Computationally efficient necking prediction using neural networks trained on virtual test data

The onset of localized necking under monotonic and non-monotonic loading can be well-predicted by the imperfection-based approach proposed by [1] (MK). However, a large number of virtual imperfections has to be investigated for an accurate necking prediction, making the MK approach computationally expensive and hence preventing the industrial application for full-scale vehicle models. To overcome these issues, a computationally efficient neural network (NN) model is proposed for replacing the MK model in the present work. An extended version of the MK model has been implemented into a User Material for an explicit crash solver. The model continuously computes the "distance to localized necking" as an important engineering quantity. Single shell element simulations are utilized for creating a comprehensive virtual test database for monotonic and non-monotonic loading for a 22MnB5 grade in an as-delivered state. A simple feed-forward NN model, featuring only one hidden layer, is trained and tested against the virtual data, where invariants of the stress and plastic strain tensors represent the input features of the NN and the "distance to necking" represents the output value of the NN. For comparison of the computational cost, the NN architecture has also been implemented in a User Material Routine for shell elements. The predictions of the NN and the MK model are in good agreement, where, due to the simple mathematical structure of the NN, the computational cost of the NN is significantly lower than for the MK implementation.