COMPLAS 2023

Using Neural Networks in Hardening Laws

  • Meyer, Knut Andreas (TU Braunschweig)
  • Ekre, Fredrik (TU Braunschweig)
  • Jänicke, Ralf (TU Braunschweig)

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The invention of data-driven mechanics has sparked numerous ways of combining data with material modeling. One direction is Physics Informed Neural Networks, which reduce the data requirements by penalizing violations of physical laws. Masi et al. encode thermodynamics directly to ensure energy conservation and facilitate the penalization of negative dissipation. Finally, using tensor invariants as network inputs ensures rotational invariance and reduces the required training data. In this contribution, we include neural networks in the plastic hardening laws. The proposed formulation uses implicit time integration, is invariant, and intrinsically fulfills the 2nd law of thermodynamics. The model can learn the standard Armstrong-Frederick and Voce hardening laws (see Figure 1 in pdf). Like most isotropic hardening laws, the Voce law assumes that the yield stress only depends on the accumulated plasticity (time-integrated plastic multiplier). However, experiments show that this is not always true (see Figure 2 in pdf). In contrast, our neural network-enhanced model can predict such behavior. As a final step, we propose new interpretable evolution laws based on the trained neural network.