Recurrent neural networks and transfer learning for elasto-plasticity in woven composites

TL;DR

This work tackles the challenge of predicting path-dependent elasto-plastic responses in woven composites by training recurrent neural networks (RNNs) on data generated from mean-field meso-scale simulations. It employs transfer learning to adapt models trained on diverse 6D loading histories (random walks) to conventional cyclic loadings, addressing initialization and data-sparsity issues. The study compares GRU and LSTM architectures, performs a comprehensive hyperparameter grid search, and demonstrates that a transfer-learning LSTM setup provides accurate stress histories with notable gains in efficiency. The results suggest that RNNs trained on mean-field surrogates can serve as practical, scalable surrogates for mesoscale homogenization in design workflows and potentially extend to limited experimental data and full-field simulations.

Abstract

As a surrogate for computationally intensive meso-scale simulation of woven composites, this article presents Recurrent Neural Network (RNN) models. Leveraging the power of transfer learning, the initialization challenges and sparse data issues inherent in cyclic shear strain loads are addressed in the RNN models. A mean-field model generates a comprehensive data set representing elasto-plastic behavior. In simulations, arbitrary six-dimensional strain histories are used to predict stresses under random walking as the source task and cyclic loading conditions as the target task. Incorporating sub-scale properties enhances RNN versatility. In order to achieve accurate predictions, the model uses a grid search method to tune network architecture and hyper-parameter configurations. The results of this study demonstrate that transfer learning can be used to effectively adapt the RNN to varying strain conditions, which establishes its potential as a useful tool for modeling path-dependent responses in woven composites.

Figures (9)

• Figure 1: t-SNE distribution of 9-dimensional static feature space described in Table \ref{['tab:materialparameters']}. Different micro-structural configurations are described by three fiber elasticity, three matrix elasticity, and three matrix plasticity feature parameters.
• Figure 2: Four samples of input strain loading paths from random walk data set (scaled between [-1,1]). Each graph contains six components of the strain tensor applied on a randomly chosen material set.
• Figure 3: Four input strain loading paths samples from a smooth cyclic path data set. Each graph contains six components of the strain tensor applied on a randomly chosen material set. The smooth cyclic loading paths include (from up-left to down-right) pure in-plain shear $\epsilon_{12}$, out-of-plain shear $\epsilon_{23}$ and bi-axial $[\epsilon_{11},\epsilon_{12}]$ and $[\epsilon_{12},\epsilon_{23}]$ loading.
• Figure 4: A schematic representation of the data flow for feeding the RNN model with one multiaxial strain history. As shown on the left side of the figure, a woven composite and strain loading paths have been randomly sampled from the data set. Each stripe represents a time step of the strain tensor ($\boldsymbol{\tilde{\epsilon}^{(n)}}$) containing six strain components ($\epsilon_{ij}$). Red dashed lines indicate time increments in a load path. Six random loads are presented in the input layer in purple. Afterwards, the data propagates through the LSTM (or GRU) network layers. The network outputs are in green. The internal variables flow can also be seen in one of the network layers. A hidden (and/or cell) state is indicated by $h_{t}$.
• Figure 5: Two examples of the training and validation loss evolutions on the random strain data set. Each network consists of three layers with 512 units of LSTM or GRU plus a $50\%$ dropout after the first layer. In both cases, the learning rate is 0.001, the $L_2$ regularization is set to 0.001, and the minibatch size is 128. Yellow and gray lines indicate the training loss calculated at each iteration. The dashed lines in red and purple indicate the loss calculated at the end of each epoch for the validation set.