PSI - Issue 71

Akash S.S. et al. / Procedia Structural Integrity 71 (2025) 180–187

184

11 = 11 12 = − 22 13 = − 33 12 = 12

11 22 = 11 21 = − 11 23 = − 12 23 =

22 22 33 = 11 22 31 = − 33 22 32 = − 23 23 13 =

33 33

11 33 22 33

13 13 Thedetailedtheoretical derivations of all these equations corresponding to boundary conditions and loading of each model arediscussed in C.T. Sun et al. (1996). 4. Deep learning model for predicting uncertainty in e ff ective material properties The number of fibers in the SVEs was varied from 10 to 200 and for each case of number of fibers, 50 di ff erent fiberdiameter distributions were randomly generated. A total of 760 SVEs with di ff erent number of fibers and fiber diameterdistributions were modelled and simulated in ABAQUS using python scripting. The e ff ective material properties E 11 , E 22 , ν 12 and G 12 were calculated using the equations mentioned in Section 3 and stored in a CSV file. Theinput parameters, i.e., mean, standard deviation and number of fibers of a given fiber diameter distribution and the corresponding output elastic constants were stored in a tabulated format for training of the deep learning model. The stress contours of one of the SVEs with 60 fibers is shown in Figure 2.

Fig.2: Stresscontours (Stress values in MPa)obtained forpredicting the e ff ective material properties Feature-wise normalization was done on the input parameters in the data. The data was split into training and test data using the 80-20 rule. As the size of the generated data is smaller, K-fold validation method is used. 20 % ofthe training data was assigned as validation dataset. For each K-fold validation dataset, the optimal neural network architecture was found using the Keras Tuner [ O’Malley et al. (2019)] which takes the training and validation data as input along with a baseline ANN model. The Keras Tuner finds the optimal