PSI - Issue 52

Vinit Vijay Deshpande et al. / Procedia Structural Integrity 52 (2024) 391–400 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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different weight initializations and the resulting extremes are shown by the shaded regions. For outer neural network, the error on test data corresponding to training dataset 1 is very high and it reduces as the training dataset is increased. In the case of hybrid neural network, the prediction from first training dataset itself is quite improved and that from dataset 3 is almost equivalent to outer neural network result for dataset 9. The predictions from the hybrid neural network converge to the best predictions of the outer neural network very fast indicating that the hybrid neural network is learning from the inner neural network. It is observed that, in our case the computational expense in generating the training data of smaller volume element is 1⁄6 th that of the larger volume element. This cost increase in the hybrid network is minimal compared to the advantage it provides.

Fig. 9. Root mean square error of outer network and hybrid network for training datasets 1 to 9. The shaded regions indicate extreme values obtained by repeating the neural network training 20 times for different weight initializations. Fig. 10 shows the actual (from FE simulations) and predicted stress-strain curves for = 45˚ from both the neural networks trained using datasets 1, 3, 7 and 9. Fig. 10 a and b shows that the outer neural network fails badly to predict the stresses as it has not idea about how to relate the two uniaxial results (dataset 1) to the biaxial case. However, the hybrid neural network predicts much better because it has learned from the inner network. The hybrid network is already predicting the stresses accurately when trained on dataset 3 as shown in Fig. 10 c and d while the outer network is still far off. The results from datasets 7 and 9 for both the networks are comparable. 5. Conclusion The article demonstrates a numerical procedure to study biaxial compression failure of brittle foams by developing artificial microstructures and conducting finite element simulations. The damage mechanisms shed light on the effect of pressure on the strength of the foam material. The hybrid neural network developed in the article demonstrates the usefulness of studying volume elements of smaller size (smaller than the representative) and then using that information to equip the neural networks to predict response of larger and representative volume elements. Such transfer learning-based strategies create neural networks that learn faster and at minimal computational cost. Based on the problem at hand, it can also help in cutting down the overall computational cost as less amount of expensive training data (data from larger volume element) will be required if the network already has some information about the material from the inner network that is trained on inexpensive data (data from smaller volume element).