A physically-informed machine learning model for freeform bending

This work aims at a fast computational process model of the free-form bending process. It proposes a novel physically-informed machine learning model, which is trained with experimental data of bending constant radii and utilizes additional physical bending knowledge by integrating Timoshenko's beam theory. The model is able to predict the resulting plastic deformation of the tube after exiting the die by computing an elastic representation of the tube's deformation with beam theory at each time step. This elastic representation serves as input for a regression model similar to a partially connected neural network. This physically-informed machine learning model generalizes the constant training radii to complex bend geometries consisting of transitional sections and true spline geometries. It is compared to a benchmark finite element simulation and has an improved prediction quality for complex kinematics while reducing the computation time by four orders of magnitude.