Multiscale Analysis of Woven Composites Using Hierarchical Physically Recurrent Neural Networks

TL;DR

The paper tackles the high cost of multiscale homogenization in woven composites by introducing a Hierarchical Physically Recurrent Neural Network (HPRNN) that embeds constitutive physics into two-scale transitions. It trains microscale PRNNs for warp/weft yarns and couples them with a matrix model in a meso-to-macro surrogate, achieving physics-consistent, data-efficient predictions across scales. The approach demonstrates improved extrapolation under cyclic loading compared to GRU and Transformer baselines, while offering computational efficiency and interpretability through explicit internal variables and a modular architecture. This framework has significant potential to accelerate and stabilize multiscale predictions in composite design and optimization, reducing reliance on costly full-order simulations.

Abstract

Multiscale homogenization of woven composites requires detailed micromechanical evaluations, leading to high computational costs. Data-driven surrogate models based on neural networks address this challenge but often suffer from big data requirements, limited interpretability, and poor extrapolation capabilities. This study introduces a Hierarchical Physically Recurrent Neural Network (HPRNN) employing two levels of surrogate modeling. First, Physically Recurrent Neural Networks (PRNNs) are trained to capture the nonlinear elasto-plastic behavior of warp and weft yarns using micromechanical data. In a second scale transition, a physics-encoded meso-to-macroscale model integrates these yarn surrogates with the matrix constitutive model, embedding physical properties directly into the latent space. Adopting HPRNNs for both scale transitions can avoid nonphysical behavior often observed in predictions from pure data-driven recurrent neural networks and transformer networks. This results in better generalization under complex cyclic loading conditions. The framework offers a computationally efficient and explainable solution for multiscale modeling of woven composites.

Figures (17)

• Figure 1: Hierarchical structure of woven composites and the transition across two scales with PRNN and the proposed HPRNN.
• Figure 2: Illustration of woven composite structures and associated simulations. Microscale images captured by E. Ghane from ghane2020entropy alongside equivalent representative volume elements (RVEs) modeled using Digimat-FE. The figure includes: (a,b) Scanning electron microscopy of fibers in two orthogonal directions (warp and weft), (c) microscale simulation of unidirectional composites, (d) top view microscopic image of a carbon fiber woven composite, (e) SEM image showing the cross-section of the woven composite, (f) mesoscale RVE, and (g) FEM simulation results with a voxel-based mesh.
• Figure 3: Samples of scaled (normalized between 1 and -1) shear strain components $\varepsilon_{j}$ generated in (a) random loading used for training and validation and (b) cyclic loading to be used in extrapolation.
• Figure 4: Details of the computational model at micro- and mesoscale: (a) Top view of the mesoscale model, (b) X-Z cross-section of the mesoscale model and the mesoscale mesh, and (c) the microscale warp yarn and the details on it mesh.
• Figure 5: Architecture of PRNN used as the transition between micro- to mesoscales. It consists of a feed-forward encoder for strain decomposition, a material layer representing the constitutive material at the microscale yarn of the woven RVE, and a feed-forward decoder for homogenization. The schematics show three bulk points, but for the 3D tensors, six are considered as one unit.