Accelerating the data-driven multiscale finite element analysis for elastoplastic materials by using proper orthogonal decomposition and transformer architecture

초록

Nonlinear history-dependent behaviors and heterogeneity render multiscale finite element (FE2) simulation of elastoplastic materials challenging. Concurrently addressing micro- and macro- scales involves discretizing the macro structure into representative volume elements (RVEs) and iteratively solving microscale problems under complex loading paths. Therefore, we proposed a novel integrated surrogate model that combines proper orthogonal decomposition (POD) with a transformer (TF) to capture the evolution of physical state variables in the local microstructure. This framework accelerates FE2 simulations at the micro level for history-dependent materials. In the microscopic offline computing stage, sequential data were obtained from FE simulations conducted on an elasto-plastic composite RVE subjected to random and cyclic loading paths. Prior to use for training, the high-dimensional micro-stress field data were reduced to low- dimensional POD coefficient data, extracting information by using a small number of modes. This reduction in data dimensions renders operation easy and maintains essential features. The encoder-based TF model effectively captured global dependencies by using a self-attention mechanism. The proposed POD-TF surrogate model constructed in this manner plays a crucial role in accelerating FE2. In the online computing stage, a nonlinear FE2 combined with the proposed POD-TF surrogate model was conducted in a single simulation on a commercial FE. Therefore, the proposed approach allows simultaneous observation of physical states distributions at both micro-and macro scales, providing a comprehensive representation of the underlying multiscale phenomena. Additionally, fine-tuning enables the pre-trained POD-TF surrogate model to efficiently adapt to small variations in microstructure and material properties, enhancing flexibility and computational efficiency.

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