typically restricted to linear elasticity and rigid cross-sections, modeling hyperelastic beams with deformable cross-sections requires multiscale beam simulations. Here, the effective strain measures of the beam serve as inputs to a microscale simulation, which evaluates the cross-sectional deformation and the beam’s effective constitutive response. However, this results in massive computational overhead, diminishing the main purpose of using a beam formulation in the first place. In this contribution, we present physics-augmented neural network constitutive models for beams and explore their application as surrogates for speeding up hyperelastic, multiscale beam simulations. Effective strains and curvatures are used as inputs for feed-forward neural networks, which represent the hyperelastic beam potential. Forces and moments are received as the gradients of the potential ensuring thermodynamic consistency. The potential is complemented with normalization terms guaranteeing stress and energy normalization. We further extend the model to transverse isotropy and a less restrictive point symmetry constraint. To improve scaling, a data augmentation is applied. Lastly, we introduce a scalar parametrization for different ring-shaped cross-sections. All models are calibrated to data of circular or ring-shaped deformable hyperelastic cross-sections, showing excellent accuracy and generalization. The straightforward applicability of the models is demonstrated in isogeometric beam simulations.
