Design of Tensor Prediction Models Based on Deep Learning: 2D Case
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Heterogeneous materials, characterized by spatially varying mechanical properties, pose significant challenges in modeling and simulation due to their complex behavior. Traditional approaches, such as asymptotic developments and numerical methods (e.g., finite elements or fast Fourier transform - FFT \cite{Paper2}), enable the computation of effective tensors but face computational limitations at high resolutions. This study presents an innovative AI-based methodology \cite{Paper} to predict first- and second-order homogenization tensors in 2D ($\mathbb{A}^{0,0}$, $\mathbb{B}^{0,1}$, and $\mathbb{C}^{0,0}$) under plane stress conditions, applied to a Representative Volume Element (RVE) not included in the initial database. The studied RVE features a resolution of $256^2$, a mechanical property contrast ranging from 10 to 1000, and a maximum relative error of predicted values below 0.7\%. The approach integrates convolutional neural networks (CNNs) \cite{Paper1}, trained on a database of 56,000 RVEs generated and simulated via FFT, with Python-based frameworks (TensorFlow/Keras). The performance of the models is evaluated against reference FFT-based simulations, demonstrating their ability to provide rapid, reliable, and automated predictions of the equivalent mechanical properties of heterogeneous materials. This work highlights the synergy between traditional numerical methods and AI, paving the way for more efficient and scalable solutions in materials science and engineering.
