A physics-informed 3D surrogate model for elastic fields in polycrystals
Polycrystalline materials, which consist of numerous crystallites or grains, exhibit complex mechanical responses due to the interaction of their microstructural features. Accurately modeling the elastic fields in polycrystals is crucial for predicting material behavior under stress.
Traditional methods, such as finite element analysis (FEA), are computationally expensive, particularly when dealing with three-dimensional (3D) microstructures. To address this challenge, physics-informed 3D surrogate models offer a promising alternative by integrating physical principles directly into machine learning frameworks.
Physics-informed neural networks (PINNs) bridge the gap between data-driven approaches and traditional physics-based models. These models encode governing equations, such as the Navier-Cauchy equations for elasticity, as part of the loss function. By enforcing physical laws during training, PINNs provide more accurate and generalizable solutions while requiring less data compared to purely empirical models.
In the context of polycrystals, a 3D surrogate model is designed to predict stress and strain fields within grains based on crystallographic orientation, boundary conditions, and external loading. The model architecture typically integrates convolutional neural networks (CNNs) with PINNs to capture spatial patterns and enforce physical consistency.
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