Improved deep artificial neural network-powered prediction of extreme mechanical performances of fractal architectures with high hierarchical rank

This work explores the mechanical performances, including anisotropy, wave propagation, and buckling resistance capability of the Menger sponge and Jerusalem fractal structures, with the high rank, using an improved deep artificial neural network (ANN) model inserted by a loop with multiple conditions. Where, the effective mechanical attributes, including Young's modulus, shear modulus, and Poisson's ratio of the Menger sponge structure with rank 4 are attained using high-performance computer cluster (HPCC) that are then used to train and also validate the ANN model. The accuracy of the deep ANN model trained by data of fractal structures with and without rank 4 is verified by the numerical model and experiment with the good agreement found or the maximum percent difference being 15.6% where the numerical and experimental data don't belong to its training samples. Remarkably, the deep ANN model demonstrates an extremely low cost, but very fast compared with the numerical and experimental works. Namely, the improved deep ANN model implemented by a regular computer can accurately predict the mechanical attributes of Menger sponge fractal structures with full ranks in 3 min. While it takes a week for numerical work using HPCC or experiment method to produce the same mechanical properties of the Menger sponge with only rank 4, displaying at least thousands of times slower than the ANN model. The ANN results indicate that the onset of anisotropy of considered fractal structures is from rank 1, and the reversal of anisotropy will take place upon an increase in the rank while such reversal is not seen for the case of lattice structure. The anisotropy reversal could be one of main reasons why the fractal structure tends to have a high rank in nature. In addition, the buckling stress and phase wave velocity are observed to decrease with rising rank, with a nonlinear pattern.