Finite strain FE2 analysis with data-driven homogenization using deep neural networks
Finite strain FE2 analysis with data-driven homogenization using deep neural networks
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DOI：
10.1016/j.compstruc.2022.106742
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发表时间：
2022-04
影响因子：
4.7
通讯作者：
Nan Feng;Guodong Zhang;Kapil Khandelwal
中科院分区：
文献类型：
--
作者：
Nan Feng;Guodong Zhang;Kapil Khandelwal
提出了一种基于数据驱动的深度神经网络(DNN)方法来加速FE2分析，由于在每个宏观积分点上需要进行独立的微观有限元分析，因此执行多尺度FE2分析的计算代价很高。为了减轻这一计算负担，提出了基于DNN的非线性均匀化方法，可作为有效的宏观材料模型。提出了一种基于概率的代理开发方法，并采用了一种有效的宏观变形空间数据采样策略来生成训练和验证数据集。一致地处理宏观材料行为的帧无关性，并比较了两种训练方法--通过L2损失函数仅将输入/输出对包括在训练数据集中的常规训练方法，以及还将导数数据与Sobolev损失函数一起使用的Soblev训练方法。数值结果表明，与常规训练相比，Sobolev训练具有更高的测试精度，DNN可以作为计算代价较高的多尺度FE2分析中非线性齐化的有效和准确的替代。
A data-driven deep neural network (DNN) based approach is presented to accelerate FE2analysis.It is computationally expensive to perform multiscale FE2analysis since at each macroscopic integration point an independent microscopic finite element analysis is needed. To alleviate this computational burden, DNN based surrogates are proposed for nonlinear homogenization that can serve as effective macroscale material models. A probabilistic approach is considered for surrogates’ development, and an efficient data sampling strategy from the macroscopic deformation space is used for generating training and validation datasets. Frame indifference of macroscopic material behavior is consistently handled, and two training methods – regular training where only input/output pairs are included in the training dataset via L2loss function, and Sobolev training where the derivative data is also used with the Sobolev loss function – are compared. Numerical results demonstrate that Sobolev training leads to a higher testing accuracy as compared to regular training, and DNNs can serve as efficient and accurate surrogates for nonlinear homogenization in computationally expensive multiscale FE2analysis.