TY - JOUR

T1 - A machine learning based plasticity model using proper orthogonal decomposition

AU - Huang, Dengpeng

AU - Fuhg, Jan Niklas

AU - Weißenfels, Christian

AU - Wriggers, Peter

N1 - Funding Information: The first author would like to thank the China Scholarship Council (CSC) and the Graduate Academy of Leibniz Universität Hannover for the financial support. The second author acknowledges the financial support from the Deutsche Forschungsgemeinschaft under Germanys Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453). The last author acknowledges the support of Deutsche Forschungsgemeinschaft for the project C2 within the collaborative research center/Transregio TR73.

PY - 2020/6/15

Y1 - 2020/6/15

N2 - Data-driven material models have many advantages over classical numerical approaches, such as the direct utilization of experimental data and the possibility to improve performance of predictions when additional data is available. One approach to develop a data-driven material model is to use machine learning tools. These can be trained offline to fit an observed material behaviour and then be applied in online applications. However, learning and predicting history dependent material models, such as plasticity, is still challenging. In this work, a machine learning based material modelling framework is proposed for both elasticity and plasticity. The machine learning based hyperelasticity model is developed with the Feed forward Neural Network (FNN) directly whereas the machine learning based plasticity model is developed by using of a novel method called Proper Orthogonal Decomposition Feed forward Neural Network (PODFNN). In order to account for the loading history, the accumulated absolute strain is proposed to be the history variable of the plasticity model. Additionally, the strain–stress sequence data for plasticity is collected from different loading–unloading paths based on the concept of sequence for plasticity. By means of the POD, the multi-dimensional stress sequence is decoupled leading to independent one dimensional coefficient sequences. In this case, the neural network with multiple output is replaced by multiple independent neural networks each possessing a one-dimensional output, which leads to less training time and better training performance. To apply the machine learning based material model in finite element analysis, the tangent matrix is derived by the automatic symbolic differentiation tool AceGen. The effectiveness and generalization of the presented models are investigated by a series of numerical examples using both 2D and 3D finite element analysis.

AB - Data-driven material models have many advantages over classical numerical approaches, such as the direct utilization of experimental data and the possibility to improve performance of predictions when additional data is available. One approach to develop a data-driven material model is to use machine learning tools. These can be trained offline to fit an observed material behaviour and then be applied in online applications. However, learning and predicting history dependent material models, such as plasticity, is still challenging. In this work, a machine learning based material modelling framework is proposed for both elasticity and plasticity. The machine learning based hyperelasticity model is developed with the Feed forward Neural Network (FNN) directly whereas the machine learning based plasticity model is developed by using of a novel method called Proper Orthogonal Decomposition Feed forward Neural Network (PODFNN). In order to account for the loading history, the accumulated absolute strain is proposed to be the history variable of the plasticity model. Additionally, the strain–stress sequence data for plasticity is collected from different loading–unloading paths based on the concept of sequence for plasticity. By means of the POD, the multi-dimensional stress sequence is decoupled leading to independent one dimensional coefficient sequences. In this case, the neural network with multiple output is replaced by multiple independent neural networks each possessing a one-dimensional output, which leads to less training time and better training performance. To apply the machine learning based material model in finite element analysis, the tangent matrix is derived by the automatic symbolic differentiation tool AceGen. The effectiveness and generalization of the presented models are investigated by a series of numerical examples using both 2D and 3D finite element analysis.

KW - Artificial neural network

KW - Finite element method

KW - Machine learning

KW - Plasticity

KW - Proper orthogonal decomposition

UR - http://www.scopus.com/inward/record.url?scp=85082671315&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2020.113008

DO - 10.1016/j.cma.2020.113008

M3 - Article

AN - SCOPUS:85082671315

VL - 365

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 113008

ER -