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.

本研究提出了一种基于机器学习的材料模型框架，分别适用于弹性和塑性模型，其中弹性模型采用前馈神经网络（FNN）直接建立，而塑性模型则采用 Proper Orthogonal Decomposition Feed forward Neural Network（PODFNN）建立，处理多维组合多轴应变应力数据。本文还研究了如何将机器学习材料模型应用于有限元分析中，通过数值算例展示了该方法的有效性和普适性。