{"title":"利用基于网格的子图几何深度学习多晶体塑性","authors":"Hanfeng Zhai","doi":"arxiv-2409.05169","DOIUrl":null,"url":null,"abstract":"Polycrystal plasticity in metals is characterized by nonlinear behavior and\nstrain hardening, making numerical models computationally intensive. We employ\nGraph Neural Network (GNN) to surrogate polycrystal plasticity from finite\nelement method (FEM) simulations. We present a novel message-passing GNN that\nencodes nodal strain and edge distances between FEM mesh cells, aggregates them\nto obtain embeddings, and combines the decoded embeddings with the nodal\nstrains to predict stress tensors on graph nodes. We demonstrate training GNN\nbased on subgraphs generated from FEM mesh-graphs, in which the mesh cells are\nconverted to nodes and edges are created between adjacent cells. The GNN is\ntrained on 72 graphs and tested on 18 graphs. We apply the trained GNN to\nperiodic polycrystals and learn the stress-strain maps based on strain-gradient\nplasticity theory. The GNN is accurately trained based on FEM graphs, in which\nthe $R^2$ for both training and testing sets are 0.993. The proposed GNN\nplasticity constitutive model speeds up more than 150 times compared with the\nbenchmark FEM method on randomly selected test polycrystals. We also apply the\ntrained GNN to 30 unseen FEM simulations and the GNN generalizes well with an\noverall $R^2$ of 0.992. Analysis of the von Mises stress distributions in\npolycrystals shows that the GNN model accurately learns the stress distribution\nwith low error. By comparing the error distribution across training, testing,\nand unseen datasets, we can deduce that the proposed model does not overfit and\ngeneralizes well beyond the training data. This work is expected to pave the\nway for using graphs as surrogates in polycrystal plasticity modeling.","PeriodicalId":501234,"journal":{"name":"arXiv - PHYS - Materials Science","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Learning polycrystal plasticity using mesh-based subgraph geometric deep learning\",\"authors\":\"Hanfeng Zhai\",\"doi\":\"arxiv-2409.05169\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Polycrystal plasticity in metals is characterized by nonlinear behavior and\\nstrain hardening, making numerical models computationally intensive. We employ\\nGraph Neural Network (GNN) to surrogate polycrystal plasticity from finite\\nelement method (FEM) simulations. We present a novel message-passing GNN that\\nencodes nodal strain and edge distances between FEM mesh cells, aggregates them\\nto obtain embeddings, and combines the decoded embeddings with the nodal\\nstrains to predict stress tensors on graph nodes. We demonstrate training GNN\\nbased on subgraphs generated from FEM mesh-graphs, in which the mesh cells are\\nconverted to nodes and edges are created between adjacent cells. The GNN is\\ntrained on 72 graphs and tested on 18 graphs. We apply the trained GNN to\\nperiodic polycrystals and learn the stress-strain maps based on strain-gradient\\nplasticity theory. The GNN is accurately trained based on FEM graphs, in which\\nthe $R^2$ for both training and testing sets are 0.993. The proposed GNN\\nplasticity constitutive model speeds up more than 150 times compared with the\\nbenchmark FEM method on randomly selected test polycrystals. We also apply the\\ntrained GNN to 30 unseen FEM simulations and the GNN generalizes well with an\\noverall $R^2$ of 0.992. Analysis of the von Mises stress distributions in\\npolycrystals shows that the GNN model accurately learns the stress distribution\\nwith low error. By comparing the error distribution across training, testing,\\nand unseen datasets, we can deduce that the proposed model does not overfit and\\ngeneralizes well beyond the training data. This work is expected to pave the\\nway for using graphs as surrogates in polycrystal plasticity modeling.\",\"PeriodicalId\":501234,\"journal\":{\"name\":\"arXiv - PHYS - Materials Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Materials Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.05169\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Materials Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05169","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Learning polycrystal plasticity using mesh-based subgraph geometric deep learning
Polycrystal plasticity in metals is characterized by nonlinear behavior and
strain hardening, making numerical models computationally intensive. We employ
Graph Neural Network (GNN) to surrogate polycrystal plasticity from finite
element method (FEM) simulations. We present a novel message-passing GNN that
encodes nodal strain and edge distances between FEM mesh cells, aggregates them
to obtain embeddings, and combines the decoded embeddings with the nodal
strains to predict stress tensors on graph nodes. We demonstrate training GNN
based on subgraphs generated from FEM mesh-graphs, in which the mesh cells are
converted to nodes and edges are created between adjacent cells. The GNN is
trained on 72 graphs and tested on 18 graphs. We apply the trained GNN to
periodic polycrystals and learn the stress-strain maps based on strain-gradient
plasticity theory. The GNN is accurately trained based on FEM graphs, in which
the $R^2$ for both training and testing sets are 0.993. The proposed GNN
plasticity constitutive model speeds up more than 150 times compared with the
benchmark FEM method on randomly selected test polycrystals. We also apply the
trained GNN to 30 unseen FEM simulations and the GNN generalizes well with an
overall $R^2$ of 0.992. Analysis of the von Mises stress distributions in
polycrystals shows that the GNN model accurately learns the stress distribution
with low error. By comparing the error distribution across training, testing,
and unseen datasets, we can deduce that the proposed model does not overfit and
generalizes well beyond the training data. This work is expected to pave the
way for using graphs as surrogates in polycrystal plasticity modeling.