ECCOMAS 2024

Multiscale Modeling of Viscoelastic Shell Structures with Artificial Neural Networks

  • Geiger, Jeremy (Karlsruhe Institute of Technology)
  • Wagner, Werner (Karlsruhe Institute of Technology)
  • Freitag, Steffen (Karlsruhe Institute of Technology)

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Multiscale methods capture the effective material behavior of complex microstructureswithin a numerical homogenization scheme. In [1], a coupled two-scale shell model has been developed, which is capable of capturing the mechanical behavior of heterogenous shell structures. In order to surpass the time consuming two-scale model, alternative approaches aim to replace the boundary value problem at the lower scale with suitablesurrogate models. Artificial neural networks (ANN) have shown to be a promising alternative approach toconventional material modeling. In this contribution, the ANN defines the relationship between the shell strains and stress resultants for a non-linear shell model, focusing on the application to viscoelastic material behavior. While an ANN for elastic materials can solely be defined on strain input data, further input variables have to be defined to capture the history and rate dependence for viscoelastic materials. An overview on different ANN architectures for the one dimensional case can be found in [2]. Here, conventional ANN training is furthermore enhanced with additional constraints in order to reduce the number of neccesary strain-stress training paths, to ensure physical consistency, as well as to increase the numerical performance. Studies include the comparison of different modeling approaches, e.g., a full scale 3D solution, coupled shell models and shells with an ANN surrogate model, within challenging numerical examples. REFERENCES [1] Gruttmann, F. and Wagner., W.: A coupled two-scale shell modell with applications to layered structures. International Journal for Numerical Methods in Engineering 94(13), pp. 1233-1254, 2013. [2] Rosenkranz, M, Kalina, K.A., Brummund, J., Kästner, M.: A comparative study on different neural network architectures to model inelasticity. International Journal for Numerical Methods in Engineering 124(21), pp. 4802-4840, 2023.