UC San Diego

Hierarchical multiscale simulations of composite materials face difficulties due to the enormous computational cost they require. Recent research has found that multiscale finite element methods based on homogenization and Recurrent Neural Networks (RNN) have the potential to address this challenge. In this research, we implement a Gated Recurrent Unit (GRU) based multiscale computational mechanics framework for nonlinear composite materials. We propose a Fortran algorithm to reconstruct a trained GRU model in ABAQUS UMAT as the surrogate model and implement it in multiscale finite element simulations. We use our UMAT code with a trained GRU model to solve a collection of 3D and 2D numerical problems under different load cases and geometry in this thesis to verify the performance of our model in multiscale simulation. We also test the performance of our GRU model at the integration points. Meanwhile, we also propose a novel sampling algorithm based on random increments and selection, which enables the generated strain series to provide more information on the material's plastic stage.

In the expanding research, we design a transformer-based surrogate model to address the issue of GRU performance decline with long sequences and to further improve the accuracy of the surrogate model. Additionally, we propose a random extract training algorithm to enhance the generalization capability of the transformer model. We conducted tests and comparisons of the transformer and GRU models using longer sequences, demonstrating that the transformer surrogate model exhibits superior accuracy and stability in processing longer sequences.