Predicting stress, strain and deformation fields in materials and structures with graph neural networks

Abstract

Developing accurate yet fast computational tools to simulate complex physical phenomena is a long-standing problem. Recent advances in machine learning have revolutionized the way simulations are approached, shifting from a purely physics- to AI-based paradigm. Although impressive achievements have been reached, efficiently predicting complex physical phenomena in materials and structures remains a challenge. Here, we present an AI-based general framework, implemented through graph neural networks, able to learn complex mechanical behavior of materials from a few hundreds data. Harnessing the natural mesh-to-graph mapping, our deep learning model predicts deformation, stress, and strain fields in various material systems, like fiber and stratified composites, and lattice metamaterials. The model can capture complex nonlinear phenomena, from plasticity to buckling instability, seemingly learning physical relationships between the predicted physical fields. Owing to its flexibility, this graph-based framework aims at connecting materials’ microstructure, base materials’ properties, and boundary conditions to a physical response, opening new avenues towards graph-AI-based surrogate modeling.

Deep Learning in Mechanical Metamaterials: From Prediction and Generation to Inverse Design

“…Reproduced under the terms of the Creative Commons CC‐BY license. [ 154 ] Copyright 2022, The authors. b) Mapping 3D lattice metamaterials into dominant deformation mechanism with a GNN model.…”

“…In addition to modeling parameters and pixels/voxels, other design representations, such as meshes and lattices, can also be used as input to predict effective properties with a specific DL model, like GNNs. [ 154–156,170,171 ] In GNNs, the prior step is to convert these design representations into a graph representation. Maurizi et al.…”

“…a) Mapping the meshes of 2D material or structural systems into physical fields via a GNN model.The meshes are converted into encoded nodes and edges before passing to the GNN model. Reproduced under the terms of the Creative Commons CC-BY license [154]. Copyright 2022, The authors.…”

Predictions of electromotive force of magnetic shape memory alloy (MSMA) using constitutive model and generalized regression neural network

“…For the first time, this offset angle was considered in constitutive modeling for better emf prediction which was one of the novelties of this study. Furthermore, in order to predict mechanical behavior, besides using constitutive modeling, machine learning-based modeling is getting popular [9][10][11][12][13]. Machine learning-based modeling, specifically neural networks can predict nonlinear behavior very well.…”

Hierarchical Generative Network: A Hierarchical Multitask Learning Approach for Accelerated Composite Material Design and Discovery

“…In recent years, deep learning (DL) methods employing neural networks (NNs) and computational simulation advances have emerged as a promising avenue for predicting intricate structureresponse relationships and tackling design space challenges across various scales. DL methods that incorporate finite element method (FEM) modeling have expedited predictions of mechanical properties like stiffness and strength, [7][8][9] internal stress/ strain fields, [10][11][12] and crack propagation behavior [13,14] from material configurations as input images, providing swift, and costeffective solutions. Yet, conventional DL models encounter limitations in composite design, especially when the training dataset size is relatively small compared to potential composite constituent combinations.…”