Finite strain FE2 analysis with data-driven homogenization using deep neural networks

Abstract

A data-driven deep neural network (DNN) based approach is presented to accelerate FE2 analysis.It is computationally expensive to perform multiscale FE2 analysis 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 L2 loss 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 FE2 analysis.