Multiscale Analysis of Woven Composites Using Hierarchical Physically Recurrent Neural Networks

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.

Integration of Active Learning and MCMC Sampling for Efficient Bayesian Calibration of Mechanical Properties

Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models and cutting-edge MCMC algorithms, often depend on ad-hoc decisions. A systematic assessment of their combined influence on analytical accuracy and efficiency is notably lacking. The present work offers a comprehensive comparative study, employing a scalable case study in computational mechanics focused on the inference of spatially varying material parameters, that sheds light on the impact of methodological choices for surrogate modelling and sampling. We show that a priori training of the surrogate model introduces large errors in the posterior estimation even in low to moderate dimensions. We introduce a simple active learning strategy based on the path of the MCMC algorithm that is superior to all a priori trained models, and determine its training data requirements. We demonstrate that the choice of the MCMC algorithm has only a small influence on the amount of training data but no significant influence on the accuracy of the resulting surrogate model. Further, we show that the accuracy of the posterior estimation largely depends on the surrogate model, but not even a tailored surrogate guarantees convergence of the MCMC.Finally, we identify the forward model as the bottleneck in the inference process, not the MCMC algorithm. While related works focus on employing advanced MCMC algorithms, we demonstrate that the training data requirements render the surrogate modelling approach infeasible before the benefits of these gradient-based MCMC algorithms on cheap models can be reaped.