PSI - Issue 72

Stefan Hildebrand et al. / Procedia Structural Integrity 72 (2025) 520–528

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Test 2 - Pure shear test.

The pure shear test considers prescribed shear strains with linearly increasing amplitude

s f a         end t t 

(17)

  t

  t

sin



12

,0

with the scaling factor f s =  , the initial proportionality constant a = 0.2 and time step width ∆t = 0.1.The model exhibits good accuracy, the amplitudes of shear stresses are overestimated for about 20% (Figs. 6, 7). 5 Y E

Fig. 6. Comparison of stress results for test 2, 12 component.

Fig. 7. Comparison of stress-strain results for test 2, 12 component.

Test 3 - Multiaxial test with randomly generated strain values.

This test is generated as a Gaussian random process with sampling parameters similar to those used in training data generation. Here, the model again exhibits very high accuracy in all directions (Figs. 8 and 9).

Fig. 8. Stress results (ML vs. RRM) for test 3, 11 component.

Fig. 9. Stress results (ML vs. RRM) for test 3, 12 component.

4. Conclusions and Outlook The stateless RNN model for the simulation of cyclic plasticity relies on an assumption for the loss function including a standard data-driven term but also further regularizing terms stipulating the compliance with the yield criterion and the evolution of plastic strains. The regularizations significantly contribute to the cyclic stability and high accuracy. Meanwhile, the associativity of the yield function is not required as regularization. Accordingly, it is expected that a similar setup can be applied for the non-associative plasticity. Compared to existing models dealing with two-dimensional examples, the NN architecture used here is simpler and thus more efficient. The training data sets are of significantly smaller extent while training a complete three-dimensional material model. A further advantage of the suggested stateless approach is that the inputs and outputs are similar to those of conventional material routines, thus facilitating the implementation into FE software packages, which is planned for future work. Further important aspects of the NN architecture are an information flow designed to off-load the NN to the maximal possible extent and the explainability of the feedback quantities.