Multiscale Finite Element Method Based on Deep Learning for Arbitrary Composite Material Structure
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The exceptional mechanical properties of composite materials make them indispensable in advanced manufacturing. During the manufacturing and processing of composite materials, defects such as uneven fiber spatial distribution and the presence of voids are inevitable. However, their complex multiscale nature poses significant computational challenges for traditional high-fidelity finite element analysis, often rendering detailed simulations prohibitively expensive. Compared to homogenization methods, the Extended Multiscale Finite Element Method proposed by Zhang et al.[1] has improved the efficiency of numerical simulation, but the efficiency of the analysis of the composite with complex microstructure is not very satisfactory. To address this bottleneck, this study presents an innovative, AIaccelerated multiscale finite element method framework that enables high-accuracy simulations on computationally efficient coarse grids. The core of the method lies in establishing a rapid mapping from a material's microscopic structure to its macroscopic mechanical response. Instead of relying on explicit homogenization, a Convolutional Neural Network is employed to extract critical features directly from images of the material's random microstructure. Subsequently, a Conditional Generative Adversarial Network[2] is utilized to predict the equivalent stiffness matrices and multiscale shape functions for these coarse grids. This AI-driven approach effectively learns the underlying physical laws from data, creating a surrogate model that bypasses the need for exhaustive fine-scale calculations. This pipeline facilitates a swift transition from a defined microstructure to a low-resolution grid and, finally, to a high-resolution physical field prediction. This approach aims not to fully replace finite element analysis but to reduce the number of elements required for composite material analysis. The results demonstrate that the proposed method delivers physical field accuracy comparable to traditional fine-grid finite element method. Crucially, it achieves this with a dramatic reduction in both computational time and memory usage. The framework is robust, applicable to composites with diverse inclusion shapes, constituent properties, and geometric distributions. Through validation, this method demonstrates outstanding transferability, making it widely applicable
